Fast Algorithms for Surface Reconstruction from Point Cloud

Yuchen He, Martin Huska, Sung Ha Kang*, Hao Liu

*Corresponding author for this work

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Title of host publicationMathematical Methods in Image Processing and Inverse Problems
Subtitle of host publicationIPIP 2018, Beijing, China, April 21–24
EditorsXue-Cheng Tai, Suhua Wei, Haiguang Liu
PublisherSpringer Singapore
Number of pages20
ISBN (Electronic)9789811627019
ISBN (Print)9789811627002
Publication statusPublished - 26 Sept 2021
EventInternational Workshop on Image Processing and Inverse Problems, IPIP 2018 - Beijing, China
Duration: 21 Apr 201824 Apr 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017
NameIPIP: International Workshop On Image Processing and Inverse Problems


ConferenceInternational Workshop on Image Processing and Inverse Problems, IPIP 2018

Scopus Subject Areas

  • Mathematics(all)

User-Defined Keywords

  • Augmented Lagrangian method
  • Point cloud
  • Semi-implicit method
  • Surface reconstruction


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