TY - GEN
T1 - Fast Algorithms for Surface Reconstruction from Point Cloud
AU - He, Yuchen
AU - Huska, Martin
AU - Kang, Sung Ha
AU - Liu, Hao
N1 - Publisher Copyright:
© 2021, Springer Nature Singapore Pte Ltd.
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
UR - http://www.scopus.com/inward/record.url?scp=85116430927&partnerID=8YFLogxK
U2 - 10.1007/978-981-16-2701-9_4
DO - 10.1007/978-981-16-2701-9_4
M3 - Conference contribution
AN - SCOPUS:85116430927
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
A2 - Wei, Suhua
A2 - Liu, Haiguang
PB - Springer Singapore
T2 - International Workshop on Image Processing and Inverse Problems, IPIP 2018
Y2 - 21 April 2018 through 24 April 2018
ER -