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Monge-Ampere Regularization for Learning Arbitrary Shapes From Point Clouds

delete2025-08-01
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PRE
AI
C
Charles C. Yang
周元峰 封面图
周元峰 (Yuanfeng Zhou)
G
Guangshun Wei
L
Long Ma
J
Junhui Hou
Y
Yuan Liu
Wang, Wenping 封面图
Wang, Wenping (Wenping Wang)
DOI：10.1109/TPAMI.2025.3563601delete
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摘要

摘要

En 中文
作为常用的隐式几何表示，符号距离函数（SDF）仅限于建模水密形状，而无符号距离函数（UDF）能够表示各种表面。然而，其固有的理论缺陷，即零级集处的非可微性，会导致次优的重建质量。在本文中，我们提出了缩放平方距离函数（S²DF），一种用于建模任意表面类型的隐式曲面表示。S²DF不区分内部和外部区域，同时有效解决了UDF在零级集处的非可微性问题。我们证明了S²DF满足一个二阶Monge-Ampere型偏微分方程，这使得我们能够开发一个利用新颖的Monge-Ampere正则化的学习流程，直接从原始无定向点云中学习S²DF，而无需来自真实S²DF值的监督。在多个数据集上的广泛实验表明，我们的方法显著优于需要将真实表面信息作为训练监督信号的最先进监督方法。
Keyword:
Implicit neural representation
distance function
surface reconstruction

期刊

IEEE Transactions on Pattern Analysis and Machine Intelligence 封面图
IEEE Transactions on Pattern Analysis and Machine Intelligence
IF:
18.6
论文数:
1.0K
被引数:
9.8W

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C
college station
学者数:
1.4K
论文数: 643
被引数: 6
N
Nanyang Technological University
学者数:
4.9W
论文数: 4.8W
被引数: 8.1W
C
City University of Hong Kong
学者数:
2.3W
论文数: 3.0W
被引数: 6.1W
S
shandong university
学者数:
9.5W
论文数: 6.4W
被引数: 94
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