Projective and Illumination Invariant Representation of Disjoint Shapes

Abstract

A projectively invariant representation for groups of planar disjoint contours is proposed as a simultaneous polar reparametrization of multiple curves. Its origin is an invariant point and for each ray orientation, the cross-ratio of the intersections with its closest curves is taken as a value associated to the radius. The sequence of cross-ratio values for all orientations represents a signature. With respect to other methods this representation is less reliant on single curve properties, both for the construction of the projective basis and for calculating the signature. The proposed representation has been originally developed for planar shapes, but an extension is proposed and validated for trihedral corners. Illumination invariant measures are introduced into the representation to increase it discrimination capability. The whole approach is applied to shape-based retrieval from image databases. Experiments are reported on a database of real trademarks.