Recognition of projectively transformed planar figures. I. Analysis and invariant mapping of segmented ovals
We consider the problem of projectively invariant recognition of smooth planar figures (ovals) having no pronounced reference elements (such as commonly used salient points, double tangency points, etc., which are intrinsically invariant with respect to projective transformation of the figure) but possessing, by virtue of the mechanism of their generation, smooth conjunctions of a few fragments, each of these being analytically described by a corresponding set of shape coefficients, whose number can be unique for the whole oval, different for different fragments of the oval, or even absent (in the case when the fragment is not an algebraic curve). We propose original methods for detecting the conjunction points of the segments, discuss their role in building either a global or a local invariant basis of the figure, which ensures its recognition, independent of perspective transformations of the oval on the sensor plane of the detecting optical system and depending on the chosen angle of view (within the approximation of a central planar projection).