基于点云数据的快速曲面重建算法
Fast Algorithms for Surface Reconstruction from Point Cloud
摘要：
我们考虑从一组给定的点云数据构造一个曲面。在[Zhao，Osher，Merriman和Kang，Comp.Vision and Image Under.，80（3）：295-319，2000]。采用半隐式方法（SIM）的方法通过放松时间步长约束提高了计算效率。基于增广拉格朗日方法的算法通过一种乘子型算法的交替方向法来减少运行时间，有效地解决了每个子问题。我们分析了参数对水平集演化的影响，并探讨了这两种方法之间的联系。我们提出的数值例子来验证我们的算法在其精度和效率。
英文摘要：
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.
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