Fast Algorithms for Surface Reconstruction from Point Cloud

Yuchen He; Martin Huska; Sung Ha Kang; Hao Liu

doi:10.1007/978-981-16-2701-9_4

Fast Algorithms for Surface Reconstruction from Point Cloud

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

^*Corresponding author for this work

Department of Mathematics

Research output: Chapter in book/report/conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

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.

Original language	English
Title of host publication	Mathematical Methods in Image Processing and Inverse Problems
Subtitle of host publication	IPIP 2018, Beijing, China, April 21–24
Editors	Xue-Cheng Tai, Suhua Wei, Haiguang Liu
Publisher	Springer Singapore
Pages	61-80
Number of pages	20
Edition	1st
ISBN (Electronic)	9789811627019
ISBN (Print)	9789811627002
DOIs	https://doi.org/10.1007/978-981-16-2701-9_4
Publication status	Published - 26 Sept 2021
Event	International Workshop on Image Processing and Inverse Problems, IPIP 2018 - Beijing, China Duration: 21 Apr 2018 → 24 Apr 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	360
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Name	IPIP: International Workshop On Image Processing and Inverse Problems

Conference

Conference	International Workshop on Image Processing and Inverse Problems, IPIP 2018
Country/Territory	China
City	Beijing
Period	21/04/18 → 24/04/18

Scopus Subject Areas

Mathematics(all)

User-Defined Keywords

Augmented Lagrangian method
Point cloud
Semi-implicit method
Surface reconstruction

Access to Document

10.1007/978-981-16-2701-9_4

Cite this

He, Y., Huska, M., Kang, S. H., & Liu, H. (2021). Fast Algorithms for Surface Reconstruction from Point Cloud. In X-C. Tai, S. Wei, & H. Liu (Eds.), Mathematical Methods in Image Processing and Inverse Problems: IPIP 2018, Beijing, China, April 21–24 (1st ed., pp. 61-80). (Springer Proceedings in Mathematics and Statistics; Vol. 360), (IPIP: International Workshop On Image Processing and Inverse Problems). Springer Singapore. https://doi.org/10.1007/978-981-16-2701-9_4

He, Yuchen ; Huska, Martin ; Kang, Sung Ha et al. / Fast Algorithms for Surface Reconstruction from Point Cloud. Mathematical Methods in Image Processing and Inverse Problems: IPIP 2018, Beijing, China, April 21–24. editor / Xue-Cheng Tai ; Suhua Wei ; Haiguang Liu. 1st. ed. Springer Singapore, 2021. pp. 61-80 (Springer Proceedings in Mathematics and Statistics). (IPIP: International Workshop On Image Processing and Inverse Problems).

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title = "Fast Algorithms for Surface Reconstruction from Point Cloud",

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.",

keywords = "Augmented Lagrangian method, Point cloud, Semi-implicit method, Surface reconstruction",

author = "Yuchen He and Martin Huska and Kang, {Sung Ha} and Hao Liu",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Singapore Pte Ltd.; International Workshop on Image Processing and Inverse Problems, IPIP 2018 ; Conference date: 21-04-2018 Through 24-04-2018",

year = "2021",

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doi = "10.1007/978-981-16-2701-9_4",

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series = "Springer Proceedings in Mathematics and Statistics",

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He, Y, Huska, M, Kang, SH & Liu, H 2021, Fast Algorithms for Surface Reconstruction from Point Cloud. in X-C Tai, S Wei & H Liu (eds), Mathematical Methods in Image Processing and Inverse Problems: IPIP 2018, Beijing, China, April 21–24. 1st edn, Springer Proceedings in Mathematics and Statistics, vol. 360, IPIP: International Workshop On Image Processing and Inverse Problems, Springer Singapore, pp. 61-80, International Workshop on Image Processing and Inverse Problems, IPIP 2018, Beijing, China, 21/04/18. https://doi.org/10.1007/978-981-16-2701-9_4

Fast Algorithms for Surface Reconstruction from Point Cloud. / He, Yuchen; Huska, Martin; Kang, Sung Ha et al.

Mathematical Methods in Image Processing and Inverse Problems: IPIP 2018, Beijing, China, April 21–24. ed. / Xue-Cheng Tai; Suhua Wei; Haiguang Liu. 1st. ed. Springer Singapore, 2021. p. 61-80 (Springer Proceedings in Mathematics and Statistics; Vol. 360), (IPIP: International Workshop On Image Processing and Inverse Problems).

Research output: Chapter in book/report/conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Fast Algorithms for Surface Reconstruction from Point Cloud

AU - He, Yuchen

AU - Huska, Martin

AU - Kang, Sung Ha

AU - Liu, Hao

PY - 2021/9/26

Y1 - 2021/9/26

N2 - 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.

AB - 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.

KW - Augmented Lagrangian method

KW - Point cloud

KW - Semi-implicit method

KW - Surface reconstruction

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SN - 9789811627002

T3 - Springer Proceedings in Mathematics and Statistics

SP - 61

EP - 80

BT - Mathematical Methods in Image Processing and Inverse Problems

A2 - Tai, Xue-Cheng

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He Y, Huska M, Kang SH, Liu H. Fast Algorithms for Surface Reconstruction from Point Cloud. In Tai X-C, Wei S, Liu H, editors, Mathematical Methods in Image Processing and Inverse Problems: IPIP 2018, Beijing, China, April 21–24. 1st ed. Springer Singapore. 2021. p. 61-80. (Springer Proceedings in Mathematics and Statistics). (IPIP: International Workshop On Image Processing and Inverse Problems). doi: 10.1007/978-981-16-2701-9_4

Fast Algorithms for Surface Reconstruction from Point Cloud

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