Determining the Similarity of Deformable Shapes

R. Basri and L. Costa and D. Geiger and D. Jacobs

This paper considers how to measure the degree of similarity between two image contours. We propose a method for comparing contours that takes into account deformations in object shape, the articulation of parts, and variations in the shape and size of portions of objects. Our method is based on using dynamic programming to find the minimum cost set of local deformations of one shape that will match it with the other. Using this as a starting point, we investiage the properties that such a cost function should have to model human performance and to perform usefully in a computer vision system. We suggest novel conditions on this cost function that help capture the part-based nature of objects without requiring any explicit decomposition of shapes into their parts. We then suggest several possible cost functions based on different physical models of contours, and describe experiments with these costs. Representation and Self-Similarity of Shapes

Representation and Self-Similarity of Shapes

Tyng-Luh Liu and Davi Geiger and Robert V. Kohn

Representing shapes is a significant problem for vision systems that must recognize or classify objects. We derive a representation for a given shape by investigating its self-similarities, and constructing its shape axis(SA) and shape axis tree (SA-tree). We start with a shape, its boundary contour, and two different parameterizations for the contour. To measure its self-similarity we consider matching pairs of points (and their tangents) along the boundary contour, i.e., matching the two parameterizations. The matching, or self-similarity criteria may vary, e.g., co-circularity, parallelism, distance, region homogeneity. The loci of middle points of the pairing contour points are the shape axis and they can be grouped into a unique tree graph, the SA-tree. The shape axis for the co-circularity criteria is compared to the symmetry axis. An interpretation in terms of object parts is also presented.