Fast Algorithms for Surface Reconstruction from Point Cloud

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 co...

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Bibliographic Details
Main Authors He, Yuchen, Huska, Martin, Kang, Sung Ha, Liu, Hao
Format Journal Article
LanguageEnglish
Published 01.07.2019
Subjects
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
Mathematics - Optimization and Control
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Summary: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.
DOI:10.48550/arxiv.1907.01142