A multiscale representation method for nonrigid shapes with a single closed contour

In this paper, we discuss the criteria that should be satisfied by a descriptor for nonrigid shapes with a single closed contour. We then propose a shape representation method that ful-fills these criteria. In the proposed approach, contour convexities and concavities at different scale levels are represented using a two-dimensional (2-D) matrix. The representation can be visual-ized as a 2-D surface, where hills and valleys represent contour convexities and concavities, respectively. The optimal matching of two shape representations is achieved using dynamic programming and a dissimilarity measure is defined based on this matching. The proposed algorithm is very efficient and invariant to several kinds of transformations including some articulations and modest oc-clusions. The retrieval performance of the approach is illustrated using the MPEG-7 shape database, which is one of the most complete shape databases currently available. Our experiments indicate that the proposed representation is well suited for object in-dexing and retrieval in large databases. Furthermore, the representation can be used as a starting point to obtain more compact descriptors.