An Efficient Iterative Method for Reconstructing Surface from Point Clouds

Abstract

Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The surface is implicitly represented by indicator functions and the energy functional is then approximated based on such representations using heat kernel convolutions. We then develop a novel iterative method to minimize the approximate energy and prove the energy decaying property during each iteration. Asymptotic expansion is also performed to illustrate the dynamics of the surface during iterations. Extensive numerical experiments are performed in both 2- and 3- dimensional Euclidean spaces to show that the proposed method is simple, efficient, and accurate.