An efficient iterative method for reconstructing surface from point clouds

TL;DR

This paper introduces an efficient iterative variational method for surface reconstruction from point clouds, utilizing heat kernel convolutions and implicit surface representations, with proven energy decay and demonstrated accuracy in 2D and 3D.

Contribution

The paper presents a novel iterative algorithm that minimizes an approximate energy functional for surface reconstruction, linking it to active contour models and proving its energy decay.

Findings

Method is simple, efficient, and accurate.

Proven energy decay during iterations.

Effective in both 2D and 3D reconstructions.

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. We then use asymptotic expansion to give a connection between the proposed algorithm and active contour models. Extensive numerical experiments are performed in both 2- and 3- dimensional Euclidean spaces to show that the proposed method is simple, efficient, and accurate.