3D Model Retrieval Using Medial Surfaces

Abstract

Graphs derived from medial representations have been used for 2D object matching and retrieval with considerable success (Pelillo et al., 1999; Siddiqi et al., 1999b; Sebastian et al., 2001). In this chapter we consider consider the use of graphs derived from medial surfaces for 3D object matching and retrieval. The medial reprsentation 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 of parts. The formulation discussed in this chapter uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. Comparative retrieval results are presented against the techniques of shape distributions (Osada et al., 2002) and harmonic spheres (Kazhdan et al., 2003b) on 425 models representing 19 object classes. These results demonstrate that medial surface based graph matching outperforms these techniques for objects with articulating parts.