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We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation and deformation of parts. We demonstrate the use of this representation for both indexing and matching 3-D object models. Our formulation uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. We present comparative results against the techniques of shape distributions [17] and harmonic spheres [12] on a database of 320 models representing 13 object classes. The results demonstrate that medial surface based graph matching significantly outperforms these techniques for objects with articulating parts.

Retrieving Articulated 3-D Models Using Medial Surfaces and Their Graph Spectra