Fast Algorithms for Surface Reconstruction from Point Cloud

TL;DR

This paper introduces two fast algorithms for surface reconstruction from point clouds, improving computational efficiency and accuracy through semi-implicit and augmented Lagrangian methods, validated by numerical experiments.

Contribution

The paper presents novel fast algorithms using SIM and ALM for surface reconstruction, enhancing efficiency over previous methods.

Findings

SIM improves computational speed via relaxation techniques.

ALM reduces run-time with efficient sub-problem solving.

Numerical examples demonstrate accuracy and efficiency of the algorithms.

Abstract

We consider constructing a surface from a given set of point cloud data. We explore two fast algorithms to minimize the weighted minimum surface energy in [Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319, 2000]. An approach using Semi-Implicit Method (SIM) improves the computational efficiency through relaxation on the time-step constraint. An approach based on Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating Direction Method of Multipliers-type algorithm, where each sub-problem is solved efficiently. We analyze the effects of the parameters on the level-set evolution and explore the connection between these two approaches. We present numerical examples to validate our algorithms in terms of their accuracy and efficiency.