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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| Format | Journal Article |
| Language | English |
| Published |
01.07.2019
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| 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. |
|---|---|
| AbstractList | 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. |
| Author | Liu, Hao Huska, Martin He, Yuchen Kang, Sung Ha |
| Author_xml | – sequence: 1 givenname: Yuchen surname: He fullname: He, Yuchen – sequence: 2 givenname: Martin surname: Huska fullname: Huska, Martin – sequence: 3 givenname: Sung Ha surname: Kang fullname: Kang, Sung Ha – sequence: 4 givenname: Hao surname: Liu fullname: Liu, Hao |
| BackLink | https://doi.org/10.48550/arXiv.1907.01142$$DView paper in arXiv |
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| Snippet | 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... |
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| SubjectTerms | Computer Science - Numerical Analysis Mathematics - Numerical Analysis Mathematics - Optimization and Control |
| Title | Fast Algorithms for Surface Reconstruction from Point Cloud |
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