Shape Decomposition and Shape Similarity Measure

We propose a simple and natural rule for decomposition of 2D objects into parts of visual form. The hierarchical convexity rule states that visual parts axe enclosed by maximal convex boundary arcs (with respect to the object) at various levels of curve evolution. The proposed rule is based on a novel curve evolution method by digital linearization in which a significant visual part will become a convex part at some level of the evolution. The hierarchical convexity rule determines not only parts of boundary curves but directly the visual parts of objects, and the evolution hierarchy induces a hierarchical structure of the obtained visual parts.Further, we derive a shape similarity measure based on the decomposition into visual parts and apply it to shape matching of object contours in an image database. The experimental results justify that our shape matching procedure is stable and robust with respect to noise deformations and gives an intuitive shape correspondence.