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Robust and Efficient Implicit Surface Reconstruction for Point Clouds Based on Convexified Image Segmentation

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Abstract

We present an implicit surface reconstruction algorithm for point clouds. We view the implicit surface reconstruction as a three dimensional binary image segmentation problem that segments the entire space \(\mathbb R ^3\) or the computational domain into an interior region and an exterior region while the boundary between these two regions fits the data points properly. The key points with using an image segmentation formulation are: (1) an edge indicator function that gives a sharp indicator of the surface location, and (2) an initial image function that provides a good initial guess of the interior and exterior regions. In this work we propose novel ways to build both functions directly from the point cloud data. We then adopt recent convexified image segmentation models and fast computational algorithms to achieve efficient and robust implicit surface reconstruction for point clouds. We test our methods on various data sets that are noisy, non-uniform, and with holes or with open boundaries. Moreover, comparisons are also made to current state of the art point cloud surface reconstruction techniques.

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Acknowledgments

This work is partially supported by ARO/MURI grant W911NF-07-1-0185, ONR grant N00014-11-1-0602 and NGA NURI HM1582-10-1-0012. The authors would like to thank Edward Castillo for graciously providing us with his code for computing surface normals to PC data. The author would like to express their thanks to the Stanford 3D scanning Repository for their generosity in distributing their 3D data. The authors would also like to thank Professor Michael Kazhdan for graciously distributing his source code for Poisson surface reconstruction.

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  1. Department of Mathematics, University of California, Irvine, Irvine, CA, USA

    Jian Liang & Hongkai Zhao

  2. Department of Mathematics, Whittier College, Whittier, CA, USA

    Frederick Park

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  1. Jian Liang
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  2. Frederick Park
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Liang, J., Park, F. & Zhao, H. Robust and Efficient Implicit Surface Reconstruction for Point Clouds Based on Convexified Image Segmentation. J Sci Comput 54, 577–602 (2013). https://doi.org/10.1007/s10915-012-9674-8

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