(A) spectral approach to shape matching using a heat kernel function

Abstract

In this thesis, we present an efficient algorithm that automatically finds the point-to-point correspondences between two different 3D objects based on spectral analysis and a heat kernel function. The spectral matching is an efficient technique to find correspondences between two point sets by measuring the affinity between each point pair from different sets and the consistency between point pairs. Although it does not iteratively search possible correspondences, it can efficiently find the correspondences by combining intrinsic and extrinsic geometric features. The accurate and robust results are produced from the spectral analysis. To measure the affinity of potential correspondences, Heat Kernel Signature (HKS) and diffusion distance are introduced. Comparing to other conventional geometric descriptors, both of them have intrinsic and stable properties inherited from the heat diffusion process. Moreover, based on the Laplace-Beltrami operator, both can be obtained from eigenvalues and eigenfunctions of the operator. The orientation factor that cannot be obtained by the intrinsic features is added by combining local coordinates based on PCA. The efficacy of the proposed spectral-based matching method is demonstrated through experiments. We show that the matching results are comparable both in accuracy and robustness to state-of-the-art techniques using a set of benchmark shape data.