Anisotropic Laplace-Beltrami Operators for Shape Analysis

Abstract. This paper introduces an anisotropic Laplace-Beltrami op-erator for shape analysis. While keeping useful properties of the stan-dard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffu-sion have already been noted in the area of mesh processing (e.g. surface regularization), focusing on the Laplacian itself, rather than on the dif-fusion process it induces, opens the possibility to effectively replace the omnipresent Laplace-Beltrami operator in many shape analysis meth-ods. After providing a mathematical formulation and analysis of this new operator, we derive a practical implementation on discrete meshes. Further, we demonstrate the effectiveness of our new operator when em-ployed in conjunction with different methods for shape segmentation and matching