Point cloud surface segmentation based on volumetric eigenfunctions of the Laplace-Beltrami operator

Abstract

In the process of surface modeling from scanned point data, a segmentation that partitions a point cloud into meaningful regions or extracts important features from the 3D point data plays an important role in compressing the scanned data and fitting surface patches. In this paper, a new spectral point cloud surface segmentation method is proposed based on volumetric eigenfunctions of the Laplace-Beltrami operator. The proposed algorithm consists of two main steps. Firstly, the point cloud surface is modeled as the union of a bunch of level set surfaces, on which the eigenfunctions are computed from the level set form of the Laplace-Beltrami operator using the finite element method. Secondly, a new vectorial volumetric eigenfunction segmentation model is developed based on the classical Mumford-Shah model, in which we approximate volumetric eigenfunctions by piecewise-constant functions, and the point cloud surface is segmented via segmenting the volumetric eigenfunctions. Instead of solving the Euler-Lagrange equation by evolution implementation, the split Bregman iteration, which is shown to be a fast algorithm, is utilized. Experimental results demonstrate that our volumetric eigenfunction based technique yields superior segmentation results in terms of accuracy and robustness, compared with the surface eigenfunction based method.