Daily Papers

Estimating the 6D pose of unseen objects from monocular RGB images remains a challenging problem, especially due to the lack of prior object-specific knowledge. To tackle this issue, we propose RefPose, an innovative approach to object pose estimation that leverages a reference image and geometric correspondence as guidance. RefPose first predicts an initial pose by using object templates to render the reference image and establish the geometric correspondence needed for the refinement stage. During the refinement stage, RefPose estimates the geometric correspondence of the query based on the generated references and iteratively refines the pose through a render-and-compare approach. To enhance this estimation, we introduce a correlation volume-guided attention mechanism that effectively captures correlations between the query and reference images. Unlike traditional methods that depend on pre-defined object models, RefPose dynamically adapts to new object shapes by leveraging a reference image and geometric correspondence. This results in robust performance across previously unseen objects. Extensive evaluation on the BOP benchmark datasets shows that RefPose achieves state-of-the-art results while maintaining a competitive runtime.

3D object part segmentation is essential in computer vision applications. While substantial progress has been made in 2D object part segmentation, the 3D counterpart has received less attention, in part due to the scarcity of annotated 3D datasets, which are expensive to collect. In this work, we propose to leverage a few annotated 3D shapes or richly annotated 2D datasets to perform 3D object part segmentation. We present our novel approach, termed 3-By-2 that achieves SOTA performance on different benchmarks with various granularity levels. By using features from pretrained foundation models and exploiting semantic and geometric correspondences, we are able to overcome the challenges of limited 3D annotations. Our approach leverages available 2D labels, enabling effective 3D object part segmentation. Our method 3-By-2 can accommodate various part taxonomies and granularities, demonstrating interesting part label transfer ability across different object categories. Project website: https://ngailapdi.github.io/projects/3by2/.

Current methods for 3D semantic segmentation propose training models with limited annotations to address the difficulty of annotating large, irregular, and unordered 3D point cloud data. They usually focus on the 3D domain only, without leveraging the complementary nature of 2D and 3D data. Besides, some methods extend original labels or generate pseudo labels to guide the training, but they often fail to fully use these labels or address the noise within them. Meanwhile, the emergence of comprehensive and adaptable foundation models has offered effective solutions for segmenting 2D data. Leveraging this advancement, we present a novel approach that maximizes the utility of sparsely available 3D annotations by incorporating segmentation masks generated by 2D foundation models. We further propagate the 2D segmentation masks into the 3D space by establishing geometric correspondences between 3D scenes and 2D views. We extend the highly sparse annotations to encompass the areas delineated by 3D masks, thereby substantially augmenting the pool of available labels. Furthermore, we apply confidence- and uncertainty-based consistency regularization on augmentations of the 3D point cloud and select the reliable pseudo labels, which are further spread on the 3D masks to generate more labels. This innovative strategy bridges the gap between limited 3D annotations and the powerful capabilities of 2D foundation models, ultimately improving the performance of 3D weakly supervised segmentation.

A prominent approach to visual Reinforcement Learning (RL) is to learn an internal state representation using self-supervised methods, which has the potential benefit of improved sample-efficiency and generalization through additional learning signal and inductive biases. However, while the real world is inherently 3D, prior efforts have largely been focused on leveraging 2D computer vision techniques as auxiliary self-supervision. In this work, we present a unified framework for self-supervised learning of 3D representations for motor control. Our proposed framework consists of two phases: a pretraining phase where a deep voxel-based 3D autoencoder is pretrained on a large object-centric dataset, and a finetuning phase where the representation is jointly finetuned together with RL on in-domain data. We empirically show that our method enjoys improved sample efficiency in simulated manipulation tasks compared to 2D representation learning methods. Additionally, our learned policies transfer zero-shot to a real robot setup with only approximate geometric correspondence, and successfully solve motor control tasks that involve grasping and lifting from a single, uncalibrated RGB camera. Code and videos are available at https://yanjieze.com/3d4rl/ .

Multi-view consistency remains a challenge for image diffusion models. Even within the Text-to-Texture problem, where perfect geometric correspondences are known a priori, many methods fail to yield aligned predictions across views, necessitating non-trivial fusion methods to incorporate the results onto the original mesh. We explore this issue for a Collaborative Control workflow specifically in PBR Text-to-Texture. Collaborative Control directly models PBR image probability distributions, including normal bump maps; to our knowledge, the only diffusion model to directly output full PBR stacks. We discuss the design decisions involved in making this model multi-view consistent, and demonstrate the effectiveness of our approach in ablation studies, as well as practical applications.

Multi-view understanding, the ability to reconcile visual information across diverse viewpoints for effective navigation, manipulation, and 3D scene comprehension, is a fundamental challenge in Multi-Modal Large Language Models (MLLMs) to be used as embodied agents. While recent MLLMs have shown impressive advances in high-level reasoning and planning, they frequently fall short when confronted with multi-view geometric consistency and cross-view correspondence. To comprehensively evaluate the challenges of MLLMs in multi-view scene reasoning, we propose All-Angles Bench, a benchmark of over 2,100 human carefully annotated multi-view question-answer pairs across 90 diverse real-world scenes. Our six tasks (counting, attribute identification, relative distance, relative direction, object manipulation, and camera pose estimation) specifically test model's geometric correspondence and the capacity to align information consistently across views. Our extensive experiments, benchmark on 27 representative MLLMs including Gemini-2.0-Flash, Claude-3.7-Sonnet, and GPT-4o against human evaluators reveals a substantial performance gap, indicating that current MLLMs remain far from human-level proficiency. Through in-depth analysis, we show that MLLMs are particularly underperforming under two aspects: (1) cross-view correspondence for partially occluded views and (2) establishing the coarse camera poses. These findings highlight the necessity of domain-specific refinements or modules that embed stronger multi-view awareness. We believe that our All-Angles Bench offers valuable insights and contribute to bridging the gap between MLLMs and human-level multi-view understanding. The project and benchmark are publicly available at https://danielchyeh.github.io/All-Angles-Bench/.

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving beyond traditional hand-crafted and data-driven feature learning methods, we incorporate spectral methods with deep learning, focusing on functional maps (FMs) and optimal transport (OT). Traditional OT-based approaches, often reliant on entropy regularization OT in learning-based framework, face computational challenges due to their quadratic cost. Our key contribution is to employ the sliced Wasserstein distance (SWD) for OT, which is a valid fast optimal transport metric in an unsupervised shape matching framework. This unsupervised framework integrates functional map regularizers with a novel OT-based loss derived from SWD, enhancing feature alignment between shapes treated as discrete probability measures. We also introduce an adaptive refinement process utilizing entropy regularized OT, further refining feature alignments for accurate point-to-point correspondences. Our method demonstrates superior performance in non-rigid shape matching, including near-isometric and non-isometric scenarios, and excels in downstream tasks like segmentation transfer. The empirical results on diverse datasets highlight our framework's effectiveness and generalization capabilities, setting new standards in non-rigid shape matching with efficient OT metrics and an adaptive refinement module.

Affine correspondences have received significant attention due to their benefits in tasks like image matching and pose estimation. Existing methods for extracting affine correspondences still have many limitations in terms of performance; thus, exploring a new paradigm is crucial. In this paper, we present a new pipeline designed for extracting accurate affine correspondences by integrating dense matching and geometric constraints. Specifically, a novel extraction framework is introduced, with the aid of dense matching and a novel keypoint scale and orientation estimator. For this purpose, we propose loss functions based on geometric constraints, which can effectively improve accuracy by supervising neural networks to learn feature geometry. The experimental show that the accuracy and robustness of our method outperform the existing ones in image matching tasks. To further demonstrate the effectiveness of the proposed method, we applied it to relative pose estimation. Affine correspondences extracted by our method lead to more accurate poses than the baselines on a range of real-world datasets. The code is available at https://github.com/stilcrad/DenseAffine.

Learning spatial-temporal correspondences in cardiac motion from images is important for understanding the underlying dynamics of cardiac anatomical structures. Many methods explicitly impose smoothness constraints such as the L_2 norm on the displacement vector field (DVF), while usually ignoring biomechanical feasibility in the transformation. Other geometric constraints either regularize specific regions of interest such as imposing incompressibility on the myocardium or introduce additional steps such as training a separate network-based regularizer on physically simulated datasets. In this work, we propose an explicit biomechanics-informed prior as regularization on the predicted DVF in modeling a more generic biomechanically plausible transformation within all cardiac structures without introducing additional training complexity. We validate our methods on two publicly available datasets in the context of 2D MRI data and perform extensive experiments to illustrate the effectiveness and robustness of our proposed methods compared to other competing regularization schemes. Our proposed methods better preserve biomechanical properties by visual assessment and show advantages in segmentation performance using quantitative evaluation metrics. The code is publicly available at https://github.com/Voldemort108X/bioinformed_reg.

In-context segmentation aims at segmenting novel images using a few labeled example images, termed as "in-context examples", exploring content similarities between examples and the target. The resulting models can be generalized seamlessly to novel segmentation tasks, significantly reducing the labeling and training costs compared with conventional pipelines. However, in-context segmentation is more challenging than classic ones due to its meta-learning nature, requiring the model to learn segmentation rules conditioned on a few samples, not just the segmentation. Unlike previous work with ad-hoc or non-end-to-end designs, we propose SEGIC, an end-to-end segment-in-context framework built upon a single vision foundation model (VFM). In particular, SEGIC leverages the emergent correspondence within VFM to capture dense relationships between target images and in-context samples. As such, information from in-context samples is then extracted into three types of instructions, i.e. geometric, visual, and meta instructions, serving as explicit conditions for the final mask prediction. SEGIC is a straightforward yet effective approach that yields state-of-the-art performance on one-shot segmentation benchmarks. Notably, SEGIC can be easily generalized to diverse tasks, including video object segmentation and open-vocabulary segmentation. Code will be available at https://github.com/MengLcool/SEGIC.

Point cloud registration approaches often fail when the overlap between point clouds is low due to noisy point correspondences. This work introduces a novel cross-attention mechanism tailored for Transformer-based architectures that tackles this problem, by fusing information from coordinates and features at the super-point level between point clouds. This formulation has remained unexplored primarily because it must guarantee rotation and translation invariance since point clouds reside in different and independent reference frames. We integrate the Gromov-Wasserstein distance into the cross-attention formulation to jointly compute distances between points across different point clouds and account for their geometric structure. By doing so, points from two distinct point clouds can attend to each other under arbitrary rigid transformations. At the point level, we also devise a self-attention mechanism that aggregates the local geometric structure information into point features for fine matching. Our formulation boosts the number of inlier correspondences, thereby yielding more precise registration results compared to state-of-the-art approaches. We have conducted an extensive evaluation on 3DMatch, 3DLoMatch, KITTI, and 3DCSR datasets.

There has been a recent surge of interest in learning to perceive depth from monocular videos in an unsupervised fashion. A key challenge in this field is achieving robust and accurate depth estimation in challenging scenarios, particularly in regions with weak textures or where dynamic objects are present. This study makes three major contributions by delving deeply into dense correspondence priors to provide existing frameworks with explicit geometric constraints. The first novelty is a contextual-geometric depth consistency loss, which employs depth maps triangulated from dense correspondences based on estimated ego-motion to guide the learning of depth perception from contextual information, since explicitly triangulated depth maps capture accurate relative distances among pixels. The second novelty arises from the observation that there exists an explicit, deducible relationship between optical flow divergence and depth gradient. A differential property correlation loss is, therefore, designed to refine depth estimation with a specific emphasis on local variations. The third novelty is a bidirectional stream co-adjustment strategy that enhances the interaction between rigid and optical flows, encouraging the former towards more accurate correspondence and making the latter more adaptable across various scenarios under the static scene hypotheses. DCPI-Depth, a framework that incorporates all these innovative components and couples two bidirectional and collaborative streams, achieves state-of-the-art performance and generalizability across multiple public datasets, outperforming all existing prior arts. Specifically, it demonstrates accurate depth estimation in texture-less and dynamic regions, and shows more reasonable smoothness. Our source code will be publicly available at mias.group/DCPI-Depth upon publication.

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

Vision-Language Models (VLMs) have shown remarkable performance on diverse visual and linguistic tasks, yet they remain fundamentally limited in their understanding of 3D spatial structures. We propose Geometric Distillation, a lightweight, annotation-free fine-tuning framework that injects human-inspired geometric cues into pretrained VLMs without modifying their architecture. By distilling (1) sparse correspondences, (2) relative depth relations, and (3) dense cost volumes from off-the-shelf 3D foundation models (e.g., MASt3R, VGGT), our method shapes representations to be geometry-aware while remaining compatible with natural image-text inputs. Through extensive evaluations on 3D vision-language reasoning and 3D perception benchmarks, our method consistently outperforms prior approaches, achieving improved 3D spatial reasoning with significantly lower computational cost. Our work demonstrates a scalable and efficient path to bridge 2D-trained VLMs with 3D understanding, opening up wider use in spatially grounded multimodal tasks.

Finding correspondences between images is a fundamental problem in computer vision. In this paper, we show that correspondence emerges in image diffusion models without any explicit supervision. We propose a simple strategy to extract this implicit knowledge out of diffusion networks as image features, namely DIffusion FeaTures (DIFT), and use them to establish correspondences between real images. Without any additional fine-tuning or supervision on the task-specific data or annotations, DIFT is able to outperform both weakly-supervised methods and competitive off-the-shelf features in identifying semantic, geometric, and temporal correspondences. Particularly for semantic correspondence, DIFT from Stable Diffusion is able to outperform DINO and OpenCLIP by 19 and 14 accuracy points respectively on the challenging SPair-71k benchmark. It even outperforms the state-of-the-art supervised methods on 9 out of 18 categories while remaining on par for the overall performance. Project page: https://diffusionfeatures.github.io

In the task of reference-based image inpainting, an additional reference image is provided to restore a damaged target image to its original state. The advancement of diffusion models, particularly Stable Diffusion, allows for simple formulations in this task. However, existing diffusion-based methods often lack explicit constraints on the correlation between the reference and damaged images, resulting in lower faithfulness to the reference images in the inpainting results. In this work, we propose CorrFill, a training-free module designed to enhance the awareness of geometric correlations between the reference and target images. This enhancement is achieved by guiding the inpainting process with correspondence constraints estimated during inpainting, utilizing attention masking in self-attention layers and an objective function to update the input tensor according to the constraints. Experimental results demonstrate that CorrFill significantly enhances the performance of multiple baseline diffusion-based methods, including state-of-the-art approaches, by emphasizing faithfulness to the reference images.

We propose a novel zero-shot approach to computing correspondences between 3D shapes. Existing approaches mainly focus on isometric and near-isometric shape pairs (e.g., human vs. human), but less attention has been given to strongly non-isometric and inter-class shape matching (e.g., human vs. cow). To this end, we introduce a fully automatic method that exploits the exceptional reasoning capabilities of recent foundation models in language and vision to tackle difficult shape correspondence problems. Our approach comprises multiple stages. First, we classify the 3D shapes in a zero-shot manner by feeding rendered shape views to a language-vision model (e.g., BLIP2) to generate a list of class proposals per shape. These proposals are unified into a single class per shape by employing the reasoning capabilities of ChatGPT. Second, we attempt to segment the two shapes in a zero-shot manner, but in contrast to the co-segmentation problem, we do not require a mutual set of semantic regions. Instead, we propose to exploit the in-context learning capabilities of ChatGPT to generate two different sets of semantic regions for each shape and a semantic mapping between them. This enables our approach to match strongly non-isometric shapes with significant differences in geometric structure. Finally, we employ the generated semantic mapping to produce coarse correspondences that can further be refined by the functional maps framework to produce dense point-to-point maps. Our approach, despite its simplicity, produces highly plausible results in a zero-shot manner, especially between strongly non-isometric shapes.

Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on convolutional matching and propose an effective geometric matching algorithm, dubbed Convolutional Hough Matching (CHM). The method distributes similarities of candidate matches over a geometric transformation space and evaluates them in a convolutional manner. We cast it into a trainable neural layer with a semi-isotropic high-dimensional kernel, which learns non-rigid matching with a small number of interpretable parameters. To further improve the efficiency of high-dimensional voting, we also propose to use an efficient kernel decomposition with center-pivot neighbors, which significantly sparsifies the proposed semi-isotropic kernels without performance degradation. To validate the proposed techniques, we develop the neural network with CHM layers that perform convolutional matching in the space of translation and scaling. Our method sets a new state of the art on standard benchmarks for semantic visual correspondence, proving its strong robustness to challenging intra-class variations.

Given a pair of partially overlapping source and target images and a keypoint in the source image, the keypoint's correspondent in the target image can be either visible, occluded or outside the field of view. Local feature matching methods are only able to identify the correspondent's location when it is visible, while humans can also hallucinate its location when it is occluded or outside the field of view through geometric reasoning. In this paper, we bridge this gap by training a network to output a peaked probability distribution over the correspondent's location, regardless of this correspondent being visible, occluded, or outside the field of view. We experimentally demonstrate that this network is indeed able to hallucinate correspondences on pairs of images captured in scenes that were not seen at training-time. We also apply this network to an absolute camera pose estimation problem and find it is significantly more robust than state-of-the-art local feature matching-based competitors.

Capturing and maintaining geometric interactions among different body parts is crucial for successful motion retargeting in skinned characters. Existing approaches often overlook body geometries or add a geometry correction stage after skeletal motion retargeting. This results in conflicts between skeleton interaction and geometry correction, leading to issues such as jittery, interpenetration, and contact mismatches. To address these challenges, we introduce a new retargeting framework, MeshRet, which directly models the dense geometric interactions in motion retargeting. Initially, we establish dense mesh correspondences between characters using semantically consistent sensors (SCS), effective across diverse mesh topologies. Subsequently, we develop a novel spatio-temporal representation called the dense mesh interaction (DMI) field. This field, a collection of interacting SCS feature vectors, skillfully captures both contact and non-contact interactions between body geometries. By aligning the DMI field during retargeting, MeshRet not only preserves motion semantics but also prevents self-interpenetration and ensures contact preservation. Extensive experiments on the public Mixamo dataset and our newly-collected ScanRet dataset demonstrate that MeshRet achieves state-of-the-art performance. Code available at https://github.com/abcyzj/MeshRet.

Computer vision has long relied on two kinds of correspondences: pixel correspondences in images and 3D correspondences on object surfaces. Is there another kind, and if there is, what can they do for us? In this paper, we introduce correspondences of the third kind we call reflection correspondences and show that they can help estimate camera pose by just looking at objects without relying on the background. Reflection correspondences are point correspondences in the reflected world, i.e., the scene reflected by the object surface. The object geometry and reflectance alters the scene geometrically and radiometrically, respectively, causing incorrect pixel correspondences. Geometry recovered from each image is also hampered by distortions, namely generalized bas-relief ambiguity, leading to erroneous 3D correspondences. We show that reflection correspondences can resolve the ambiguities arising from these distortions. We introduce a neural correspondence estimator and a RANSAC algorithm that fully leverages all three kinds of correspondences for robust and accurate joint camera pose and object shape estimation just from the object appearance. The method expands the horizon of numerous downstream tasks, including camera pose estimation for appearance modeling (e.g., NeRF) and motion estimation of reflective objects (e.g., cars on the road), to name a few, as it relieves the requirement of overlapping background.

Recent advances in 3D Gaussian Splatting (3DGS) have enabled RGB-only SLAM systems to achieve high-fidelity scene representation. However, the heavy reliance of existing systems on photometric rendering loss for camera tracking undermines their robustness, especially in unbounded outdoor environments with severe viewpoint and illumination changes. To address these challenges, we propose TVG-SLAM, a robust RGB-only 3DGS SLAM system that leverages a novel tri-view geometry paradigm to ensure consistent tracking and high-quality mapping. We introduce a dense tri-view matching module that aggregates reliable pairwise correspondences into consistent tri-view matches, forming robust geometric constraints across frames. For tracking, we propose Hybrid Geometric Constraints, which leverage tri-view matches to construct complementary geometric cues alongside photometric loss, ensuring accurate and stable pose estimation even under drastic viewpoint shifts and lighting variations. For mapping, we propose a new probabilistic initialization strategy that encodes geometric uncertainty from tri-view correspondences into newly initialized Gaussians. Additionally, we design a Dynamic Attenuation of Rendering Trust mechanism to mitigate tracking drift caused by mapping latency. Experiments on multiple public outdoor datasets show that our TVG-SLAM outperforms prior RGB-only 3DGS-based SLAM systems. Notably, in the most challenging dataset, our method improves tracking robustness, reducing the average Absolute Trajectory Error (ATE) by 69.0\% while achieving state-of-the-art rendering quality. The implementation of our method will be released as open-source.

We investigate the problem of training generative models on a very sparse collection of 3D models. We use geometrically motivated energies to augment and thus boost a sparse collection of example (training) models. We analyze the Hessian of the as-rigid-as-possible (ARAP) energy to sample from and project to the underlying (local) shape space, and use the augmented dataset to train a variational autoencoder (VAE). We iterate the process of building latent spaces of VAE and augmenting the associated dataset, to progressively reveal a richer and more expressive generative space for creating geometrically and semantically valid samples. Our framework allows us to train generative 3D models even with a small set of good quality 3D models, which are typically hard to curate. We extensively evaluate our method against a set of strong baselines, provide ablation studies and demonstrate application towards establishing shape correspondences. We present multiple examples of interesting and meaningful shape variations even when starting from as few as 3-10 training shapes.

Semi-dense feature matching methods have shown strong performance in challenging scenarios. However, the existing pipeline relies on a global search across the entire feature map to establish coarse matches, limiting further improvements in accuracy and efficiency. Motivated by this limitation, we propose a novel pipeline, CasP, which leverages cascaded correspondence priors for guidance. Specifically, the matching stage is decomposed into two progressive phases, bridged by a region-based selective cross-attention mechanism designed to enhance feature discriminability. In the second phase, one-to-one matches are determined by restricting the search range to the one-to-many prior areas identified in the first phase. Additionally, this pipeline benefits from incorporating high-level features, which helps reduce the computational costs of low-level feature extraction. The acceleration gains of CasP increase with higher resolution, and our lite model achieves a speedup of sim2.2times at a resolution of 1152 compared to the most efficient method, ELoFTR. Furthermore, extensive experiments demonstrate its superiority in geometric estimation, particularly with impressive cross-domain generalization. These advantages highlight its potential for latency-sensitive and high-robustness applications, such as SLAM and UAV systems. Code is available at https://github.com/pq-chen/CasP.

The reliance on implicit point matching via attention has become a core bottleneck in drag-based editing, resulting in a fundamental compromise on weakened inversion strength and costly test-time optimization (TTO). This compromise severely limits the generative capabilities of diffusion models, suppressing high-fidelity inpainting and text-guided creation. In this paper, we introduce LazyDrag, the first drag-based image editing method for Multi-Modal Diffusion Transformers, which directly eliminates the reliance on implicit point matching. In concrete terms, our method generates an explicit correspondence map from user drag inputs as a reliable reference to boost the attention control. This reliable reference opens the potential for a stable full-strength inversion process, which is the first in the drag-based editing task. It obviates the necessity for TTO and unlocks the generative capability of models. Therefore, LazyDrag naturally unifies precise geometric control with text guidance, enabling complex edits that were previously out of reach: opening the mouth of a dog and inpainting its interior, generating new objects like a ``tennis ball'', or for ambiguous drags, making context-aware changes like moving a hand into a pocket. Additionally, LazyDrag supports multi-round workflows with simultaneous move and scale operations. Evaluated on the DragBench, our method outperforms baselines in drag accuracy and perceptual quality, as validated by VIEScore and human evaluation. LazyDrag not only establishes new state-of-the-art performance, but also paves a new way to editing paradigms.

This paper introduces a Transformer-based integrative feature and cost aggregation network designed for dense matching tasks. In the context of dense matching, many works benefit from one of two forms of aggregation: feature aggregation, which pertains to the alignment of similar features, or cost aggregation, a procedure aimed at instilling coherence in the flow estimates across neighboring pixels. In this work, we first show that feature aggregation and cost aggregation exhibit distinct characteristics and reveal the potential for substantial benefits stemming from the judicious use of both aggregation processes. We then introduce a simple yet effective architecture that harnesses self- and cross-attention mechanisms to show that our approach unifies feature aggregation and cost aggregation and effectively harnesses the strengths of both techniques. Within the proposed attention layers, the features and cost volume both complement each other, and the attention layers are interleaved through a coarse-to-fine design to further promote accurate correspondence estimation. Finally at inference, our network produces multi-scale predictions, computes their confidence scores, and selects the most confident flow for final prediction. Our framework is evaluated on standard benchmarks for semantic matching, and also applied to geometric matching, where we show that our approach achieves significant improvements compared to existing methods.

Since a building's floorplans are easily accessible, consistent over time, and inherently robust to changes in visual appearance, self-localization within the floorplan has attracted researchers' interest. However, since floorplans are minimalist representations of a building's structure, modal and geometric differences between visual perceptions and floorplans pose challenges to this task. While existing methods cleverly utilize 2D geometric features and pose filters to achieve promising performance, they fail to address the localization errors caused by frequent visual changes and view occlusions due to variously shaped 3D objects. To tackle these issues, this paper views the 2D Floorplan Localization (FLoc) problem from a higher dimension by injecting 3D geometric priors into the visual FLoc algorithm. For the 3D geometric prior modeling, we first model geometrically aware view invariance using multi-view constraints, i.e., leveraging imaging geometric principles to provide matching constraints between multiple images that see the same points. Then, we further model the view-scene aligned geometric priors, enhancing the cross-modal geometry-color correspondences by associating the scene's surface reconstruction with the RGB frames of the sequence. Both 3D priors are modeled through self-supervised contrastive learning, thus no additional geometric or semantic annotations are required. These 3D priors summarized in extensive realistic scenes bridge the modal gap while improving localization success without increasing the computational burden on the FLoc algorithm. Sufficient comparative studies demonstrate that our method significantly outperforms state-of-the-art methods and substantially boosts the FLoc accuracy. All data and code will be released after the anonymous review.

Dense contrastive representation learning (DCRL) has greatly improved the learning efficiency for image-dense prediction tasks, showing its great potential to reduce the large costs of medical image collection and dense annotation. However, the properties of medical images make unreliable correspondence discovery, bringing an open problem of large-scale false positive and negative (FP&N) pairs in DCRL. In this paper, we propose GEoMetric vIsual deNse sImilarity (GEMINI) learning which embeds the homeomorphism prior to DCRL and enables a reliable correspondence discovery for effective dense contrast. We propose a deformable homeomorphism learning (DHL) which models the homeomorphism of medical images and learns to estimate a deformable mapping to predict the pixels' correspondence under topological preservation. It effectively reduces the searching space of pairing and drives an implicit and soft learning of negative pairs via a gradient. We also propose a geometric semantic similarity (GSS) which extracts semantic information in features to measure the alignment degree for the correspondence learning. It will promote the learning efficiency and performance of deformation, constructing positive pairs reliably. We implement two practical variants on two typical representation learning tasks in our experiments. Our promising results on seven datasets which outperform the existing methods show our great superiority. We will release our code on a companion link: https://github.com/YutingHe-list/GEMINI.

Matching cross-modality features between images and point clouds is a fundamental problem for image-to-point cloud registration. However, due to the modality difference between images and points, it is difficult to learn robust and discriminative cross-modality features by existing metric learning methods for feature matching. Instead of applying metric learning on cross-modality data, we propose to unify the modality between images and point clouds by pretrained large-scale models first, and then establish robust correspondence within the same modality. We show that the intermediate features, called diffusion features, extracted by depth-to-image diffusion models are semantically consistent between images and point clouds, which enables the building of coarse but robust cross-modality correspondences. We further extract geometric features on depth maps produced by the monocular depth estimator. By matching such geometric features, we significantly improve the accuracy of the coarse correspondences produced by diffusion features. Extensive experiments demonstrate that without any task-specific training, direct utilization of both features produces accurate image-to-point cloud registration. On three public indoor and outdoor benchmarks, the proposed method averagely achieves a 20.6 percent improvement in Inlier Ratio, a three-fold higher Inlier Number, and a 48.6 percent improvement in Registration Recall than existing state-of-the-arts.

Point cloud registration is a task to estimate the rigid transformation between two unaligned scans, which plays an important role in many computer vision applications. Previous learning-based works commonly focus on supervised registration, which have limitations in practice. Recently, with the advance of inexpensive RGB-D sensors, several learning-based works utilize RGB-D data to achieve unsupervised registration. However, most of existing unsupervised methods follow a cascaded design or fuse RGB-D data in a unidirectional manner, which do not fully exploit the complementary information in the RGB-D data. To leverage the complementary information more effectively, we propose a network implementing multi-scale bidirectional fusion between RGB images and point clouds generated from depth images. By bidirectionally fusing visual and geometric features in multi-scales, more distinctive deep features for correspondence estimation can be obtained, making our registration more accurate. Extensive experiments on ScanNet and 3DMatch demonstrate that our method achieves new state-of-the-art performance. Code will be released at https://github.com/phdymz/PointMBF

Recently, methods leveraging diffusion model priors to assist monocular geometric estimation (e.g., depth and normal) have gained significant attention due to their strong generalization ability. However, most existing works focus on estimating geometric properties within the camera coordinate system of individual video frames, neglecting the inherent ability of diffusion models to determine inter-frame correspondence. In this work, we demonstrate that, through appropriate design and fine-tuning, the intrinsic consistency of video generation models can be effectively harnessed for consistent geometric estimation. Specifically, we 1) select geometric attributes in the global coordinate system that share the same correspondence with video frames as the prediction targets, 2) introduce a novel and efficient conditioning method by reusing positional encodings, and 3) enhance performance through joint training on multiple geometric attributes that share the same correspondence. Our results achieve superior performance in predicting global geometric attributes in videos and can be directly applied to reconstruction tasks. Even when trained solely on static video data, our approach exhibits the potential to generalize to dynamic video scenes.

Point cloud registration is the task of estimating the rigid transformation that aligns a pair of point cloud fragments. We present an efficient and robust framework for pairwise registration of real-world 3D scans, leveraging Hough voting in the 6D transformation parameter space. First, deep geometric features are extracted from a point cloud pair to compute putative correspondences. We then construct a set of triplets of correspondences to cast votes on the 6D Hough space, representing the transformation parameters in sparse tensors. Next, a fully convolutional refinement module is applied to refine the noisy votes. Finally, we identify the consensus among the correspondences from the Hough space, which we use to predict our final transformation parameters. Our method outperforms state-of-the-art methods on 3DMatch and 3DLoMatch benchmarks while achieving comparable performance on KITTI odometry dataset. We further demonstrate the generalizability of our approach by setting a new state-of-the-art on ICL-NUIM dataset, where we integrate our module into a multi-way registration pipeline.

Multiview diffusion models have shown considerable success in image-to-3D generation for general objects. However, when applied to human data, existing methods have yet to deliver promising results, largely due to the challenges of scaling multiview attention to higher resolutions. In this paper, we explore human multiview diffusion models at the megapixel level and introduce a solution called mesh attention to enable training at 1024x1024 resolution. Using a clothed human mesh as a central coarse geometric representation, the proposed mesh attention leverages rasterization and projection to establish direct cross-view coordinate correspondences. This approach significantly reduces the complexity of multiview attention while maintaining cross-view consistency. Building on this foundation, we devise a mesh attention block and combine it with keypoint conditioning to create our human-specific multiview diffusion model, MEAT. In addition, we present valuable insights into applying multiview human motion videos for diffusion training, addressing the longstanding issue of data scarcity. Extensive experiments show that MEAT effectively generates dense, consistent multiview human images at the megapixel level, outperforming existing multiview diffusion methods.

Monocular object pose estimation, as a pivotal task in computer vision and robotics, heavily depends on accurate 2D-3D correspondences, which often demand costly CAD models that may not be readily available. Object 3D reconstruction methods offer an alternative, among which recent advancements in 3D Gaussian Splatting (3DGS) afford a compelling potential. Yet its performance still suffers and tends to overfit with fewer input views. Embracing this challenge, we introduce SGPose, a novel framework for sparse view object pose estimation using Gaussian-based methods. Given as few as ten views, SGPose generates a geometric-aware representation by starting with a random cuboid initialization, eschewing reliance on Structure-from-Motion (SfM) pipeline-derived geometry as required by traditional 3DGS methods. SGPose removes the dependence on CAD models by regressing dense 2D-3D correspondences between images and the reconstructed model from sparse input and random initialization, while the geometric-consistent depth supervision and online synthetic view warping are key to the success. Experiments on typical benchmarks, especially on the Occlusion LM-O dataset, demonstrate that SGPose outperforms existing methods even under sparse view constraints, under-scoring its potential in real-world applications.

Cross-modal place recognition methods are flexible GPS-alternatives under varying environment conditions and sensor setups. However, this task is non-trivial since extracting consistent and robust global descriptors from different modalities is challenging. To tackle this issue, we propose Voxel-Cross-Pixel (VXP), a novel camera-to-LiDAR place recognition framework that enforces local similarities in a self-supervised manner and effectively brings global context from images and LiDAR scans into a shared feature space. Specifically, VXP is trained in three stages: first, we deploy a visual transformer to compactly represent input images. Secondly, we establish local correspondences between image-based and point cloud-based feature spaces using our novel geometric alignment module. We then aggregate local similarities into an expressive shared latent space. Extensive experiments on the three benchmarks (Oxford RobotCar, ViViD++ and KITTI) demonstrate that our method surpasses the state-of-the-art cross-modal retrieval by a large margin. Our evaluations show that the proposed method is accurate, efficient and light-weight. Our project page is available at: https://yunjinli.github.io/projects-vxp/

Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on convolutional matching and propose an effective geometric matching algorithm, dubbed Convolutional Hough Matching (CHM). The method distributes similarities of candidate matches over a geometric transformation space and evaluate them in a convolutional manner. We cast it into a trainable neural layer with a semi-isotropic high-dimensional kernel, which learns non-rigid matching with a small number of interpretable parameters. To validate the effect, we develop the neural network with CHM layers that perform convolutional matching in the space of translation and scaling. Our method sets a new state of the art on standard benchmarks for semantic visual correspondence, proving its strong robustness to challenging intra-class variations.

The extraction of keypoint positions from input hand frames, known as 3D hand pose estimation, is crucial for various human-computer interaction applications. However, current approaches often struggle with the dynamic nature of self-occlusion of hands and intra-occlusion with interacting objects. To address this challenge, this paper proposes the Denoising Adaptive Graph Transformer, HandDAGT, for hand pose estimation. The proposed HandDAGT leverages a transformer structure to thoroughly explore effective geometric features from input patches. Additionally, it incorporates a novel attention mechanism to adaptively weigh the contribution of kinematic correspondence and local geometric features for the estimation of specific keypoints. This attribute enables the model to adaptively employ kinematic and local information based on the occlusion situation, enhancing its robustness and accuracy. Furthermore, we introduce a novel denoising training strategy aimed at improving the model's robust performance in the face of occlusion challenges. Experimental results show that the proposed model significantly outperforms the existing methods on four challenging hand pose benchmark datasets. Codes and pre-trained models are publicly available at https://github.com/cwc1260/HandDAGT.

Learning signed distance functions (SDFs) from 3D point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning SDFs from noisy point clouds. To overcome this challenge, we propose to learn SDFs via a noise to noise mapping, which does not require any clean point cloud or ground truth supervision for training. Our novelty lies in the noise to noise mapping which can infer a highly accurate SDF of a single object or scene from its multiple or even single noisy point cloud observations. Our novel learning manner is supported by modern Lidar systems which capture multiple noisy observations per second. We achieve this by a novel loss which enables statistical reasoning on point clouds and maintains geometric consistency although point clouds are irregular, unordered and have no point correspondence among noisy observations. Our evaluation under the widely used benchmarks demonstrates our superiority over the state-of-the-art methods in surface reconstruction, point cloud denoising and upsampling. Our code, data, and pre-trained models are available at https://github.com/mabaorui/Noise2NoiseMapping/

We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for highly non-rigid shapes. To this end, we introduce a projected Laplace-Beltrami operator (PLBO) which combines intrinsic and extrinsic geometric information to measure the deformation quality induced by predicted correspondences. We integrate the PLBO, together with an orientation-aware regulariser, into a novel MIP formulation that can be solved to global optimality for many practical problems. In contrast to previous methods, our approach is provably invariant to rigid transformations and global scaling, initialisation-free, has optimality guarantees, and scales to high resolution meshes with (empirically observed) linear time. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets, including data with inconsistent meshing, as well as applications in mesh-to-point-cloud matching.

We aim to address a significant but understudied problem in the anime industry, namely the inbetweening of cartoon line drawings. Inbetweening involves generating intermediate frames between two black-and-white line drawings and is a time-consuming and expensive process that can benefit from automation. However, existing frame interpolation methods that rely on matching and warping whole raster images are unsuitable for line inbetweening and often produce blurring artifacts that damage the intricate line structures. To preserve the precision and detail of the line drawings, we propose a new approach, AnimeInbet, which geometrizes raster line drawings into graphs of endpoints and reframes the inbetweening task as a graph fusion problem with vertex repositioning. Our method can effectively capture the sparsity and unique structure of line drawings while preserving the details during inbetweening. This is made possible via our novel modules, i.e., vertex geometric embedding, a vertex correspondence Transformer, an effective mechanism for vertex repositioning and a visibility predictor. To train our method, we introduce MixamoLine240, a new dataset of line drawings with ground truth vectorization and matching labels. Our experiments demonstrate that AnimeInbet synthesizes high-quality, clean, and complete intermediate line drawings, outperforming existing methods quantitatively and qualitatively, especially in cases with large motions. Data and code are available at https://github.com/lisiyao21/AnimeInbet.

Computer-Aided Design (CAD) generative modeling is driving significant innovations across industrial applications. Recent works have shown remarkable progress in creating solid models from various inputs such as point clouds, meshes, and text descriptions. However, these methods fundamentally diverge from traditional industrial workflows that begin with 2D engineering drawings. The automatic generation of parametric CAD models from these 2D vector drawings remains underexplored despite being a critical step in engineering design. To address this gap, our key insight is to reframe CAD generation as a sequence-to-sequence learning problem where vector drawing primitives directly inform the generation of parametric CAD operations, preserving geometric precision and design intent throughout the transformation process. We propose Drawing2CAD, a framework with three key technical components: a network-friendly vector primitive representation that preserves precise geometric information, a dual-decoder transformer architecture that decouples command type and parameter generation while maintaining precise correspondence, and a soft target distribution loss function accommodating inherent flexibility in CAD parameters. To train and evaluate Drawing2CAD, we create CAD-VGDrawing, a dataset of paired engineering drawings and parametric CAD models, and conduct thorough experiments to demonstrate the effectiveness of our method. Code and dataset are available at https://github.com/lllssc/Drawing2CAD.

We present Diff3F as a simple, robust, and class-agnostic feature descriptor that can be computed for untextured input shapes (meshes or point clouds). Our method distills diffusion features from image foundational models onto input shapes. Specifically, we use the input shapes to produce depth and normal maps as guidance for conditional image synthesis. In the process, we produce (diffusion) features in 2D that we subsequently lift and aggregate on the original surface. Our key observation is that even if the conditional image generations obtained from multi-view rendering of the input shapes are inconsistent, the associated image features are robust and, hence, can be directly aggregated across views. This produces semantic features on the input shapes, without requiring additional data or training. We perform extensive experiments on multiple benchmarks (SHREC'19, SHREC'20, FAUST, and TOSCA) and demonstrate that our features, being semantic instead of geometric, produce reliable correspondence across both isometric and non-isometrically related shape families. Code is available via the project page at https://diff3f.github.io/

We study the problem of reconstructing 3D feature curves of an object from a set of calibrated multi-view images. To do so, we learn a neural implicit field representing the density distribution of 3D edges which we refer to as Neural Edge Field (NEF). Inspired by NeRF, NEF is optimized with a view-based rendering loss where a 2D edge map is rendered at a given view and is compared to the ground-truth edge map extracted from the image of that view. The rendering-based differentiable optimization of NEF fully exploits 2D edge detection, without needing a supervision of 3D edges, a 3D geometric operator or cross-view edge correspondence. Several technical designs are devised to ensure learning a range-limited and view-independent NEF for robust edge extraction. The final parametric 3D curves are extracted from NEF with an iterative optimization method. On our benchmark with synthetic data, we demonstrate that NEF outperforms existing state-of-the-art methods on all metrics. Project page: https://yunfan1202.github.io/NEF/.

In this paper, we present DV-Matcher, a novel learning-based framework for estimating dense correspondences between non-rigidly deformable point clouds. Learning directly from unstructured point clouds without meshing or manual labelling, our framework delivers high-quality dense correspondences, which is of significant practical utility in point cloud processing. Our key contributions are two-fold: First, we propose a scheme to inject prior knowledge from pre-trained vision models into geometric feature learning, which effectively complements the local nature of geometric features with global and semantic information; Second, we propose a novel deformation-based module to promote the extrinsic alignment induced by the learned correspondences, which effectively enhances the feature learning. Experimental results show that our method achieves state-of-the-art results in matching non-rigid point clouds in both near-isometric and heterogeneous shape collection as well as more realistic partial and noisy data.

While pre-trained large-scale vision models have shown significant promise for semantic correspondence, their features often struggle to grasp the geometry and orientation of instances. This paper identifies the importance of being geometry-aware for semantic correspondence and reveals a limitation of the features of current foundation models under simple post-processing. We show that incorporating this information can markedly enhance semantic correspondence performance with simple but effective solutions in both zero-shot and supervised settings. We also construct a new challenging benchmark for semantic correspondence built from an existing animal pose estimation dataset, for both pre-training validating models. Our method achieves a [email protected] score of 65.4 (zero-shot) and 85.6 (supervised) on the challenging SPair-71k dataset, outperforming the state of the art by 5.5p and 11.0p absolute gains, respectively. Our code and datasets are publicly available at: https://telling-left-from-right.github.io/.

We present a new generalizable NeRF method that is able to directly generalize to new unseen scenarios and perform novel view synthesis with as few as two source views. The key to our approach lies in the explicitly modeled correspondence matching information, so as to provide the geometry prior to the prediction of NeRF color and density for volume rendering. The explicit correspondence matching is quantified with the cosine similarity between image features sampled at the 2D projections of a 3D point on different views, which is able to provide reliable cues about the surface geometry. Unlike previous methods where image features are extracted independently for each view, we consider modeling the cross-view interactions via Transformer cross-attention, which greatly improves the feature matching quality. Our method achieves state-of-the-art results on different evaluation settings, with the experiments showing a strong correlation between our learned cosine feature similarity and volume density, demonstrating the effectiveness and superiority of our proposed method. Code is at https://github.com/donydchen/matchnerf

In this work, we focus on the task of learning and representing dense correspondences in deformable object categories. While this problem has been considered before, solutions so far have been rather ad-hoc for specific object types (i.e., humans), often with significant manual work involved. However, scaling the geometry understanding to all objects in nature requires more automated approaches that can also express correspondences between related, but geometrically different objects. To this end, we propose a new, learnable image-based representation of dense correspondences. Our model predicts, for each pixel in a 2D image, an embedding vector of the corresponding vertex in the object mesh, therefore establishing dense correspondences between image pixels and 3D object geometry. We demonstrate that the proposed approach performs on par or better than the state-of-the-art methods for dense pose estimation for humans, while being conceptually simpler. We also collect a new in-the-wild dataset of dense correspondences for animal classes and demonstrate that our framework scales naturally to the new deformable object categories.

We introduce ReMatching, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate re-meshing paradigm, can target shape-matching tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

A Neural Radiance Field (NeRF) encodes the specific relation of 3D geometry and appearance of a scene. We here ask the question whether we can transfer the appearance from a source NeRF onto a target 3D geometry in a semantically meaningful way, such that the resulting new NeRF retains the target geometry but has an appearance that is an analogy to the source NeRF. To this end, we generalize classic image analogies from 2D images to NeRFs. We leverage correspondence transfer along semantic affinity that is driven by semantic features from large, pre-trained 2D image models to achieve multi-view consistent appearance transfer. Our method allows exploring the mix-and-match product space of 3D geometry and appearance. We show that our method outperforms traditional stylization-based methods and that a large majority of users prefer our method over several typical baselines.

Multimodal large language models (MLLMs) have made significant progress in integrating visual and linguistic understanding. Existing benchmarks typically focus on high-level semantic capabilities, such as scene understanding and visual reasoning, but often overlook a crucial, foundational ability: geometric perception. Geometric perception involves understanding geometric shapes, structures, and spatial relationships, which are essential for supporting higher-level semantic tasks. Despite its importance, this capability remains underexplored in current MLLM research. To address this gap, we introduce GePBench, a novel benchmark designed to assess the geometric perception abilities of MLLMs. Our extensive evaluations reveal that current state-of-the-art MLLMs exhibit significant deficiencies in geometric perception tasks. Furthermore, we show that models trained with GePBench data demonstrate substantial improvements on a wide range of benchmark tasks, highlighting the critical role of geometric perception in enabling advanced multimodal applications. Our code and datasets will be publicly available.

In document image rectification, there exist rich geometric constraints between the distorted image and the ground truth one. However, such geometric constraints are largely ignored in existing advanced solutions, which limits the rectification performance. To this end, we present DocGeoNet for document image rectification by introducing explicit geometric representation. Technically, two typical attributes of the document image are involved in the proposed geometric representation learning, i.e., 3D shape and textlines. Our motivation arises from the insight that 3D shape provides global unwarping cues for rectifying a distorted document image while overlooking the local structure. On the other hand, textlines complementarily provide explicit geometric constraints for local patterns. The learned geometric representation effectively bridges the distorted image and the ground truth one. Extensive experiments show the effectiveness of our framework and demonstrate the superiority of our DocGeoNet over state-of-the-art methods on both the DocUNet Benchmark dataset and our proposed DIR300 test set. The code is available at https://github.com/fh2019ustc/DocGeoNet.

Both geometry and texture are fundamental aspects of visual style. Existing style transfer methods, however, primarily focus on texture, almost entirely ignoring geometry. We propose deformable style transfer (DST), an optimization-based approach that jointly stylizes the texture and geometry of a content image to better match a style image. Unlike previous geometry-aware stylization methods, our approach is neither restricted to a particular domain (such as human faces), nor does it require training sets of matching style/content pairs. We demonstrate our method on a diverse set of content and style images including portraits, animals, objects, scenes, and paintings. Code has been made publicly available at https://github.com/sunniesuhyoung/DST.

Existing Large Multimodal Models (LMMs) struggle with mathematical geometric reasoning due to a lack of high-quality image-text paired data. Current geometric data generation approaches, which apply preset templates to generate geometric data or use Large Language Models (LLMs) to rephrase questions and answers (Q&A), unavoidably limit data accuracy and diversity. To synthesize higher-quality data, we propose a two-stage Reverse Chain-of-Thought (R-CoT) geometry problem generation pipeline. First, we introduce GeoChain to produce high-fidelity geometric images and corresponding descriptions highlighting relations among geometric elements. We then design a Reverse A&Q method that reasons step-by-step based on the descriptions and generates questions in reverse from the reasoning results. Experiments demonstrate that the proposed method brings significant and consistent improvements on multiple LMM baselines, achieving new performance records in the 2B, 7B, and 8B settings. Notably, R-CoT-8B significantly outperforms previous state-of-the-art open-source mathematical models by 16.6% on MathVista and 9.2% on GeoQA, while also surpassing the closed-source model GPT-4o by an average of 13% across both datasets. The code is available at https://github.com/dle666/R-CoT.

Semantic correspondence, the task of determining relationships between different parts of images, underpins various applications including 3D reconstruction, image-to-image translation, object tracking, and visual place recognition. Recent studies have begun to explore representations learned in large generative image models for semantic correspondence, demonstrating promising results. Building on this progress, current state-of-the-art methods rely on combining multiple large models, resulting in high computational demands and reduced efficiency. In this work, we address this challenge by proposing a more computationally efficient approach. We propose a novel knowledge distillation technique to overcome the problem of reduced efficiency. We show how to use two large vision foundation models and distill the capabilities of these complementary models into one smaller model that maintains high accuracy at reduced computational cost. Furthermore, we demonstrate that by incorporating 3D data, we are able to further improve performance, without the need for human-annotated correspondences. Overall, our empirical results demonstrate that our distilled model with 3D data augmentation achieves performance superior to current state-of-the-art methods while significantly reducing computational load and enhancing practicality for real-world applications, such as semantic video correspondence. Our code and weights are publicly available on our project page.

In this note we establish a 1-to-1 correspondence between the class of generalized quadrangles with ovoids and the class of balanced incomplete block designs that posses a non-triangular local resolution system and have the appropriate parameters. We present a non-triangular local resolution system for a difference family BIBD construction of Sprott.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

We present a computational framework that transforms single images into 3D physical objects. The visual geometry of a physical object in an image is determined by three orthogonal attributes: mechanical properties, external forces, and rest-shape geometry. Existing single-view 3D reconstruction methods often overlook this underlying composition, presuming rigidity or neglecting external forces. Consequently, the reconstructed objects fail to withstand real-world physical forces, resulting in instability or undesirable deformation -- diverging from their intended designs as depicted in the image. Our optimization framework addresses this by embedding physical compatibility into the reconstruction process. We explicitly decompose the three physical attributes and link them through static equilibrium, which serves as a hard constraint, ensuring that the optimized physical shapes exhibit desired physical behaviors. Evaluations on a dataset collected from Objaverse demonstrate that our framework consistently enhances the physical realism of 3D models over existing methods. The utility of our framework extends to practical applications in dynamic simulations and 3D printing, where adherence to physical compatibility is paramount.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

Previous methods solve feature matching and pose estimation using a two-stage process by first finding matches and then estimating the pose. As they ignore the geometric relationships between the two tasks, they focus on either improving the quality of matches or filtering potential outliers, leading to limited efficiency or accuracy. In contrast, we propose an iterative matching and pose estimation framework (IMP) leveraging the geometric connections between the two tasks: a few good matches are enough for a roughly accurate pose estimation; a roughly accurate pose can be used to guide the matching by providing geometric constraints. To this end, we implement a geometry-aware recurrent attention-based module which jointly outputs sparse matches and camera poses. Specifically, for each iteration, we first implicitly embed geometric information into the module via a pose-consistency loss, allowing it to predict geometry-aware matches progressively. Second, we introduce an efficient IMP, called EIMP, to dynamically discard keypoints without potential matches, avoiding redundant updating and significantly reducing the quadratic time complexity of attention computation in transformers. Experiments on YFCC100m, Scannet, and Aachen Day-Night datasets demonstrate that the proposed method outperforms previous approaches in terms of accuracy and efficiency.

A promising direction for pre-training 3D point clouds is to leverage the massive amount of data in 2D, whereas the domain gap between 2D and 3D creates a fundamental challenge. This paper proposes a novel approach to point-cloud pre-training that learns 3D representations by leveraging pre-trained 2D networks. Different from the popular practice of predicting 2D features first and then obtaining 3D features through dimensionality lifting, our approach directly uses a 3D network for feature extraction. We train the 3D feature extraction network with the help of the novel 2D knowledge transfer loss, which enforces the 2D projections of the 3D feature to be consistent with the output of pre-trained 2D networks. To prevent the feature from discarding 3D signals, we introduce the multi-view consistency loss that additionally encourages the projected 2D feature representations to capture pixel-wise correspondences across different views. Such correspondences induce 3D geometry and effectively retain 3D features in the projected 2D features. Experimental results demonstrate that our pre-trained model can be successfully transferred to various downstream tasks, including 3D shape classification, part segmentation, 3D object detection, and semantic segmentation, achieving state-of-the-art performance.

We present a new method for real-time non-rigid dense correspondence between point clouds based on structured shape construction. Our method, termed Deep Point Correspondence (DPC), requires a fraction of the training data compared to previous techniques and presents better generalization capabilities. Until now, two main approaches have been suggested for the dense correspondence problem. The first is a spectral-based approach that obtains great results on synthetic datasets but requires mesh connectivity of the shapes and long inference processing time while being unstable in real-world scenarios. The second is a spatial approach that uses an encoder-decoder framework to regress an ordered point cloud for the matching alignment from an irregular input. Unfortunately, the decoder brings considerable disadvantages, as it requires a large amount of training data and struggles to generalize well in cross-dataset evaluations. DPC's novelty lies in its lack of a decoder component. Instead, we use latent similarity and the input coordinates themselves to construct the point cloud and determine correspondence, replacing the coordinate regression done by the decoder. Extensive experiments show that our construction scheme leads to a performance boost in comparison to recent state-of-the-art correspondence methods. Our code is publicly available at https://github.com/dvirginz/DPC.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

While impressive progress has recently been made in image-oriented facial attribute translation, shape-oriented 3D facial attribute translation remains an unsolved issue. This is primarily limited by the lack of 3D generative models and ineffective usage of 3D facial data. We propose a learning framework for 3D facial attribute translation to relieve these limitations. Firstly, we customize a novel geometric map for 3D shape representation and embed it in an end-to-end generative adversarial network. The geometric map represents 3D shapes symmetrically on a square image grid, while preserving the neighboring relationship of 3D vertices in a local least-square sense. This enables effective learning for the latent representation of data with different attributes. Secondly, we employ a unified and unpaired learning framework for multi-domain attribute translation. It not only makes effective usage of data correlation from multiple domains, but also mitigates the constraint for hardly accessible paired data. Finally, we propose a hierarchical architecture for the discriminator to guarantee robust results against both global and local artifacts. We conduct extensive experiments to demonstrate the advantage of the proposed framework over the state-of-the-art in generating high-fidelity facial shapes. Given an input 3D facial shape, the proposed framework is able to synthesize novel shapes of different attributes, which covers some downstream applications, such as expression transfer, gender translation, and aging. Code at https://github.com/NaughtyZZ/3D_facial_shape_attribute_translation_ssgmap.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

We propose a system for rearranging objects in a scene to achieve a desired object-scene placing relationship, such as a book inserted in an open slot of a bookshelf. The pipeline generalizes to novel geometries, poses, and layouts of both scenes and objects, and is trained from demonstrations to operate directly on 3D point clouds. Our system overcomes challenges associated with the existence of many geometrically-similar rearrangement solutions for a given scene. By leveraging an iterative pose de-noising training procedure, we can fit multi-modal demonstration data and produce multi-modal outputs while remaining precise and accurate. We also show the advantages of conditioning on relevant local geometric features while ignoring irrelevant global structure that harms both generalization and precision. We demonstrate our approach on three distinct rearrangement tasks that require handling multi-modality and generalization over object shape and pose in both simulation and the real world. Project website, code, and videos: https://anthonysimeonov.github.io/rpdiff-multi-modal/

We present 3DRegNet, a novel deep learning architecture for the registration of 3D scans. Given a set of 3D point correspondences, we build a deep neural network to address the following two challenges: (i) classification of the point correspondences into inliers/outliers, and (ii) regression of the motion parameters that align the scans into a common reference frame. With regard to regression, we present two alternative approaches: (i) a Deep Neural Network (DNN) registration and (ii) a Procrustes approach using SVD to estimate the transformation. Our correspondence-based approach achieves a higher speedup compared to competing baselines. We further propose the use of a refinement network, which consists of a smaller 3DRegNet as a refinement to improve the accuracy of the registration. Extensive experiments on two challenging datasets demonstrate that we outperform other methods and achieve state-of-the-art results. The code is available.

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design process, we explore the problem of reverse engineering from unconstrained real-world CAD images that can be easily captured by users of all experiences. However, the scarcity of real-world CAD data poses challenges in directly training such models. To tackle these challenges, we propose CADCrafter, an image-to-parametric CAD model generation framework that trains solely on synthetic textureless CAD data while testing on real-world images. To bridge the significant representation disparity between images and parametric CAD models, we introduce a geometry encoder to accurately capture diverse geometric features. Moreover, the texture-invariant properties of the geometric features can also facilitate the generalization to real-world scenarios. Since compiling CAD parameter sequences into explicit CAD models is a non-differentiable process, the network training inherently lacks explicit geometric supervision. To impose geometric validity constraints, we employ direct preference optimization (DPO) to fine-tune our model with the automatic code checker feedback on CAD sequence quality. Furthermore, we collected a real-world dataset, comprised of multi-view images and corresponding CAD command sequence pairs, to evaluate our method. Experimental results demonstrate that our approach can robustly handle real unconstrained CAD images, and even generalize to unseen general objects.

Shape assembly aims to reassemble parts (or fragments) into a complete object, which is a common task in our daily life. Different from the semantic part assembly (e.g., assembling a chair's semantic parts like legs into a whole chair), geometric part assembly (e.g., assembling bowl fragments into a complete bowl) is an emerging task in computer vision and robotics. Instead of semantic information, this task focuses on geometric information of parts. As the both geometric and pose space of fractured parts are exceptionally large, shape pose disentanglement of part representations is beneficial to geometric shape assembly. In our paper, we propose to leverage SE(3) equivariance for such shape pose disentanglement. Moreover, while previous works in vision and robotics only consider SE(3) equivariance for the representations of single objects, we move a step forward and propose leveraging SE(3) equivariance for representations considering multi-part correlations, which further boosts the performance of the multi-part assembly. Experiments demonstrate the significance of SE(3) equivariance and our proposed method for geometric shape assembly. Project page: https://crtie.github.io/SE-3-part-assembly/

Recent advances in dense 3D reconstruction have led to significant progress, yet achieving accurate unified geometric prediction remains a major challenge. Most existing methods are limited to predicting a single geometry quantity from input images. However, geometric quantities such as depth, surface normals, and point maps are inherently correlated, and estimating them in isolation often fails to ensure consistency, thereby limiting both accuracy and practical applicability. This motivates us to explore a unified framework that explicitly models the structural coupling among different geometric properties to enable joint regression. In this paper, we present Dens3R, a 3D foundation model designed for joint geometric dense prediction and adaptable to a wide range of downstream tasks. Dens3R adopts a two-stage training framework to progressively build a pointmap representation that is both generalizable and intrinsically invariant. Specifically, we design a lightweight shared encoder-decoder backbone and introduce position-interpolated rotary positional encoding to maintain expressive power while enhancing robustness to high-resolution inputs. By integrating image-pair matching features with intrinsic invariance modeling, Dens3R accurately regresses multiple geometric quantities such as surface normals and depth, achieving consistent geometry perception from single-view to multi-view inputs. Additionally, we propose a post-processing pipeline that supports geometrically consistent multi-view inference. Extensive experiments demonstrate the superior performance of Dens3R across various dense 3D prediction tasks and highlight its potential for broader applications.

Generating high-quality 3D objects from textual descriptions remains a challenging problem due to computational cost, the scarcity of 3D data, and complex 3D representations. We introduce Geometry Image Diffusion (GIMDiffusion), a novel Text-to-3D model that utilizes geometry images to efficiently represent 3D shapes using 2D images, thereby avoiding the need for complex 3D-aware architectures. By integrating a Collaborative Control mechanism, we exploit the rich 2D priors of existing Text-to-Image models such as Stable Diffusion. This enables strong generalization even with limited 3D training data (allowing us to use only high-quality training data) as well as retaining compatibility with guidance techniques such as IPAdapter. In short, GIMDiffusion enables the generation of 3D assets at speeds comparable to current Text-to-Image models. The generated objects consist of semantically meaningful, separate parts and include internal structures, enhancing both usability and versatility.

It is inherently ambiguous to lift 2D results from pre-trained diffusion models to a 3D world for text-to-3D generation. 2D diffusion models solely learn view-agnostic priors and thus lack 3D knowledge during the lifting, leading to the multi-view inconsistency problem. We find that this problem primarily stems from geometric inconsistency, and avoiding misplaced geometric structures substantially mitigates the problem in the final outputs. Therefore, we improve the consistency by aligning the 2D geometric priors in diffusion models with well-defined 3D shapes during the lifting, addressing the vast majority of the problem. This is achieved by fine-tuning the 2D diffusion model to be viewpoint-aware and to produce view-specific coordinate maps of canonically oriented 3D objects. In our process, only coarse 3D information is used for aligning. This "coarse" alignment not only resolves the multi-view inconsistency in geometries but also retains the ability in 2D diffusion models to generate detailed and diversified high-quality objects unseen in the 3D datasets. Furthermore, our aligned geometric priors (AGP) are generic and can be seamlessly integrated into various state-of-the-art pipelines, obtaining high generalizability in terms of unseen shapes and visual appearance while greatly alleviating the multi-view inconsistency problem. Our method represents a new state-of-the-art performance with an 85+% consistency rate by human evaluation, while many previous methods are around 30%. Our project page is https://sweetdreamer3d.github.io/

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

3D reconstruction in dynamic scenes primarily relies on the combination of geometry estimation and matching modules where the latter task is pivotal for distinguishing dynamic regions which can help to mitigate the interference introduced by camera and object motion. Furthermore, the matching module explicitly models object motion, enabling the tracking of specific targets and advancing motion understanding in complex scenarios. Recently, the proposed representation of pointmap in DUSt3R suggests a potential solution to unify both geometry estimation and matching in 3D space, but it still struggles with ambiguous matching in dynamic regions, which may hamper further improvement. In this work, we present POMATO, a unified framework for dynamic 3D reconstruction by marrying pointmap matching with temporal motion. Specifically, our method first learns an explicit matching relationship by mapping RGB pixels from both dynamic and static regions across different views to 3D pointmaps within a unified coordinate system. Furthermore, we introduce a temporal motion module for dynamic motions that ensures scale consistency across different frames and enhances performance in tasks requiring both precise geometry and reliable matching, most notably 3D point tracking. We show the effectiveness of the proposed pointmap matching and temporal fusion paradigm by demonstrating the remarkable performance across multiple downstream tasks, including video depth estimation, 3D point tracking, and pose estimation. Code and models are publicly available at https://github.com/wyddmw/POMATO.

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry challenges and readable AI automated reasoning. Within this formal framework, we have been able to seamlessly integrate modern AI models with our formal system. AI is now capable of providing deductive reasoning solutions to IMO-level plane geometry problems, just like handling other natural languages, and these proofs are readable, traceable, and verifiable. We propose the geometry formalization theory (GFT) to guide the development of the geometry formal system. Based on the GFT, we have established the FormalGeo, which consists of 88 geometric predicates and 196 theorems. It can represent, validate, and solve IMO-level geometry problems. we also have crafted the FGPS (formal geometry problem solver) in Python. It serves as both an interactive assistant for verifying problem-solving processes and an automated problem solver. We've annotated the formalgeo7k and formalgeo-imo datasets. The former contains 6,981 (expand to 133,818 through data augmentation) geometry problems, while the latter includes 18 (expand to 2,627 and continuously increasing) IMO-level challenging geometry problems. All annotated problems include detailed formal language descriptions and solutions. Implementation of the formal system and experiments validate the correctness and utility of the GFT. The backward depth-first search method only yields a 2.42% problem-solving failure rate, and we can incorporate deep learning techniques to achieve lower one. The source code of FGPS and datasets are available at https://github.com/BitSecret/FGPS.

Line segments are powerful features complementary to points. They offer structural cues, robust to drastic viewpoint and illumination changes, and can be present even in texture-less areas. However, describing and matching them is more challenging compared to points due to partial occlusions, lack of texture, or repetitiveness. This paper introduces a new matching paradigm, where points, lines, and their descriptors are unified into a single wireframe structure. We propose GlueStick, a deep matching Graph Neural Network (GNN) that takes two wireframes from different images and leverages the connectivity information between nodes to better glue them together. In addition to the increased efficiency brought by the joint matching, we also demonstrate a large boost of performance when leveraging the complementary nature of these two features in a single architecture. We show that our matching strategy outperforms the state-of-the-art approaches independently matching line segments and points for a wide variety of datasets and tasks. The code is available at https://github.com/cvg/GlueStick.

3D scene reconstruction is a long-standing vision task. Existing approaches can be categorized into geometry-based and learning-based methods. The former leverages multi-view geometry but can face catastrophic failures due to the reliance on accurate pixel correspondence across views. The latter was proffered to mitigate these issues by learning 2D or 3D representation directly. However, without a large-scale video or 3D training data, it can hardly generalize to diverse real-world scenarios due to the presence of tens of millions or even billions of optimization parameters in the deep network. Recently, robust monocular depth estimation models trained with large-scale datasets have been proven to possess weak 3D geometry prior, but they are insufficient for reconstruction due to the unknown camera parameters, the affine-invariant property, and inter-frame inconsistency. Here, we propose a novel test-time optimization approach that can transfer the robustness of affine-invariant depth models such as LeReS to challenging diverse scenes while ensuring inter-frame consistency, with only dozens of parameters to optimize per video frame. Specifically, our approach involves freezing the pre-trained affine-invariant depth model's depth predictions, rectifying them by optimizing the unknown scale-shift values with a geometric consistency alignment module, and employing the resulting scale-consistent depth maps to robustly obtain camera poses and achieve dense scene reconstruction, even in low-texture regions. Experiments show that our method achieves state-of-the-art cross-dataset reconstruction on five zero-shot testing datasets.

Existing RGB-based imitation learning approaches typically employ traditional vision encoders such as ResNet or ViT, which lack explicit 3D reasoning capabilities. Recent geometry-grounded vision models, such as VGGT~wang2025vggt, provide robust spatial understanding and are promising candidates to address this limitation. This work investigates the integration of geometry-aware visual representations into robotic manipulation. Our results suggest that incorporating the geometry-aware vision encoder into imitation learning frameworks, including ACT and DP, yields up to 6.5% improvement over standard vision encoders in success rate across single- and bi-manual manipulation tasks in both simulation and real-world settings. Despite these benefits, most geometry-grounded models require high computational cost, limiting their deployment in practical robotic systems. To address this challenge, we propose eVGGT, an efficient geometry-aware encoder distilled from VGGT. eVGGT is nearly 9 times faster and 5 times smaller than VGGT, while preserving strong 3D reasoning capabilities. Code and pretrained models will be released to facilitate further research in geometry-aware robotics.

In this paper we show that visual diffusion models can serve as effective geometric solvers: they can directly reason about geometric problems by working in pixel space. We first demonstrate this on the Inscribed Square Problem, a long-standing problem in geometry that asks whether every Jordan curve contains four points forming a square. We then extend the approach to two other well-known hard geometric problems: the Steiner Tree Problem and the Simple Polygon Problem. Our method treats each problem instance as an image and trains a standard visual diffusion model that transforms Gaussian noise into an image representing a valid approximate solution that closely matches the exact one. The model learns to transform noisy geometric structures into correct configurations, effectively recasting geometric reasoning as image generation. Unlike prior work that necessitates specialized architectures and domain-specific adaptations when applying diffusion to parametric geometric representations, we employ a standard visual diffusion model that operates on the visual representation of the problem. This simplicity highlights a surprising bridge between generative modeling and geometric problem solving. Beyond the specific problems studied here, our results point toward a broader paradigm: operating in image space provides a general and practical framework for approximating notoriously hard problems, and opens the door to tackling a far wider class of challenging geometric tasks.

We introduce GeoDANO, a geometric vision-language model (VLM) with a domain-agnostic vision encoder, for solving plane geometry problems. Although VLMs have been employed for solving geometry problems, their ability to recognize geometric features remains insufficiently analyzed. To address this gap, we propose a benchmark that evaluates the recognition of visual geometric features, including primitives such as dots and lines, and relations such as orthogonality. Our preliminary study shows that vision encoders often used in general-purpose VLMs, e.g., OpenCLIP, fail to detect these features and struggle to generalize across domains. We develop GeoCLIP, a CLIP based model trained on synthetic geometric diagram-caption pairs to overcome the limitation. Benchmark results show that GeoCLIP outperforms existing vision encoders in recognizing geometric features. We then propose our VLM, GeoDANO, which augments GeoCLIP with a domain adaptation strategy for unseen diagram styles. GeoDANO outperforms specialized methods for plane geometry problems and GPT-4o on MathVerse.

Recent progress in Sign Language Translation (SLT) has focussed primarily on improving the representational capacity of large language models to incorporate Sign Language features. This work explores an alternative direction: enhancing the geometric properties of skeletal representations themselves. We propose Geo-Sign, a method that leverages the properties of hyperbolic geometry to model the hierarchical structure inherent in sign language kinematics. By projecting skeletal features derived from Spatio-Temporal Graph Convolutional Networks (ST-GCNs) into the Poincar\'e ball model, we aim to create more discriminative embeddings, particularly for fine-grained motions like finger articulations. We introduce a hyperbolic projection layer, a weighted Fr\'echet mean aggregation scheme, and a geometric contrastive loss operating directly in hyperbolic space. These components are integrated into an end-to-end translation framework as a regularisation function, to enhance the representations within the language model. This work demonstrates the potential of hyperbolic geometry to improve skeletal representations for Sign Language Translation, improving on SOTA RGB methods while preserving privacy and improving computational efficiency. Code available here: https://github.com/ed-fish/geo-sign.

Recent advances in data-driven geometric multi-view 3D reconstruction foundation models (e.g., DUSt3R) have shown remarkable performance across various 3D vision tasks, facilitated by the release of large-scale, high-quality 3D datasets. However, as we observed, constrained by their matching-based principles, the reconstruction quality of existing models suffers significant degradation in challenging regions with limited matching cues, particularly in weakly textured areas and low-light conditions. To mitigate these limitations, we propose to harness the inherent robustness of monocular geometry estimation to compensate for the inherent shortcomings of matching-based methods. Specifically, we introduce a monocular-guided refinement module that integrates monocular geometric priors into multi-view reconstruction frameworks. This integration substantially enhances the robustness of multi-view reconstruction systems, leading to high-quality feed-forward reconstructions. Comprehensive experiments across multiple benchmarks demonstrate that our method achieves substantial improvements in both mutli-view camera pose estimation and point cloud accuracy.

We propose GeoUni, the first unified geometry expert model capable of generating problem solutions and diagrams within a single framework in a way that enables the creation of unique and individualized geometry problems. Traditionally, solving geometry problems and generating diagrams have been treated as separate tasks in machine learning, with no models successfully integrating both to support problem creation. However, we believe that mastery in geometry requires frictionless integration of all of these skills, from solving problems to visualizing geometric relationships, and finally, crafting tailored problems. Our extensive experiments demonstrate that GeoUni, with only 1.5B parameters, achieves performance comparable to larger models such as DeepSeek-R1 with 671B parameters in geometric reasoning tasks. GeoUni also excels in generating precise geometric diagrams, surpassing both text-to-image models and unified models, including the GPT-4o image generation. Most importantly, GeoUni is the only model capable of successfully generating textual problems with matching diagrams based on specific knowledge points, thus offering a wider range of capabilities that extend beyond current models.

Transferring appearance to 3D assets using different representations of the appearance object - such as images or text - has garnered interest due to its wide range of applications in industries like gaming, augmented reality, and digital content creation. However, state-of-the-art methods still fail when the geometry between the input and appearance objects is significantly different. A straightforward approach is to directly apply a 3D generative model, but we show that this ultimately fails to produce appealing results. Instead, we propose a principled approach inspired by universal guidance. Given a pretrained rectified flow model conditioned on image or text, our training-free method interacts with the sampling process by periodically adding guidance. This guidance can be modeled as a differentiable loss function, and we experiment with two different types of guidance including part-aware losses for appearance and self-similarity. Our experiments show that our approach successfully transfers texture and geometric details to the input 3D asset, outperforming baselines both qualitatively and quantitatively. We also show that traditional metrics are not suitable for evaluating the task due to their inability of focusing on local details and comparing dissimilar inputs, in absence of ground truth data. We thus evaluate appearance transfer quality with a GPT-based system objectively ranking outputs, ensuring robust and human-like assessment, as further confirmed by our user study. Beyond showcased scenarios, our method is general and could be extended to different types of diffusion models and guidance functions.

We propose a Geometry-aware Policy Imitation (GPI) approach that rethinks imitation learning by treating demonstrations as geometric curves rather than collections of state-action samples. From these curves, GPI derives distance fields that give rise to two complementary control primitives: a progression flow that advances along expert trajectories and an attraction flow that corrects deviations. Their combination defines a controllable, non-parametric vector field that directly guides robot behavior. This formulation decouples metric learning from policy synthesis, enabling modular adaptation across low-dimensional robot states and high-dimensional perceptual inputs. GPI naturally supports multimodality by preserving distinct demonstrations as separate models and allows efficient composition of new demonstrations through simple additions to the distance field. We evaluate GPI in simulation and on real robots across diverse tasks. Experiments show that GPI achieves higher success rates than diffusion-based policies while running 20 times faster, requiring less memory, and remaining robust to perturbations. These results establish GPI as an efficient, interpretable, and scalable alternative to generative approaches for robotic imitation learning. Project website: https://yimingli1998.github.io/projects/GPI/

Estimating relative camera poses between images has been a central problem in computer vision. Methods that find correspondences and solve for the fundamental matrix offer high precision in most cases. Conversely, methods predicting pose directly using neural networks are more robust to limited overlap and can infer absolute translation scale, but at the expense of reduced precision. We show how to combine the best of both methods; our approach yields results that are both precise and robust, while also accurately inferring translation scales. At the heart of our model lies a Transformer that (1) learns to balance between solved and learned pose estimations, and (2) provides a prior to guide a solver. A comprehensive analysis supports our design choices and demonstrates that our method adapts flexibly to various feature extractors and correspondence estimators, showing state-of-the-art performance in 6DoF pose estimation on Matterport3D, InteriorNet, StreetLearn, and Map-free Relocalization.

We present DreamPolisher, a novel Gaussian Splatting based method with geometric guidance, tailored to learn cross-view consistency and intricate detail from textual descriptions. While recent progress on text-to-3D generation methods have been promising, prevailing methods often fail to ensure view-consistency and textural richness. This problem becomes particularly noticeable for methods that work with text input alone. To address this, we propose a two-stage Gaussian Splatting based approach that enforces geometric consistency among views. Initially, a coarse 3D generation undergoes refinement via geometric optimization. Subsequently, we use a ControlNet driven refiner coupled with the geometric consistency term to improve both texture fidelity and overall consistency of the generated 3D asset. Empirical evaluations across diverse textual prompts spanning various object categories demonstrate the efficacy of DreamPolisher in generating consistent and realistic 3D objects, aligning closely with the semantics of the textual instructions.

In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric properties of these developable surfaces, we study the geometry of gluing two surfaces.

In this paper, we propose a novel learning-based framework for 3D shape registration, which overcomes the challenges of significant non-rigid deformation and partiality undergoing among input shapes, and, remarkably, requires no correspondence annotation during training. Our key insight is to incorporate neural features learned by deep learning-based shape matching networks into an iterative, geometric shape registration pipeline. The advantage of our approach is two-fold -- On one hand, neural features provide more accurate and semantically meaningful correspondence estimation than spatial features (e.g., coordinates), which is critical in the presence of large non-rigid deformations; On the other hand, the correspondences are dynamically updated according to the intermediate registrations and filtered by consistency prior, which prominently robustify the overall pipeline. Empirical results show that, with as few as dozens of training shapes of limited variability, our pipeline achieves state-of-the-art results on several benchmarks of non-rigid point cloud matching and partial shape matching across varying settings, but also delivers high-quality correspondences between unseen challenging shape pairs that undergo both significant extrinsic and intrinsic deformations, in which case neither traditional registration methods nor intrinsic methods work.

This paper proposes a simple self-supervised approach for learning a representation for visual correspondence from raw video. We cast correspondence as prediction of links in a space-time graph constructed from video. In this graph, the nodes are patches sampled from each frame, and nodes adjacent in time can share a directed edge. We learn a representation in which pairwise similarity defines transition probability of a random walk, so that long-range correspondence is computed as a walk along the graph. We optimize the representation to place high probability along paths of similarity. Targets for learning are formed without supervision, by cycle-consistency: the objective is to maximize the likelihood of returning to the initial node when walking along a graph constructed from a palindrome of frames. Thus, a single path-level constraint implicitly supervises chains of intermediate comparisons. When used as a similarity metric without adaptation, the learned representation outperforms the self-supervised state-of-the-art on label propagation tasks involving objects, semantic parts, and pose. Moreover, we demonstrate that a technique we call edge dropout, as well as self-supervised adaptation at test-time, further improve transfer for object-centric correspondence.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

Multimodal large language models (MLLMs) have made rapid progress in recent years, yet continue to struggle with low-level visual perception (LLVP) -- particularly the ability to accurately describe the geometric details of an image. This capability is crucial for applications in areas such as robotics, medical image analysis, and manufacturing. In this paper, we first introduce Geoperception, a benchmark designed to evaluate an MLLM's ability to accurately transcribe 2D geometric information from an image. Using this benchmark, we demonstrate the limitations of leading MLLMs, and then conduct a comprehensive empirical study to explore strategies for improving their performance on geometric tasks. Our findings highlight the benefits of certain model architectures, training techniques, and data strategies, including the use of high-fidelity synthetic data and multi-stage training with a data curriculum. Notably, we find that a data curriculum enables models to learn challenging geometry understanding tasks which they fail to learn from scratch. Leveraging these insights, we develop Euclid, a family of models specifically optimized for strong low-level geometric perception. Although purely trained on synthetic multimodal data, Euclid shows strong generalization ability to novel geometry shapes. For instance, Euclid outperforms the best closed-source model, Gemini-1.5-Pro, by up to 58.56% on certain Geoperception benchmark tasks and 10.65% on average across all tasks.

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.

Feature matching is a challenging computer vision task that involves finding correspondences between two images of a 3D scene. In this paper we consider the dense approach instead of the more common sparse paradigm, thus striving to find all correspondences. Perhaps counter-intuitively, dense methods have previously shown inferior performance to their sparse and semi-sparse counterparts for estimation of two-view geometry. This changes with our novel dense method, which outperforms both dense and sparse methods on geometry estimation. The novelty is threefold: First, we propose a kernel regression global matcher. Secondly, we propose warp refinement through stacked feature maps and depthwise convolution kernels. Thirdly, we propose learning dense confidence through consistent depth and a balanced sampling approach for dense confidence maps. Through extensive experiments we confirm that our proposed dense method, Dense Kernelized Feature Matching, sets a new state-of-the-art on multiple geometry estimation benchmarks. In particular, we achieve an improvement on MegaDepth-1500 of +4.9 and +8.9 AUC@5^{circ} compared to the best previous sparse method and dense method respectively. Our code is provided at https://github.com/Parskatt/dkm

Modern 3D generation methods can rapidly create shapes from sparse or single views, but their outputs often lack geometric detail due to computational constraints. We present DetailGen3D, a generative approach specifically designed to enhance these generated 3D shapes. Our key insight is to model the coarse-to-fine transformation directly through data-dependent flows in latent space, avoiding the computational overhead of large-scale 3D generative models. We introduce a token matching strategy that ensures accurate spatial correspondence during refinement, enabling local detail synthesis while preserving global structure. By carefully designing our training data to match the characteristics of synthesized coarse shapes, our method can effectively enhance shapes produced by various 3D generation and reconstruction approaches, from single-view to sparse multi-view inputs. Extensive experiments demonstrate that DetailGen3D achieves high-fidelity geometric detail synthesis while maintaining efficiency in training.

This paper presents an unpaired method for creating line drawings from photographs. Current methods often rely on high quality paired datasets to generate line drawings. However, these datasets often have limitations due to the subjects of the drawings belonging to a specific domain, or in the amount of data collected. Although recent work in unsupervised image-to-image translation has shown much progress, the latest methods still struggle to generate compelling line drawings. We observe that line drawings are encodings of scene information and seek to convey 3D shape and semantic meaning. We build these observations into a set of objectives and train an image translation to map photographs into line drawings. We introduce a geometry loss which predicts depth information from the image features of a line drawing, and a semantic loss which matches the CLIP features of a line drawing with its corresponding photograph. Our approach outperforms state-of-the-art unpaired image translation and line drawing generation methods on creating line drawings from arbitrary photographs. For code and demo visit our webpage carolineec.github.io/informative_drawings

Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K-12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference efficiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence.

The rapid development of Large Multimodal Models (LMMs) has led to remarkable progress in 2D visual understanding; however, extending these capabilities to 3D scene understanding remains a significant challenge. Existing approaches predominantly rely on text-only supervision, which fails to provide the geometric constraints required for learning robust 3D spatial representations. In this paper, we introduce Reg3D, a novel Reconstructive Geometry Instruction Tuning framework that addresses this limitation by incorporating geometry-aware supervision directly into the training process. Our key insight is that effective 3D understanding necessitates reconstructing underlying geometric structures rather than merely describing them. Unlike existing methods that inject 3D information solely at the input level, Reg3D adopts a dual-supervision paradigm that leverages 3D geometric information both as input and as explicit learning targets. Specifically, we design complementary object-level and frame-level reconstruction tasks within a dual-encoder architecture, enforcing geometric consistency to encourage the development of spatial reasoning capabilities. Extensive experiments on ScanQA, Scan2Cap, ScanRefer, and SQA3D demonstrate that Reg3D delivers substantial performance improvements, establishing a new training paradigm for spatially aware multimodal models.

Accurate reconstruction of both the geometric and topological details of a 3D object from a single 2D image embodies a fundamental challenge in computer vision. Existing explicit/implicit solutions to this problem struggle to recover self-occluded geometry and/or faithfully reconstruct topological shape structures. To resolve this dilemma, we introduce LIST, a novel neural architecture that leverages local and global image features to accurately reconstruct the geometric and topological structure of a 3D object from a single image. We utilize global 2D features to predict a coarse shape of the target object and then use it as a base for higher-resolution reconstruction. By leveraging both local 2D features from the image and 3D features from the coarse prediction, we can predict the signed distance between an arbitrary point and the target surface via an implicit predictor with great accuracy. Furthermore, our model does not require camera estimation or pixel alignment. It provides an uninfluenced reconstruction from the input-view direction. Through qualitative and quantitative analysis, we show the superiority of our model in reconstructing 3D objects from both synthetic and real-world images against the state of the art.

Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 theorem prover. LeanGeo features a comprehensive library of high-level geometric theorems with Lean's foundational logic, enabling rigorous proof verification and seamless integration with Mathlib. We also present LeanGeo-Bench, a formal geometry benchmark in LeanGeo, comprising problems from the International Mathematical Olympiad (IMO) and other advanced sources. Our evaluation demonstrates the capabilities and limitations of state-of-the-art Large Language Models on this benchmark, highlighting the need for further advancements in automated geometric reasoning. We open source the theorem library and the benchmark of LeanGeo at https://github.com/project-numina/LeanGeo/tree/master.

Image Matching is a core component of all best-performing algorithms and pipelines in 3D vision. Yet despite matching being fundamentally a 3D problem, intrinsically linked to camera pose and scene geometry, it is typically treated as a 2D problem. This makes sense as the goal of matching is to establish correspondences between 2D pixel fields, but also seems like a potentially hazardous choice. In this work, we take a different stance and propose to cast matching as a 3D task with DUSt3R, a recent and powerful 3D reconstruction framework based on Transformers. Based on pointmaps regression, this method displayed impressive robustness in matching views with extreme viewpoint changes, yet with limited accuracy. We aim here to improve the matching capabilities of such an approach while preserving its robustness. We thus propose to augment the DUSt3R network with a new head that outputs dense local features, trained with an additional matching loss. We further address the issue of quadratic complexity of dense matching, which becomes prohibitively slow for downstream applications if not carefully treated. We introduce a fast reciprocal matching scheme that not only accelerates matching by orders of magnitude, but also comes with theoretical guarantees and, lastly, yields improved results. Extensive experiments show that our approach, coined MASt3R, significantly outperforms the state of the art on multiple matching tasks. In particular, it beats the best published methods by 30% (absolute improvement) in VCRE AUC on the extremely challenging Map-free localization dataset.

Remarkable advances have been achieved recently in learning neural representations that characterize object geometry, while generating textured objects suitable for downstream applications and 3D rendering remains at an early stage. In particular, reconstructing textured geometry from images of real objects is a significant challenge -- reconstructed geometry is often inexact, making realistic texturing a significant challenge. We present Mesh2Tex, which learns a realistic object texture manifold from uncorrelated collections of 3D object geometry and photorealistic RGB images, by leveraging a hybrid mesh-neural-field texture representation. Our texture representation enables compact encoding of high-resolution textures as a neural field in the barycentric coordinate system of the mesh faces. The learned texture manifold enables effective navigation to generate an object texture for a given 3D object geometry that matches to an input RGB image, which maintains robustness even under challenging real-world scenarios where the mesh geometry approximates an inexact match to the underlying geometry in the RGB image. Mesh2Tex can effectively generate realistic object textures for an object mesh to match real images observations towards digitization of real environments, significantly improving over previous state of the art.

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

Point cloud registration has seen significant advancements with the application of deep learning techniques. However, existing approaches often overlook the potential of integrating radiometric information from RGB images. This limitation reduces their effectiveness in aligning point clouds pairs, especially in regions where geometric data alone is insufficient. When used effectively, radiometric information can enhance the registration process by providing context that is missing from purely geometric data. In this paper, we propose CoFF, a novel Cross-modal Feature Fusion method that utilizes both point cloud geometry and RGB images for pairwise point cloud registration. Assuming that the co-registration between point clouds and RGB images is available, CoFF explicitly addresses the challenges where geometric information alone is unclear, such as in regions with symmetric similarity or planar structures, through a two-stage fusion of 3D point cloud features and 2D image features. It incorporates a cross-modal feature fusion module that assigns pixel-wise image features to 3D input point clouds to enhance learned 3D point features, and integrates patch-wise image features with superpoint features to improve the quality of coarse matching. This is followed by a coarse-to-fine matching module that accurately establishes correspondences using the fused features. We extensively evaluate CoFF on four common datasets: 3DMatch, 3DLoMatch, IndoorLRS, and the recently released ScanNet++ datasets. In addition, we assess CoFF on specific subset datasets containing geometrically ambiguous cases. Our experimental results demonstrate that CoFF achieves state-of-the-art registration performance across all benchmarks, including remarkable registration recalls of 95.9% and 81.6% on the widely-used 3DMatch and 3DLoMatch datasets, respectively...(Truncated to fit arXiv abstract length)

In this paper, we develop a new method to automatically convert 2D line drawings from three orthographic views into 3D CAD models. Existing methods for this problem reconstruct 3D models by back-projecting the 2D observations into 3D space while maintaining explicit correspondence between the input and output. Such methods are sensitive to errors and noises in the input, thus often fail in practice where the input drawings created by human designers are imperfect. To overcome this difficulty, we leverage the attention mechanism in a Transformer-based sequence generation model to learn flexible mappings between the input and output. Further, we design shape programs which are suitable for generating the objects of interest to boost the reconstruction accuracy and facilitate CAD modeling applications. Experiments on a new benchmark dataset show that our method significantly outperforms existing ones when the inputs are noisy or incomplete.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

The popularity of pre-trained large models has revolutionized downstream tasks across diverse fields, such as language, vision, and multi-modality. To minimize the adaption cost for downstream tasks, many Parameter-Efficient Fine-Tuning (PEFT) techniques are proposed for language and 2D image pre-trained models. However, the specialized PEFT method for 3D pre-trained models is still under-explored. To this end, we introduce Point-PEFT, a novel framework for adapting point cloud pre-trained models with minimal learnable parameters. Specifically, for a pre-trained 3D model, we freeze most of its parameters, and only tune the newly added PEFT modules on downstream tasks, which consist of a Point-prior Prompt and a Geometry-aware Adapter. The Point-prior Prompt adopts a set of learnable prompt tokens, for which we propose to construct a memory bank with domain-specific knowledge, and utilize a parameter-free attention to enhance the prompt tokens. The Geometry-aware Adapter aims to aggregate point cloud features within spatial neighborhoods to capture fine-grained geometric information through local interactions. Extensive experiments indicate that our Point-PEFT can achieve better performance than the full fine-tuning on various downstream tasks, while using only 5% of the trainable parameters, demonstrating the efficiency and effectiveness of our approach. Code is released at https://github.com/Ivan-Tang-3D/Point-PEFT.

Mapping high-fidelity 3D geometry to a representation that allows for intuitive edits remains an elusive goal in computer vision and graphics. The key challenge is the need to model both continuous and discrete shape variations. Current approaches, such as implicit shape representation, lack straightforward interpretable encoding, while others that employ procedural methods output coarse geometry. We present GeoCode, a technique for 3D shape synthesis using an intuitively editable parameter space. We build a novel program that enforces a complex set of rules and enables users to perform intuitive and controlled high-level edits that procedurally propagate at a low level to the entire shape. Our program produces high-quality mesh outputs by construction. We use a neural network to map a given point cloud or sketch to our interpretable parameter space. Once produced by our procedural program, shapes can be easily modified. Empirically, we show that GeoCode can infer and recover 3D shapes more accurately compared to existing techniques and we demonstrate its ability to perform controlled local and global shape manipulations.

Poster layout is a crucial aspect of poster design. Prior methods primarily focus on the correlation between visual content and graphic elements. However, a pleasant layout should also consider the relationship between visual and textual contents and the relationship between elements. In this study, we introduce a relation-aware diffusion model for poster layout generation that incorporates these two relationships in the generation process. Firstly, we devise a visual-textual relation-aware module that aligns the visual and textual representations across modalities, thereby enhancing the layout's efficacy in conveying textual information. Subsequently, we propose a geometry relation-aware module that learns the geometry relationship between elements by comprehensively considering contextual information. Additionally, the proposed method can generate diverse layouts based on user constraints. To advance research in this field, we have constructed a poster layout dataset named CGL-Dataset V2. Our proposed method outperforms state-of-the-art methods on CGL-Dataset V2. The data and code will be available at https://github.com/liuan0803/RADM.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

General object composition (GOC) aims to seamlessly integrate a target object into a background scene with desired geometric properties, while simultaneously preserving its fine-grained appearance details. Recent approaches derive semantic embeddings and integrate them into advanced diffusion models to enable geometry-editable generation. However, these highly compact embeddings encode only high-level semantic cues and inevitably discard fine-grained appearance details. We introduce a Disentangled Geometry-editable and Appearance-preserving Diffusion (DGAD) model that first leverages semantic embeddings to implicitly capture the desired geometric transformations and then employs a cross-attention retrieval mechanism to align fine-grained appearance features with the geometry-edited representation, facilitating both precise geometry editing and faithful appearance preservation in object composition. Specifically, DGAD builds on CLIP/DINO-derived and reference networks to extract semantic embeddings and appearance-preserving representations, which are then seamlessly integrated into the encoding and decoding pipelines in a disentangled manner. We first integrate the semantic embeddings into pre-trained diffusion models that exhibit strong spatial reasoning capabilities to implicitly capture object geometry, thereby facilitating flexible object manipulation and ensuring effective editability. Then, we design a dense cross-attention mechanism that leverages the implicitly learned object geometry to retrieve and spatially align appearance features with their corresponding regions, ensuring faithful appearance consistency. Extensive experiments on public benchmarks demonstrate the effectiveness of the proposed DGAD framework.

Emerging 3D geometric foundation models, such as DUSt3R, offer a promising approach for in-the-wild 3D vision tasks. However, due to the high-dimensional nature of the problem space and scarcity of high-quality 3D data, these pre-trained models still struggle to generalize to many challenging circumstances, such as limited view overlap or low lighting. To address this, we propose LoRA3D, an efficient self-calibration pipeline to specialize the pre-trained models to target scenes using their own multi-view predictions. Taking sparse RGB images as input, we leverage robust optimization techniques to refine multi-view predictions and align them into a global coordinate frame. In particular, we incorporate prediction confidence into the geometric optimization process, automatically re-weighting the confidence to better reflect point estimation accuracy. We use the calibrated confidence to generate high-quality pseudo labels for the calibrating views and use low-rank adaptation (LoRA) to fine-tune the models on the pseudo-labeled data. Our method does not require any external priors or manual labels. It completes the self-calibration process on a single standard GPU within just 5 minutes. Each low-rank adapter requires only 18MB of storage. We evaluated our method on more than 160 scenes from the Replica, TUM and Waymo Open datasets, achieving up to 88% performance improvement on 3D reconstruction, multi-view pose estimation and novel-view rendering.

Automatic math problem solving has recently attracted increasing attention as a long-standing AI benchmark. In this paper, we focus on solving geometric problems, which requires a comprehensive understanding of textual descriptions, visual diagrams, and theorem knowledge. However, the existing methods were highly dependent on handcraft rules and were merely evaluated on small-scale datasets. Therefore, we propose a Geometric Question Answering dataset GeoQA, containing 4,998 geometric problems with corresponding annotated programs, which illustrate the solving process of the given problems. Compared with another publicly available dataset GeoS, GeoQA is 25 times larger, in which the program annotations can provide a practical testbed for future research on explicit and explainable numerical reasoning. Moreover, we introduce a Neural Geometric Solver (NGS) to address geometric problems by comprehensively parsing multimodal information and generating interpretable programs. We further add multiple self-supervised auxiliary tasks on NGS to enhance cross-modal semantic representation. Extensive experiments on GeoQA validate the effectiveness of our proposed NGS and auxiliary tasks. However, the results are still significantly lower than human performance, which leaves large room for future research. Our benchmark and code are released at https://github.com/chen-judge/GeoQA .

Recently, "visual o1" began to enter people's vision, with expectations that this slow-thinking design can solve visual reasoning tasks, especially geometric math problems. However, the reality is that current LVLMs (Large Vision Language Models) can hardly even accurately copy a geometric figure, let alone truly understand the complex inherent logic and spatial relationships within geometric shapes. We believe accurate copying (strong perception) is the first step to visual o1. Accordingly, we introduce the concept of "slow perception" (SP), which guides the model to gradually perceive basic point-line combinations, as our humans, reconstruct complex geometric structures progressively. There are two-fold stages in SP: a) perception decomposition. Perception is not instantaneous. In this stage, complex geometric figures are broken down into basic simple units to unify geometry representation. b) perception flow, which acknowledges that accurately tracing a line is not an easy task. This stage aims to avoid "long visual jumps" in regressing line segments by using a proposed "perceptual ruler" to trace each line stroke-by-stroke. Surprisingly, such a human-like perception manner enjoys an inference time scaling law -- the slower, the better. Researchers strive to speed up the model's perception in the past, but we slow it down again, allowing the model to read the image step-by-step and carefully.

We present PVSeRF, a learning framework that reconstructs neural radiance fields from single-view RGB images, for novel view synthesis. Previous solutions, such as pixelNeRF, rely only on pixel-aligned features and suffer from feature ambiguity issues. As a result, they struggle with the disentanglement of geometry and appearance, leading to implausible geometries and blurry results. To address this challenge, we propose to incorporate explicit geometry reasoning and combine it with pixel-aligned features for radiance field prediction. Specifically, in addition to pixel-aligned features, we further constrain the radiance field learning to be conditioned on i) voxel-aligned features learned from a coarse volumetric grid and ii) fine surface-aligned features extracted from a regressed point cloud. We show that the introduction of such geometry-aware features helps to achieve a better disentanglement between appearance and geometry, i.e. recovering more accurate geometries and synthesizing higher quality images of novel views. Extensive experiments against state-of-the-art methods on ShapeNet benchmarks demonstrate the superiority of our approach for single-image novel view synthesis.

Text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models has shown great promise but still suffers from inconsistent 3D geometric structures (Janus problems) and severe artifacts. The aforementioned problems mainly stem from 2D diffusion models lacking 3D awareness during the lifting. In this work, we present GeoDream, a novel method that incorporates explicit generalized 3D priors with 2D diffusion priors to enhance the capability of obtaining unambiguous 3D consistent geometric structures without sacrificing diversity or fidelity. Specifically, we first utilize a multi-view diffusion model to generate posed images and then construct cost volume from the predicted image, which serves as native 3D geometric priors, ensuring spatial consistency in 3D space. Subsequently, we further propose to harness 3D geometric priors to unlock the great potential of 3D awareness in 2D diffusion priors via a disentangled design. Notably, disentangling 2D and 3D priors allows us to refine 3D geometric priors further. We justify that the refined 3D geometric priors aid in the 3D-aware capability of 2D diffusion priors, which in turn provides superior guidance for the refinement of 3D geometric priors. Our numerical and visual comparisons demonstrate that GeoDream generates more 3D consistent textured meshes with high-resolution realistic renderings (i.e., 1024 times 1024) and adheres more closely to semantic coherence.

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we introduce an as-rigid-as-possible regulation term to estimate the deformed normals and propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.

3D pose transfer is a challenging generation task that aims to transfer the pose of a source geometry onto a target geometry with the target identity preserved. Many prior methods require keypoint annotations to find correspondence between the source and target. Current pose transfer methods allow end-to-end correspondence learning but require the desired final output as ground truth for supervision. Unsupervised methods have been proposed for graph convolutional models but they require ground truth correspondence between the source and target inputs. We present a novel self-supervised framework for 3D pose transfer which can be trained in unsupervised, semi-supervised, or fully supervised settings without any correspondence labels. We introduce two contrastive learning constraints in the latent space: a mesh-level loss for disentangling global patterns including pose and identity, and a point-level loss for discriminating local semantics. We demonstrate quantitatively and qualitatively that our method achieves state-of-the-art results in supervised 3D pose transfer, with comparable results in unsupervised and semi-supervised settings. Our method is also generalisable to unseen human and animal data with complex topologies.

Mathematical geometric reasoning is essential for scientific discovery and educational development, requiring precise logic and rigorous formal verification. While recent advances in Multimodal Large Language Models (MLLMs) have improved reasoning tasks, existing models typically struggle with formal geometric reasoning, particularly when dynamically constructing and verifying auxiliary geometric elements. To address these challenges, we introduce Geoint-R1, a multimodal reasoning framework designed to generate formally verifiable geometric solutions from textual descriptions and visual diagrams. Geoint-R1 uniquely integrates auxiliary elements construction, formal reasoning represented via Lean4, and interactive visualization. To systematically evaluate and advance formal geometric reasoning, we propose the Geoint benchmark, comprising 1,885 rigorously annotated geometry problems across diverse topics such as plane, spatial, and solid geometry. Each problem includes structured textual annotations, precise Lean4 code for auxiliary constructions, and detailed solution steps verified by experts. Extensive experiments demonstrate that Geoint-R1 significantly surpasses existing multimodal and math-specific reasoning models, particularly on challenging problems requiring explicit auxiliary element constructions.

Visual retrieval systems face significant challenges when updating models with improved representations due to misalignment between the old and new representations. The costly and resource-intensive backfilling process involves recalculating feature vectors for images in the gallery set whenever a new model is introduced. To address this, prior research has explored backward-compatible training methods that enable direct comparisons between new and old representations without backfilling. Despite these advancements, achieving a balance between backward compatibility and the performance of independently trained models remains an open problem. In this paper, we address it by expanding the representation space with additional dimensions and learning an orthogonal transformation to achieve compatibility with old models and, at the same time, integrate new information. This transformation preserves the original feature space's geometry, ensuring that our model aligns with previous versions while also learning new data. Our Orthogonal Compatible Aligned (OCA) approach eliminates the need for re-indexing during model updates and ensures that features can be compared directly across different model updates without additional mapping functions. Experimental results on CIFAR-100 and ImageNet-1k demonstrate that our method not only maintains compatibility with previous models but also achieves state-of-the-art accuracy, outperforming several existing methods.

In this work, we introduce CAD-Coder, a novel framework that reformulates text-to-CAD as the generation of CadQuery scripts - a Python-based, parametric CAD language. This representation enables direct geometric validation, a richer modeling vocabulary, and seamless integration with existing LLMs. To further enhance code validity and geometric fidelity, we propose a two-stage learning pipeline: (1) supervised fine-tuning on paired text-CadQuery data, and (2) reinforcement learning with Group Reward Policy Optimization (GRPO), guided by a CAD-specific reward comprising both a geometric reward (Chamfer Distance) and a format reward. We also introduce a chain-of-thought (CoT) planning process to improve model reasoning, and construct a large-scale, high-quality dataset of 110K text-CadQuery-3D model triplets and 1.5K CoT samples via an automated pipeline. Extensive experiments demonstrate that CAD-Coder enables LLMs to generate diverse, valid, and complex CAD models directly from natural language, advancing the state of the art of text-to-CAD generation and geometric reasoning.

This chapter presents a framework for detecting fake regions by using various methods including watermarking technique and blind approaches. In particular, we describe current categories on blind approaches which can be divided into five: pixel-based techniques, format-based techniques, camera-based techniques, physically-based techniques and geometric-based techniques. Then we take a second look on the geometric-based techniques and further categorize them in detail. In the following section, the state-of-the-art methods involved in the geometric technique are elaborated.

To address the data scarcity associated with 3D assets, 2D-lifting techniques such as Score Distillation Sampling (SDS) have become a widely adopted practice in text-to-3D generation pipelines. However, the diffusion models used in these techniques are prone to viewpoint bias and thus lead to geometric inconsistencies such as the Janus problem. To counter this, we introduce MT3D, a text-to-3D generative model that leverages a high-fidelity 3D object to overcome viewpoint bias and explicitly infuse geometric understanding into the generation pipeline. Firstly, we employ depth maps derived from a high-quality 3D model as control signals to guarantee that the generated 2D images preserve the fundamental shape and structure, thereby reducing the inherent viewpoint bias. Next, we utilize deep geometric moments to ensure geometric consistency in the 3D representation explicitly. By incorporating geometric details from a 3D asset, MT3D enables the creation of diverse and geometrically consistent objects, thereby improving the quality and usability of our 3D representations.

Matching cost aggregation plays a fundamental role in learning-based multi-view stereo networks. However, directly aggregating adjacent costs can lead to suboptimal results due to local geometric inconsistency. Related methods either seek selective aggregation or improve aggregated depth in the 2D space, both are unable to handle geometric inconsistency in the cost volume effectively. In this paper, we propose GoMVS to aggregate geometrically consistent costs, yielding better utilization of adjacent geometries. More specifically, we correspond and propagate adjacent costs to the reference pixel by leveraging the local geometric smoothness in conjunction with surface normals. We achieve this by the geometric consistent propagation (GCP) module. It computes the correspondence from the adjacent depth hypothesis space to the reference depth space using surface normals, then uses the correspondence to propagate adjacent costs to the reference geometry, followed by a convolution for aggregation. Our method achieves new state-of-the-art performance on DTU, Tanks & Temple, and ETH3D datasets. Notably, our method ranks 1st on the Tanks & Temple Advanced benchmark.

Estimating the 6-DoF pose of a rigid object from a single RGB image is a crucial yet challenging task. Recent studies have shown the great potential of dense correspondence-based solutions, yet improvements are still needed to reach practical deployment. In this paper, we propose a novel pose estimation algorithm named CheckerPose, which improves on three main aspects. Firstly, CheckerPose densely samples 3D keypoints from the surface of the 3D object and finds their 2D correspondences progressively in the 2D image. Compared to previous solutions that conduct dense sampling in the image space, our strategy enables the correspondence searching in a 2D grid (i.e., pixel coordinate). Secondly, for our 3D-to-2D correspondence, we design a compact binary code representation for 2D image locations. This representation not only allows for progressive correspondence refinement but also converts the correspondence regression to a more efficient classification problem. Thirdly, we adopt a graph neural network to explicitly model the interactions among the sampled 3D keypoints, further boosting the reliability and accuracy of the correspondences. Together, these novel components make CheckerPose a strong pose estimation algorithm. When evaluated on the popular Linemod, Linemod-O, and YCB-V object pose estimation benchmarks, CheckerPose clearly boosts the accuracy of correspondence-based methods and achieves state-of-the-art performances. Code is available at https://github.com/RuyiLian/CheckerPose.

Invariance and equivariance to geometrical transformations have proven to be very useful inductive biases when training (convolutional) neural network models, especially in the low-data regime. Much work has focused on the case where the symmetry group employed is compact or abelian, or both. Recent work has explored enlarging the class of transformations used to the case of Lie groups, principally through the use of their Lie algebra, as well as the group exponential and logarithm maps. The applicability of such methods to larger transformation groups is limited by the fact that depending on the group of interest G, the exponential map may not be surjective. Further limitations are encountered when G is neither compact nor abelian. Using the structure and geometry of Lie groups and their homogeneous spaces, we present a framework by which it is possible to work with such groups primarily focusing on the Lie groups G = GL^{+}(n, R) and G = SL(n, R), as well as their representation as affine transformations R^{n} rtimes G. Invariant integration as well as a global parametrization is realized by decomposing the `larger` groups into subgroups and submanifolds which can be handled individually. Under this framework, we show how convolution kernels can be parametrized to build models equivariant with respect to affine transformations. We evaluate the robustness and out-of-distribution generalisation capability of our model on the standard affine-invariant benchmark classification task, where we outperform all previous equivariant models as well as all Capsule Network proposals.

Humans naturally perceive the geometric structure and semantic content of a 3D world as intertwined dimensions, enabling coherent and accurate understanding of complex scenes. However, most prior approaches prioritize training large geometry models for low-level 3D reconstruction and treat high-level spatial understanding in isolation, overlooking the crucial interplay between these two fundamental aspects of 3D-scene analysis, thereby limiting generalization and leading to poor performance in downstream 3D understanding tasks. Recent attempts have mitigated this issue by simply aligning 3D models with specific language models, thus restricting perception to the aligned model's capacity and limiting adaptability to downstream tasks. In this paper, we propose InstanceGrounded Geometry Transformer (IGGT), an end-to-end large unified transformer to unify the knowledge for both spatial reconstruction and instance-level contextual understanding. Specifically, we design a 3D-Consistent Contrastive Learning strategy that guides IGGT to encode a unified representation with geometric structures and instance-grounded clustering through only 2D visual inputs. This representation supports consistent lifting of 2D visual inputs into a coherent 3D scene with explicitly distinct object instances. To facilitate this task, we further construct InsScene-15K, a large-scale dataset with high-quality RGB images, poses, depth maps, and 3D-consistent instance-level mask annotations with a novel data curation pipeline.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

We present a novel generative 3D modeling system, coined CraftsMan, which can generate high-fidelity 3D geometries with highly varied shapes, regular mesh topologies, and detailed surfaces, and, notably, allows for refining the geometry in an interactive manner. Despite the significant advancements in 3D generation, existing methods still struggle with lengthy optimization processes, irregular mesh topologies, noisy surfaces, and difficulties in accommodating user edits, consequently impeding their widespread adoption and implementation in 3D modeling software. Our work is inspired by the craftsman, who usually roughs out the holistic figure of the work first and elaborates the surface details subsequently. Specifically, we employ a 3D native diffusion model, which operates on latent space learned from latent set-based 3D representations, to generate coarse geometries with regular mesh topology in seconds. In particular, this process takes as input a text prompt or a reference image and leverages a powerful multi-view (MV) diffusion model to generate multiple views of the coarse geometry, which are fed into our MV-conditioned 3D diffusion model for generating the 3D geometry, significantly improving robustness and generalizability. Following that, a normal-based geometry refiner is used to significantly enhance the surface details. This refinement can be performed automatically, or interactively with user-supplied edits. Extensive experiments demonstrate that our method achieves high efficacy in producing superior-quality 3D assets compared to existing methods. HomePage: https://craftsman3d.github.io/, Code: https://github.com/wyysf-98/CraftsMan

We introduce pi^3, a feed-forward neural network that offers a novel approach to visual geometry reconstruction, breaking the reliance on a conventional fixed reference view. Previous methods often anchor their reconstructions to a designated viewpoint, an inductive bias that can lead to instability and failures if the reference is suboptimal. In contrast, pi^3 employs a fully permutation-equivariant architecture to predict affine-invariant camera poses and scale-invariant local point maps without any reference frames. This design makes our model inherently robust to input ordering and highly scalable. These advantages enable our simple and bias-free approach to achieve state-of-the-art performance on a wide range of tasks, including camera pose estimation, monocular/video depth estimation, and dense point map reconstruction. Code and models are publicly available.

In this paper, we present Gaussian Splatting based text-to-3D generation (GSGEN), a novel approach for generating high-quality 3D objects. Previous methods suffer from inaccurate geometry and limited fidelity due to the absence of 3D prior and proper representation. We leverage 3D Gaussian Splatting, a recent state-of-the-art representation, to address existing shortcomings by exploiting the explicit nature that enables the incorporation of 3D prior. Specifically, our method adopts a progressive optimization strategy, which includes a geometry optimization stage and an appearance refinement stage. In geometry optimization, a coarse representation is established under a 3D geometry prior along with the ordinary 2D SDS loss, ensuring a sensible and 3D-consistent rough shape. Subsequently, the obtained Gaussians undergo an iterative refinement to enrich details. In this stage, we increase the number of Gaussians by compactness-based densification to enhance continuity and improve fidelity. With these designs, our approach can generate 3D content with delicate details and more accurate geometry. Extensive evaluations demonstrate the effectiveness of our method, especially for capturing high-frequency components. Video results are provided at https://gsgen3d.github.io. Our code is available at https://github.com/gsgen3d/gsgen

Text-to-3D generation from a single-view image is a popular but challenging task in 3D vision. Although numerous methods have been proposed, existing works still suffer from the inconsistency issues, including 1) semantic inconsistency, 2) geometric inconsistency, and 3) saturation inconsistency, resulting in distorted, overfitted, and over-saturated generations. In light of the above issues, we present Consist3D, a three-stage framework Chasing for semantic-, geometric-, and saturation-Consistent Text-to-3D generation from a single image, in which the first two stages aim to learn parameterized consistency tokens, and the last stage is for optimization. Specifically, the semantic encoding stage learns a token independent of views and estimations, promoting semantic consistency and robustness. Meanwhile, the geometric encoding stage learns another token with comprehensive geometry and reconstruction constraints under novel-view estimations, reducing overfitting and encouraging geometric consistency. Finally, the optimization stage benefits from the semantic and geometric tokens, allowing a low classifier-free guidance scale and therefore preventing oversaturation. Experimental results demonstrate that Consist3D produces more consistent, faithful, and photo-realistic 3D assets compared to previous state-of-the-art methods. Furthermore, Consist3D also allows background and object editing through text prompts.

In this paper, we present CAD2Program, a new method for reconstructing 3D parametric models from 2D CAD drawings. Our proposed method is inspired by recent successes in vision-language models (VLMs), and departs from traditional methods which rely on task-specific data representations and/or algorithms. Specifically, on the input side, we simply treat the 2D CAD drawing as a raster image, regardless of its original format, and encode the image with a standard ViT model. We show that such an encoding scheme achieves competitive performance against existing methods that operate on vector-graphics inputs, while imposing substantially fewer restrictions on the 2D drawings. On the output side, our method auto-regressively predicts a general-purpose language describing 3D parametric models in text form. Compared to other sequence modeling methods for CAD which use domain-specific sequence representations with fixed-size slots, our text-based representation is more flexible, and can be easily extended to arbitrary geometric entities and semantic or functional properties. Experimental results on a large-scale dataset of cabinet models demonstrate the effectiveness of our method.

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks, their suitability for vision tasks, which typically exhibit different structural properties in their data, is questionable. We argue that existing positional encoding schemes are suboptimal for 3D vision tasks, as they do not respect their underlying 3D geometric structure. Based on this hypothesis, we propose a geometry-aware attention mechanism that encodes the geometric structure of tokens as relative transformation determined by the geometric relationship between queries and key-value pairs. By evaluating on multiple novel view synthesis (NVS) datasets in the sparse wide-baseline multi-view setting, we show that our attention, called Geometric Transform Attention (GTA), improves learning efficiency and performance of state-of-the-art transformer-based NVS models without any additional learned parameters and only minor computational overhead.

We report on a new, simple, modular, and flexible approach for automated generation of illustrations for (readable) synthetic geometry proofs. The underlying proofs are generated using the Larus automated prover for coherent logic, and corresponding illustrations are generated in the GCLC language. Animated illustrations are also supported.

Design of neural networks that incorporate symmetry is crucial for geometric deep learning. Central to this effort is the development of invariant and equivariant operations. This works presents a systematic method for constructing valid invariant and equivariant operations. It can handle inputs and outputs in the form of Cartesian tensors with different rank, as well as spherical tensors with different types. In addition, our method features a graphical representation utilizing the symmetric tensor network, which simplifies both the proofs and constructions related to invariant and equivariant functions. We also apply this approach to design the equivariant interaction message for the geometry graph neural network, and equivariant machine learning model to learn the constitutive law of materials.

The lifting of 3D structure and camera from 2D landmarks is at the cornerstone of the entire discipline of computer vision. Traditional methods have been confined to specific rigid objects, such as those in Perspective-n-Point (PnP) problems, but deep learning has expanded our capability to reconstruct a wide range of object classes (e.g. C3PDO and PAUL) with resilience to noise, occlusions, and perspective distortions. All these techniques, however, have been limited by the fundamental need to establish correspondences across the 3D training data -- significantly limiting their utility to applications where one has an abundance of "in-correspondence" 3D data. Our approach harnesses the inherent permutation equivariance of transformers to manage varying number of points per 3D data instance, withstands occlusions, and generalizes to unseen categories. We demonstrate state of the art performance across 2D-3D lifting task benchmarks. Since our approach can be trained across such a broad class of structures we refer to it simply as a 3D Lifting Foundation Model (3D-LFM) -- the first of its kind.

With the rise of generative AI, synthesizing figures from text captions becomes a compelling application. However, achieving high geometric precision and editability requires representing figures as graphics programs in languages like TikZ, and aligned training data (i.e., graphics programs with captions) remains scarce. Meanwhile, large amounts of unaligned graphics programs and captioned raster images are more readily available. We reconcile these disparate data sources by presenting TikZero, which decouples graphics program generation from text understanding by using image representations as an intermediary bridge. It enables independent training on graphics programs and captioned images and allows for zero-shot text-guided graphics program synthesis during inference. We show that our method substantially outperforms baselines that can only operate with caption-aligned graphics programs. Furthermore, when leveraging caption-aligned graphics programs as a complementary training signal, TikZero matches or exceeds the performance of much larger models, including commercial systems like GPT-4o. Our code, datasets, and select models are publicly available.

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.

3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without considering spatial consistency. As a result, these approaches exhibit limited versatility in 3D data representation and shape generation, hindering their ability to generate highly diverse 3D shapes that comply with the specified constraints. In this paper, we introduce a novel spatial-aware 3D shape generation framework that leverages 2D plane representations for enhanced 3D shape modeling. To ensure spatial coherence and reduce memory usage, we incorporate a hybrid shape representation technique that directly learns a continuous signed distance field representation of the 3D shape using orthogonal 2D planes. Additionally, we meticulously enforce spatial correspondences across distinct planes using a transformer-based autoencoder structure, promoting the preservation of spatial relationships in the generated 3D shapes. This yields an algorithm that consistently outperforms state-of-the-art 3D shape generation methods on various tasks, including unconditional shape generation, multi-modal shape completion, single-view reconstruction, and text-to-shape synthesis.

We present a method for estimating neural scenes representations of objects given only a single image. The core of our method is the estimation of a geometric scaffold for the object and its use as a guide for the reconstruction of the underlying radiance field. Our formulation is based on a generative process that first maps a latent code to a voxelized shape, and then renders it to an image, with the object appearance being controlled by a second latent code. During inference, we optimize both the latent codes and the networks to fit a test image of a new object. The explicit disentanglement of shape and appearance allows our model to be fine-tuned given a single image. We can then render new views in a geometrically consistent manner and they represent faithfully the input object. Additionally, our method is able to generalize to images outside of the training domain (more realistic renderings and even real photographs). Finally, the inferred geometric scaffold is itself an accurate estimate of the object's 3D shape. We demonstrate in several experiments the effectiveness of our approach in both synthetic and real images.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL's discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https://github.com/chaitjo/geometric-gnn-dojo

Recent developments in Multimodal Large Language Models (MLLMs) have significantly improved Vision-Language (VL) reasoning in 2D domains. However, extending these capabilities to 3D scene understanding remains a major challenge. Existing 3D Multimodal Large Language Models (3D-MLLMs) often depend on 3D data inputs, which limits scalability and generalization. To address this limitation, we propose Vid-LLM, a video-based 3D-MLLM that directly processes video inputs without requiring external 3D data, making it practical for real-world deployment. In our method, the geometric prior are directly used to improve the performance of the sceen perception. To integrate the geometric cues into the MLLM compactly, we design a Cross-Task Adapter (CTA) module to align the 3D geometric priors with the vision-language representations. To ensure geometric consistency and integrity, we introduce a Metric Depth Model that recovers real-scale geometry from the reconstruction outputs. Finally, the model is fine-tuned with a two-stage distillation optimization strategy, realizing fast convergence and stabilizes training. Extensive experiments across diverse benchmarks verified the effectiveness of our method on 3D Question Answering, 3D Dense Captioning and 3D Visual Grounding tasks, demonstrating the superior multi-task capabilities.

SymPoint is an initial attempt that utilizes point set representation to solve the panoptic symbol spotting task on CAD drawing. Despite its considerable success, it overlooks graphical layer information and suffers from prohibitively slow training convergence. To tackle this issue, we introduce SymPoint-V2, a robust and efficient solution featuring novel, streamlined designs that overcome these limitations. In particular, we first propose a Layer Feature-Enhanced module (LFE) to encode the graphical layer information into the primitive feature, which significantly boosts the performance. We also design a Position-Guided Training (PGT) method to make it easier to learn, which accelerates the convergence of the model in the early stages and further promotes performance. Extensive experiments show that our model achieves better performance and faster convergence than its predecessor SymPoint on the public benchmark. Our code and trained models are available at https://github.com/nicehuster/SymPointV2.

3D AI-generated content (AIGC) has made it increasingly accessible for anyone to become a 3D content creator. While recent methods leverage Score Distillation Sampling to distill 3D objects from pretrained image diffusion models, they often suffer from inadequate 3D priors, leading to insufficient multi-view consistency. In this work, we introduce NOVA3D, an innovative single-image-to-3D generation framework. Our key insight lies in leveraging strong 3D priors from a pretrained video diffusion model and integrating geometric information during multi-view video fine-tuning. To facilitate information exchange between color and geometric domains, we propose the Geometry-Temporal Alignment (GTA) attention mechanism, thereby improving generalization and multi-view consistency. Moreover, we introduce the de-conflict geometry fusion algorithm, which improves texture fidelity by addressing multi-view inaccuracies and resolving discrepancies in pose alignment. Extensive experiments validate the superiority of NOVA3D over existing baselines.

Automatic 3D content creation has achieved rapid progress recently due to the availability of pre-trained, large language models and image diffusion models, forming the emerging topic of text-to-3D content creation. Existing text-to-3D methods commonly use implicit scene representations, which couple the geometry and appearance via volume rendering and are suboptimal in terms of recovering finer geometries and achieving photorealistic rendering; consequently, they are less effective for generating high-quality 3D assets. In this work, we propose a new method of Fantasia3D for high-quality text-to-3D content creation. Key to Fantasia3D is the disentangled modeling and learning of geometry and appearance. For geometry learning, we rely on a hybrid scene representation, and propose to encode surface normal extracted from the representation as the input of the image diffusion model. For appearance modeling, we introduce the spatially varying bidirectional reflectance distribution function (BRDF) into the text-to-3D task, and learn the surface material for photorealistic rendering of the generated surface. Our disentangled framework is more compatible with popular graphics engines, supporting relighting, editing, and physical simulation of the generated 3D assets. We conduct thorough experiments that show the advantages of our method over existing ones under different text-to-3D task settings. Project page and source codes: https://fantasia3d.github.io/.

The scarcity of annotations poses a significant challenge in medical image analysis. Large-scale pre-training has emerged as a promising label-efficient solution, owing to the utilization of large-scale data, large models, and advanced pre-training techniques. However, its development in medical images remains underexplored. The primary challenge lies in harnessing large-scale unlabeled data and learning high-level semantics without annotations. We observe that 3D medical images exhibit consistent geometric context, i.e., consistent geometric relations between different organs, which leads to a promising way for learning consistent representations. Motivated by this, we introduce a simple-yet-effective Volume Contrast (VoCo) framework to leverage geometric context priors for self-supervision. Given an input volume, we extract base crops from different regions to construct positive and negative pairs for contrastive learning. Then we predict the contextual position of a random crop by contrasting its similarity to the base crops. In this way, VoCo encodes the inherent geometric context into model representations, facilitating high-level semantic learning without annotations. Specifically, we (1) introduce the largest medical pre-training dataset PreCT-160K; (2) investigate scaling laws and propose guidelines for tailoring different model sizes to various medical tasks; (3) build a benchmark encompassing 48 medical tasks. Extensive experiments highlight the superiority of VoCo. Codes at https://github.com/Luffy03/Large-Scale-Medical.

Dense matching methods like DUSt3R regress pairwise pointmaps for 3D reconstruction. However, the reliance on pairwise prediction and the limited generalization capability inherently restrict the global geometric consistency. In this work, we introduce Test3R, a surprisingly simple test-time learning technique that significantly boosts geometric accuracy. Using image triplets (I_1,I_2,I_3), Test3R generates reconstructions from pairs (I_1,I_2) and (I_1,I_3). The core idea is to optimize the network at test time via a self-supervised objective: maximizing the geometric consistency between these two reconstructions relative to the common image I_1. This ensures the model produces cross-pair consistent outputs, regardless of the inputs. Extensive experiments demonstrate that our technique significantly outperforms previous state-of-the-art methods on the 3D reconstruction and multi-view depth estimation tasks. Moreover, it is universally applicable and nearly cost-free, making it easily applied to other models and implemented with minimal test-time training overhead and parameter footprint. Code is available at https://github.com/nopQAQ/Test3R.

We present WorldMirror, an all-in-one, feed-forward model for versatile 3D geometric prediction tasks. Unlike existing methods constrained to image-only inputs or customized for a specific task, our framework flexibly integrates diverse geometric priors, including camera poses, intrinsics, and depth maps, while simultaneously generating multiple 3D representations: dense point clouds, multi-view depth maps, camera parameters, surface normals, and 3D Gaussians. This elegant and unified architecture leverages available prior information to resolve structural ambiguities and delivers geometrically consistent 3D outputs in a single forward pass. WorldMirror achieves state-of-the-art performance across diverse benchmarks from camera, point map, depth, and surface normal estimation to novel view synthesis, while maintaining the efficiency of feed-forward inference. Code and models will be publicly available soon.

Benefiting from contrastively trained visual encoders on large-scale natural scene images, Large Multimodal Models (LMMs) have achieved remarkable performance across various visual perception tasks. However, the inherent limitations of contrastive learning upon summarized descriptions fundamentally restrict the capabilities of models in meticulous reasoning, particularly in crucial scenarios of geometric problem-solving. To enhance geometric understanding, we propose a novel hard negative contrastive learning framework for the vision encoder, which combines image-based contrastive learning using generation-based hard negatives created by perturbing diagram generation code, and text-based contrastive learning using rule-based negatives derived from modified geometric descriptions and retrieval-based negatives selected based on caption similarity. We train CLIP using our strong negative learning method, namely MMCLIP (Multimodal Math CLIP), and subsequently train an LMM for geometric problem-solving. Experiments show that our trained model, MMGeoLM, significantly outperforms other open-source models on three geometric reasoning benchmarks. Even with a size of 7B, it can rival powerful closed-source models like GPT-4o. We further study the impact of different negative sample construction methods and the number of negative samples on the geometric reasoning performance of LMM, yielding fruitful conclusions. The code and dataset are available at https://github.com/THU-KEG/MMGeoLM.

Recent works on 3D reconstruction from posed images have demonstrated that direct inference of scene-level 3D geometry without test-time optimization is feasible using deep neural networks, showing remarkable promise and high efficiency. However, the reconstructed geometry, typically represented as a 3D truncated signed distance function (TSDF), is often coarse without fine geometric details. To address this problem, we propose three effective solutions for improving the fidelity of inference-based 3D reconstructions. We first present a resolution-agnostic TSDF supervision strategy to provide the network with a more accurate learning signal during training, avoiding the pitfalls of TSDF interpolation seen in previous work. We then introduce a depth guidance strategy using multi-view depth estimates to enhance the scene representation and recover more accurate surfaces. Finally, we develop a novel architecture for the final layers of the network, conditioning the output TSDF prediction on high-resolution image features in addition to coarse voxel features, enabling sharper reconstruction of fine details. Our method, FineRecon, produces smooth and highly accurate reconstructions, showing significant improvements across multiple depth and 3D reconstruction metrics.

We introduce Clifford Group Equivariant Simplicial Message Passing Networks, a method for steerable E(n)-equivariant message passing on simplicial complexes. Our method integrates the expressivity of Clifford group-equivariant layers with simplicial message passing, which is topologically more intricate than regular graph message passing. Clifford algebras include higher-order objects such as bivectors and trivectors, which express geometric features (e.g., areas, volumes) derived from vectors. Using this knowledge, we represent simplex features through geometric products of their vertices. To achieve efficient simplicial message passing, we share the parameters of the message network across different dimensions. Additionally, we restrict the final message to an aggregation of the incoming messages from different dimensions, leading to what we term shared simplicial message passing. Experimental results show that our method is able to outperform both equivariant and simplicial graph neural networks on a variety of geometric tasks.

Symmetry is one of the most fundamental geometric cues in computer vision, and detecting it has been an ongoing challenge. With the recent advances in vision-language models,~i.e., CLIP, we investigate whether a pre-trained CLIP model can aid symmetry detection by leveraging the additional symmetry cues found in the natural image descriptions. We propose CLIPSym, which leverages CLIP's image and language encoders and a rotation-equivariant decoder based on a hybrid of Transformer and G-Convolution to detect rotation and reflection symmetries. To fully utilize CLIP's language encoder, we have developed a novel prompting technique called Semantic-Aware Prompt Grouping (SAPG), which aggregates a diverse set of frequent object-based prompts to better integrate the semantic cues for symmetry detection. Empirically, we show that CLIPSym outperforms the current state-of-the-art on three standard symmetry detection datasets (DENDI, SDRW, and LDRS). Finally, we conduct detailed ablations verifying the benefits of CLIP's pre-training, the proposed equivariant decoder, and the SAPG technique. The code is available at https://github.com/timyoung2333/CLIPSym.

High-quality 3D assets are essential for various applications in computer graphics and 3D vision but remain scarce due to significant acquisition costs. To address this shortage, we introduce Elevate3D, a novel framework that transforms readily accessible low-quality 3D assets into higher quality. At the core of Elevate3D is HFS-SDEdit, a specialized texture enhancement method that significantly improves texture quality while preserving the appearance and geometry while fixing its degradations. Furthermore, Elevate3D operates in a view-by-view manner, alternating between texture and geometry refinement. Unlike previous methods that have largely overlooked geometry refinement, our framework leverages geometric cues from images refined with HFS-SDEdit by employing state-of-the-art monocular geometry predictors. This approach ensures detailed and accurate geometry that aligns seamlessly with the enhanced texture. Elevate3D outperforms recent competitors by achieving state-of-the-art quality in 3D model refinement, effectively addressing the scarcity of high-quality open-source 3D assets.

Computer-aided design (CAD) is crucial in prototyping 3D objects through geometric instructions (i.e., CAD programs). In practical design workflows, designers often engage in time-consuming reviews and refinements of these prototypes by comparing them with reference images. To bridge this gap, we introduce the CAD review task to automatically detect and correct potential errors, ensuring consistency between the constructed 3D objects and reference images. However, recent advanced multimodal large language models (MLLMs) struggle to recognize multiple geometric components and perform spatial geometric operations within the CAD program, leading to inaccurate reviews. In this paper, we propose the CAD program repairer (ReCAD) framework to effectively detect program errors and provide helpful feedback on error correction. Additionally, we create a dataset, CADReview, consisting of over 20K program-image pairs, with diverse errors for the CAD review task. Extensive experiments demonstrate that our ReCAD significantly outperforms existing MLLMs, which shows great potential in design applications.

Existing fully-supervised point cloud segmentation methods suffer in the dynamic testing environment with emerging new classes. Few-shot point cloud segmentation algorithms address this problem by learning to adapt to new classes at the sacrifice of segmentation accuracy for the base classes, which severely impedes its practicality. This largely motivates us to present the first attempt at a more practical paradigm of generalized few-shot point cloud segmentation, which requires the model to generalize to new categories with only a few support point clouds and simultaneously retain the capability to segment base classes. We propose the geometric words to represent geometric components shared between the base and novel classes, and incorporate them into a novel geometric-aware semantic representation to facilitate better generalization to the new classes without forgetting the old ones. Moreover, we introduce geometric prototypes to guide the segmentation with geometric prior knowledge. Extensive experiments on S3DIS and ScanNet consistently illustrate the superior performance of our method over baseline methods. Our code is available at: https://github.com/Pixie8888/GFS-3DSeg_GWs.

We propose 3D Congealing, a novel problem of 3D-aware alignment for 2D images capturing semantically similar objects. Given a collection of unlabeled Internet images, our goal is to associate the shared semantic parts from the inputs and aggregate the knowledge from 2D images to a shared 3D canonical space. We introduce a general framework that tackles the task without assuming shape templates, poses, or any camera parameters. At its core is a canonical 3D representation that encapsulates geometric and semantic information. The framework optimizes for the canonical representation together with the pose for each input image, and a per-image coordinate map that warps 2D pixel coordinates to the 3D canonical frame to account for the shape matching. The optimization procedure fuses prior knowledge from a pre-trained image generative model and semantic information from input images. The former provides strong knowledge guidance for this under-constraint task, while the latter provides the necessary information to mitigate the training data bias from the pre-trained model. Our framework can be used for various tasks such as correspondence matching, pose estimation, and image editing, achieving strong results on real-world image datasets under challenging illumination conditions and on in-the-wild online image collections.

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the Pin(p,q,r) group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable geometric templates that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods.

Generative models for 3D object synthesis have seen significant advancements with the incorporation of prior knowledge distilled from 2D diffusion models. Nevertheless, challenges persist in the form of multi-view geometric inconsistencies and slow generation speeds within the existing 3D synthesis frameworks. This can be attributed to two factors: firstly, the deficiency of abundant geometric a priori knowledge in optimization, and secondly, the entanglement issue between geometry and texture in conventional 3D generation methods.In response, we introduce MetaDreammer, a two-stage optimization approach that leverages rich 2D and 3D prior knowledge. In the first stage, our emphasis is on optimizing the geometric representation to ensure multi-view consistency and accuracy of 3D objects. In the second stage, we concentrate on fine-tuning the geometry and optimizing the texture, thereby achieving a more refined 3D object. Through leveraging 2D and 3D prior knowledge in two stages, respectively, we effectively mitigate the interdependence between geometry and texture. MetaDreamer establishes clear optimization objectives for each stage, resulting in significant time savings in the 3D generation process. Ultimately, MetaDreamer can generate high-quality 3D objects based on textual prompts within 20 minutes, and to the best of our knowledge, it is the most efficient text-to-3D generation method. Furthermore, we introduce image control into the process, enhancing the controllability of 3D generation. Extensive empirical evidence confirms that our method is not only highly efficient but also achieves a quality level that is at the forefront of current state-of-the-art 3D generation techniques.

Multimodal foundation models, such as GPT-4o, have recently made remarkable progress, but it is not clear where exactly these models stand in terms of understanding vision. In this paper, we benchmark the performance of popular multimodal foundation models (GPT-4o, o4-mini, Gemini 1.5 Pro and Gemini 2.0 Flash, Claude 3.5 Sonnet, Qwen2-VL, Llama 3.2) on standard computer vision tasks (semantic segmentation, object detection, image classification, depth and surface normal prediction) using established datasets (e.g., COCO, ImageNet and its variants, etc). The main challenges to performing this are: 1) most models are trained to output text and cannot natively express versatile domains, such as segments or 3D geometry, and 2) many leading models are proprietary and accessible only at an API level, i.e., there is no weight access to adapt them. We address these challenges by translating standard vision tasks into equivalent text-promptable and API-compatible tasks via prompt chaining to create a standardized benchmarking framework. We observe that 1) the models are not close to the state-of-the-art specialist models at any task. However, 2) they are respectable generalists; this is remarkable as they are presumably trained on primarily image-text-based tasks. 3) They perform semantic tasks notably better than geometric ones. 4) While the prompt-chaining techniques affect performance, better models exhibit less sensitivity to prompt variations. 5) GPT-4o performs the best among non-reasoning models, securing the top position in 4 out of 6 tasks, 6) reasoning models, e.g. o3, show improvements in geometric tasks, and 7) a preliminary analysis of models with native image generation, like the latest GPT-4o, shows they exhibit quirks like hallucinations and spatial misalignments.

Deep neural networks are prone to adversarial examples that maliciously alter the network's outcome. Due to the increasing popularity of 3D sensors in safety-critical systems and the vast deployment of deep learning models for 3D point sets, there is a growing interest in adversarial attacks and defenses for such models. So far, the research has focused on the semantic level, namely, deep point cloud classifiers. However, point clouds are also widely used in a geometric-related form that includes encoding and reconstructing the geometry. In this work, we are the first to consider the problem of adversarial examples at a geometric level. In this setting, the question is how to craft a small change to a clean source point cloud that leads, after passing through an autoencoder model, to the reconstruction of a different target shape. Our attack is in sharp contrast to existing semantic attacks on 3D point clouds. While such works aim to modify the predicted label by a classifier, we alter the entire reconstructed geometry. Additionally, we demonstrate the robustness of our attack in the case of defense, where we show that remnant characteristics of the target shape are still present at the output after applying the defense to the adversarial input. Our code is publicly available at https://github.com/itailang/geometric_adv.

Proving geometric theorems constitutes a hallmark of visual reasoning combining both intuitive and logical skills. Therefore, automated theorem proving of Olympiad-level geometry problems is considered a notable milestone in human-level automated reasoning. The introduction of AlphaGeometry, a neuro-symbolic model trained with 100 million synthetic samples, marked a major breakthrough. It solved 25 of 30 International Mathematical Olympiad (IMO) problems whereas the reported baseline based on Wu's method solved only ten. In this note, we revisit the IMO-AG-30 Challenge introduced with AlphaGeometry, and find that Wu's method is surprisingly strong. Wu's method alone can solve 15 problems, and some of them are not solved by any of the other methods. This leads to two key findings: (i) Combining Wu's method with the classic synthetic methods of deductive databases and angle, ratio, and distance chasing solves 21 out of 30 methods by just using a CPU-only laptop with a time limit of 5 minutes per problem. Essentially, this classic method solves just 4 problems less than AlphaGeometry and establishes the first fully symbolic baseline strong enough to rival the performance of an IMO silver medalist. (ii) Wu's method even solves 2 of the 5 problems that AlphaGeometry failed to solve. Thus, by combining AlphaGeometry with Wu's method we set a new state-of-the-art for automated theorem proving on IMO-AG-30, solving 27 out of 30 problems, the first AI method which outperforms an IMO gold medalist.

This paper aims to develop an accurate 3D geometry representation of satellite images using satellite-ground image pairs. Our focus is on the challenging problem of 3D-aware ground-views synthesis from a satellite image. We draw inspiration from the density field representation used in volumetric neural rendering and propose a new approach, called Sat2Density. Our method utilizes the properties of ground-view panoramas for the sky and non-sky regions to learn faithful density fields of 3D scenes in a geometric perspective. Unlike other methods that require extra depth information during training, our Sat2Density can automatically learn accurate and faithful 3D geometry via density representation without depth supervision. This advancement significantly improves the ground-view panorama synthesis task. Additionally, our study provides a new geometric perspective to understand the relationship between satellite and ground-view images in 3D space.

High-fidelity 3D asset generation is crucial for various industries. While recent 3D pretrained models show strong capability in producing realistic content, most are built upon diffusion models and follow a two-stage pipeline that first generates geometry and then synthesizes appearance. Such a decoupled design tends to produce geometry-texture misalignment and non-negligible cost. In this paper, we propose UniLat3D, a unified framework that encodes geometry and appearance in a single latent space, enabling direct single-stage generation. Our key contribution is a geometry-appearance Unified VAE, which compresses high-resolution sparse features into a compact latent representation -- UniLat. UniLat integrates structural and visual information into a dense low-resolution latent, which can be efficiently decoded into diverse 3D formats, e.g., 3D Gaussians and meshes. Based on this unified representation, we train a single flow-matching model to map Gaussian noise directly into UniLat, eliminating redundant stages. Trained solely on public datasets, UniLat3D produces high-quality 3D assets in seconds from a single image, achieving superior appearance fidelity and geometric quality. More demos \& code are available at https://unilat3d.github.io/

We propose transferability from Large Geometric Vicinity (LGV), a new technique to increase the transferability of black-box adversarial attacks. LGV starts from a pretrained surrogate model and collects multiple weight sets from a few additional training epochs with a constant and high learning rate. LGV exploits two geometric properties that we relate to transferability. First, models that belong to a wider weight optimum are better surrogates. Second, we identify a subspace able to generate an effective surrogate ensemble among this wider optimum. Through extensive experiments, we show that LGV alone outperforms all (combinations of) four established test-time transformations by 1.8 to 59.9 percentage points. Our findings shed new light on the importance of the geometry of the weight space to explain the transferability of adversarial examples.

In this work, we recover the underlying 3D structure of non-geometrically consistent scenes. We focus our analysis on hand-drawn images from cartoons and anime. Many cartoons are created by artists without a 3D rendering engine, which means that any new image of a scene is hand-drawn. The hand-drawn images are usually faithful representations of the world, but only in a qualitative sense, since it is difficult for humans to draw multiple perspectives of an object or scene 3D consistently. Nevertheless, people can easily perceive 3D scenes from inconsistent inputs! In this work, we correct for 2D drawing inconsistencies to recover a plausible 3D structure such that the newly warped drawings are consistent with each other. Our pipeline consists of a user-friendly annotation tool, camera pose estimation, and image deformation to recover a dense structure. Our method warps images to obey a perspective camera model, enabling our aligned results to be plugged into novel-view synthesis reconstruction methods to experience cartoons from viewpoints never drawn before. Our project page is https://toon3d.studio/.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

Recent interest in point cloud analysis has led rapid progress in designing deep learning methods for 3D models. However, state-of-the-art models are not robust to rotations, which remains an unknown prior to real applications and harms the model performance. In this work, we introduce a novel Patch-wise Rotation-invariant network (PaRot), which achieves rotation invariance via feature disentanglement and produces consistent predictions for samples with arbitrary rotations. Specifically, we design a siamese training module which disentangles rotation invariance and equivariance from patches defined over different scales, e.g., the local geometry and global shape, via a pair of rotations. However, our disentangled invariant feature loses the intrinsic pose information of each patch. To solve this problem, we propose a rotation-invariant geometric relation to restore the relative pose with equivariant information for patches defined over different scales. Utilising the pose information, we propose a hierarchical module which implements intra-scale and inter-scale feature aggregation for 3D shape learning. Moreover, we introduce a pose-aware feature propagation process with the rotation-invariant relative pose information embedded. Experiments show that our disentanglement module extracts high-quality rotation-robust features and the proposed lightweight model achieves competitive results in rotated 3D object classification and part segmentation tasks. Our project page is released at: https://patchrot.github.io/.

Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at https://github.com/ChirikjianLab/Marching-Primitives.git.

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all key problems in the 3D reconstruction of static scenes can be reduced to predicting such point maps. In this paper, we develop an analogous concept for a very different problem: the reconstruction of the 3D shape and pose of deformable objects. To this end, we introduce Dual Point Maps (DualPM), where a pair of point maps is extracted from the same image-one associating pixels to their 3D locations on the object and the other to a canonical version of the object in its rest pose. We also extend point maps to amodal reconstruction to recover the complete shape of the object, even through self-occlusions. We show that 3D reconstruction and 3D pose estimation can be reduced to the prediction of DualPMs. Empirically, we demonstrate that this representation is a suitable target for deep networks to predict. Specifically, we focus on modeling quadrupeds, showing that DualPMs can be trained purely on synthetic 3D data, consisting of one or two models per category, while generalizing effectively to real images. With this approach, we achieve significant improvements over previous methods for the 3D analysis and reconstruction of such objects.

Segment matching is an important intermediate task in computer vision that establishes correspondences between semantically or geometrically coherent regions across images. Unlike keypoint matching, which focuses on localized features, segment matching captures structured regions, offering greater robustness to occlusions, lighting variations, and viewpoint changes. In this paper, we leverage the spatial understanding of 3D foundation models to tackle wide-baseline segment matching, a challenging setting involving extreme viewpoint shifts. We propose an architecture that uses the inductive bias of these 3D foundation models to match segments across image pairs with up to 180 degree view-point change rotation. Extensive experiments show that our approach outperforms state-of-the-art methods, including the SAM2 video propagator and local feature matching methods, by up to 30% on the AUPRC metric, on ScanNet++ and Replica datasets. We further demonstrate benefits of the proposed model on relevant downstream tasks, including 3D instance mapping and object-relative navigation. Project Page: https://segmast3r.github.io/

Recent years have seen a surprising connection between the physics of scattering amplitudes and a class of mathematical objects--the positive Grassmannian, positive loop Grassmannians, tree and loop Amplituhedra--which have been loosely referred to as "positive geometries". The connection between the geometry and physics is provided by a unique differential form canonically determined by the property of having logarithmic singularities (only) on all the boundaries of the space, with residues on each boundary given by the canonical form on that boundary. In this paper we initiate an exploration of "positive geometries" and "canonical forms" as objects of study in their own right in a more general mathematical setting. We give a precise definition of positive geometries and canonical forms, introduce general methods for finding forms for more complicated positive geometries from simpler ones, and present numerous examples of positive geometries in projective spaces, Grassmannians, and toric, cluster and flag varieties. We also illustrate a number of strategies for computing canonical forms which yield interesting representations for the forms associated with wide classes of positive geometries, ranging from the simplest Amplituhedra to new expressions for the volume of arbitrary convex polytopes.

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.

Geometry problem solving is a key area of mathematical reasoning, which is widely involved in many important fields such as education, mathematical ability assessment of artificial intelligence, and multimodal ability assessment. In recent years, the rapid development of deep learning technology, especially the rise of multimodal large language models, has triggered a widespread research boom. This paper provides a survey of the applications of deep learning in geometry problem solving, including (i) a comprehensive summary of the relevant tasks in geometry problem solving; (ii) a thorough review of related deep learning methods; (iii) a detailed analysis of evaluation metrics and methods; and (iv) a critical discussion of the current challenges and future directions that can be explored. Our goal is to provide a comprehensive and practical reference of deep learning for geometry problem solving to promote further developments in this field. We create a continuously updated list of papers on GitHub: https://github.com/majianz/dl4gps.

This paper introduces a public dataset of 1.4 million procedurally-generated bicycle designs represented parametrically, as JSON files, and as rasterized images. The dataset is created through the use of a rendering engine which harnesses the BikeCAD software to generate vector graphics from parametric designs. This rendering engine is discussed in the paper and also released publicly alongside the dataset. Though this dataset has numerous applications, a principal motivation is the need to train cross-modal predictive models between parametric and image-based design representations. For example, we demonstrate that a predictive model can be trained to accurately estimate Contrastive Language-Image Pretraining (CLIP) embeddings from a parametric representation directly. This allows similarity relations to be established between parametric bicycle designs and text strings or reference images. Trained predictive models are also made public. The dataset joins the BIKED dataset family which includes thousands of mixed-representation human-designed bicycle models and several datasets quantifying design performance. The code and dataset can be found at: https://github.com/Lyleregenwetter/BIKED_multimodal/tree/main

Graph coarsening is a technique for solving large-scale graph problems by working on a smaller version of the original graph, and possibly interpolating the results back to the original graph. It has a long history in scientific computing and has recently gained popularity in machine learning, particularly in methods that preserve the graph spectrum. This work studies graph coarsening from a different perspective, developing a theory for preserving graph distances and proposing a method to achieve this. The geometric approach is useful when working with a collection of graphs, such as in graph classification and regression. In this study, we consider a graph as an element on a metric space equipped with the Gromov--Wasserstein (GW) distance, and bound the difference between the distance of two graphs and their coarsened versions. Minimizing this difference can be done using the popular weighted kernel K-means method, which improves existing spectrum-preserving methods with the proper choice of the kernel. The study includes a set of experiments to support the theory and method, including approximating the GW distance, preserving the graph spectrum, classifying graphs using spectral information, and performing regression using graph convolutional networks. Code is available at https://github.com/ychen-stat-ml/GW-Graph-Coarsening .

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the datadriven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging, requiring a good initialization. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces, which we use to regularize the implicit generator. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques. The synthetic shapes of GenCorres also achieve salient performance gains against state-of-the-art deformable shape generators.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Multi-camera 3D object detection for autonomous driving is a challenging problem that has garnered notable attention from both academia and industry. An obstacle encountered in vision-based techniques involves the precise extraction of geometry-conscious features from RGB images. Recent approaches have utilized geometric-aware image backbones pretrained on depth-relevant tasks to acquire spatial information. However, these approaches overlook the critical aspect of view transformation, resulting in inadequate performance due to the misalignment of spatial knowledge between the image backbone and view transformation. To address this issue, we propose a novel geometric-aware pretraining framework called GAPretrain. Our approach incorporates spatial and structural cues to camera networks by employing the geometric-rich modality as guidance during the pretraining phase. The transference of modal-specific attributes across different modalities is non-trivial, but we bridge this gap by using a unified bird's-eye-view (BEV) representation and structural hints derived from LiDAR point clouds to facilitate the pretraining process. GAPretrain serves as a plug-and-play solution that can be flexibly applied to multiple state-of-the-art detectors. Our experiments demonstrate the effectiveness and generalization ability of the proposed method. We achieve 46.2 mAP and 55.5 NDS on the nuScenes val set using the BEVFormer method, with a gain of 2.7 and 2.1 points, respectively. We also conduct experiments on various image backbones and view transformations to validate the efficacy of our approach. Code will be released at https://github.com/OpenDriveLab/BEVPerception-Survey-Recipe.

Vision foundation models, particularly the ViT family, have revolutionized image understanding by providing rich semantic features. However, despite their success in 2D comprehension, their abilities on grasping 3D spatial relationships are still unclear. In this work, we evaluate and enhance the 3D awareness of ViT-based models. We begin by systematically assessing their ability to learn 3D equivariant features, specifically examining the consistency of semantic embeddings across different viewpoints. Our findings indicate that improved 3D equivariance leads to better performance on various downstream tasks, including pose estimation, tracking, and semantic transfer. Building on this insight, we propose a simple yet effective finetuning strategy based on 3D correspondences, which significantly enhances the 3D correspondence understanding of existing vision models. Remarkably, even finetuning on a single object for just one iteration results in substantial performance gains. All code and resources will be made publicly available to support further advancements in 3D-aware vision models. Our code is available at https://github.com/qq456cvb/3DCorrEnhance.

The recently developed Sora model [1] has exhibited remarkable capabilities in video generation, sparking intense discussions regarding its ability to simulate real-world phenomena. Despite its growing popularity, there is a lack of established metrics to evaluate its fidelity to real-world physics quantitatively. In this paper, we introduce a new benchmark that assesses the quality of the generated videos based on their adherence to real-world physics principles. We employ a method that transforms the generated videos into 3D models, leveraging the premise that the accuracy of 3D reconstruction is heavily contingent on the video quality. From the perspective of 3D reconstruction, we use the fidelity of the geometric constraints satisfied by the constructed 3D models as a proxy to gauge the extent to which the generated videos conform to real-world physics rules. Project page: https://sora-geometrical-consistency.github.io/