Determining the Similarity Between Two Arbitrary 2-D Shapes and Its Application to Biological Objects

Abstract

Generalized shape models of objects are necessary to match and identify an object in an image. To acquire these kind of models special methods are necessary that allow to learn the similarity pair-wise similarity between shapes. They mainly concern is the establishment of point correspondences between two shapes and the detection of outlier. Known algorithm assume that the aligned shapes are quite similar in a way. But special problems arise if we have to align shapes that are very different, for example aligning concave to convex shapes. In such cases it is indispensable to take into account the order of the pointsets and to enforce legal sets of correspondences; otherwise the calculated distances are incorrect. We present our novel shape alignment algorithm which can also handle such cases. The algorithm establishes symmetric and legal one-to-one point correspondences between arbitrary shapes, represented as ordered sets of 2D-points and returns a distance measure which runs between 0 and 1.