Discretization of Laplace-Beltrami operator based on cotangent scheme and its applications

Abstract

Laplace-Beltrami operator (LBO) is the basis of describing geometric partial differential equation. It also plays an important role in computational geometry, computer graphics and image processing, such as surface parameterization, shape analysis, matching and interpolation. Due to the different application fields of Laplace-Beltrami operator need to meet the mathematical properties of different, has produced many discretization methods but cannot replace each other discretization method, different discretization method can reduce the time complexity, at the same time can improve an inefficient algorithm. In this article, We are mainly aimed at discretization based on the Laplace-Beltrami cotangent operator. We improve the original discretization method and apply it to non-rigid 3D shape retrieval tasks. Experimental results shows the effectiveness of our discretization method.