Approximate tree matching and shape similarity

We present a framework for 2D shape contour (silhouette) comparison that can account for stretchings, occlusions and region information. Topological changes due to the original 3D scenarios and articulations are also addressed. To compare the degree of similarity between any two shapes, our approach is to represent each shape contour with a free tree structure derived from a shape axis (SA) model, which we have recently proposed. We then use a tree matching scheme to find the best approximate match and the matching cost. To deal with articulations, stretchings and occlusions, three local tree matching operations, merge, cut, and merge-and-cut, are introduced to yield optimally approximate matches, which can accommodate not only one-to-one but many-to-many mappings. The optimization process gives guaranteed globally optimal match efficiently. Experimental results on a variety of shape contours are provided.