Abstract
Feature-preserving mesh reconstruction from point clouds is challenging. Implicit methods tend to fit smooth surfaces and cannot be used to reconstruct sharp features. Explicit reconstruction methods are sensitive to noise and only interpolate sharp features when points are distributed on feature lines. We propose a watertight surface reconstruction method based on optimal transport that can accurately reconstruct sharp features often present in CAD models. We formalize the surface reconstruction problem by minimizing the optimal transport cost between the point cloud and the reconstructed surface. The algorithm consists of initialization and refinement steps. In the initialization step, the convex hull of the point cloud is deformed under the guidance of a transport plan to obtain an initial approximate surface. Next, the mesh surface was optimized using operations including vertex relocation and edge collapses/flips to obtain feature-preserving results. Experiments demonstrate that our method can preserve sharp features while being robust to noise and missing data.
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Acknowledgements
This research was supported by the National Key R&D Program of China (2022YFB3303400), the National Natural Science Foundation of China (62272402, 62372389), the Natural Science Foundation of Fujian Province (2022J01001), and the Fundamental Research Funds for the Central Universities (20720220037). 3D data in this study are courtesy of AIM@Shape, Thingi10K, and Stanford 3D Scanning Repository.
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Yuanyan Ye received her B.S. degree from Xiamen University in 2020, where she is currently pursuing the M.S. degree. Her research interests include computer graphics and digital geometry processing.
Yubo Wang received his B.S. degree from Xiamen University in 2019, and M.S. degree from the same university in 2022. His research interests include computer graphics and digital geometricy processing.
Juan Cao is a professor in the School of Mathematical Sciences, Xiamen University, China. She received her Ph.D. degree in applied mathematics from Zhejiang University, China, in 2009. Her research interests include computer-aided geometric designs and computer graphics.
Zhonggui Chen received his B.S. and Ph.D. degrees in applied mathematics from Zhejiang University, in 2004 and 2009, respectively. He is currently as a professor at the School of Informatics, Xiamen University, China. His research interests include computer graphics, computational geometry, and digital image processing. For more information, please visit http://graphics.xmu.edu.cn/~zgchen/
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Ye, Y., Wang, Y., Cao, J. et al. Watertight surface reconstruction method for CAD models based on optimal transport. Comp. Visual Media (2024). https://doi.org/10.1007/s41095-023-0355-3
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DOI: https://doi.org/10.1007/s41095-023-0355-3