Papers › Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds
Monge-Ampere Regularization for Learning Arbitrary Shapes from Point Clouds
Chuanxiang Yang, Yuanfeng Zhou, Guangshun Wei, Long Ma, Junhui Hou, YuAn Liu, Wenping Wang
As commonly used implicit geometry representations, the signed distance function (SDF) is limited to modeling watertight shapes, while the unsigned distance function (UDF) is capable of representing various surfaces. However, its inherent theoretical shortcoming, i.e., the non-differentiability at the zero level set, would result in sub-optimal reconstruction quality. In this paper, we propose the scaled-squared distance function (S²DF), a novel implicit surface representation for modeling arbitrary surface types. S²DF does not distinguish between inside and outside regions while effectively addressing the non-differentiability issue of UDF at the zero level set. We demonstrate that S²DF satisfies a second-order partial differential equation of Monge-Ampere-type, allowing us to develop a learning pipeline that leverages a novel Monge-Ampere regularization to directly learn S²DF from raw unoriented point clouds without supervision from ground-truth S²DF values. Extensive experiments across multiple datasets show that our method significantly outperforms state-of-the-art supervised approaches that require ground-truth surface information as supervision for training. The code will be publicly available at https://github.com/chuanxiang-yang/S2DF.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections