A Projective Invariant Description of Ovals with Three Possible Symmetry Genera
This investigation deals with a conceptual approach to the problem of projectively invariant recognition of the planar curves and scheme of its numerical implementation that makes it possible to obtain projectively invariant descriptions of planar ovals with elements of the three genera of hidden symmetry - rotational, radial (central) and axial - not using for that purpose (as an element of the basis) a location of any contour point with a "special" projectively resistant characteristics. The author proposed to form a description relying upon some integral properties of the curve by means of secondary invariant structure called the tangential image of the oval. The latter structure can be computed in the end of the processing stage that estimates the location of the "image of the center of symmetry". Wherein earlier we had proposed, modeled and described the numerical search schemes for the coordinates of the center image. The author also discussed the application methods of the introduced analytical tools for the invariant description of ovals that do not have symmetry elements in the presence of additional point fixed outside the figure's outline.