Matching Hierarchies of Deformable Shapes

This paper presents an approach to matching parts of deformable shapes. Multiscale salient parts of the two shapes are first identified. Then, these parts are matched if their immediate properties are similar, the same holds recursively for their subparts, and the same holds for their neighbor parts. The shapes are represented by hierarchical attributed graphs whose node attributes encode the photometric and geometric properties of corresponding parts, and edge attributes capture the strength of neighbor and part-of interactions between the parts. Their matching is formulated as finding the subgraph isomorphism that minimizes a quadratic cost. The dimensionality of the matching space is dramatically reduced by convexifying the cost. Experimental evaluation on the benchmark MPEG-7 and Brown datasets demonstrates that the proposed approach is robust.