Indexing and matching articulated 3-D models using medial surfaces

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 (DAG) 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 compare our algorithm with the techniques of harmonic spheres (Kazhdan et al., 2003c) and shape distributions (Osada et al., 2002). The results demonstrate the significant potential of medial surface-based representations and their graph spectra in the context of 3-D model retrieval in computer graphics