Salient geometric features for partial shape matching and similarity

Abstract

This article introduces a method for partial matching of surfaces represented by triangular meshes. Our method matches surface regions that are numerically and topologically dissimilar, but approximately similar regions. We introduce novel local surface descriptors which efficiently represent the geometry of local regions of the surface. The descriptors are defined independently of the underlying triangulation, and form a compatible representation that allows matching of surfaces with different triangulations. To cope with the combinatorial complexity of partial matching of large meshes, we introduce the abstraction of salient geometric features and present a method to construct them. A salient geometric feature is a compound high-level feature of nontrivial local shapes. We show that a relatively small number of such salient geometric features characterizes the surface well for various similarity applications. Matching salient geometric features is based on indexing rotation-invariant features and a voting scheme accelerated by geometric hashing. We demonstrate the effectiveness of our method with a number of applications, such as computing self-similarity, alignments, and subparts similarity.