提出新方法优化神经符号距离函数，解决重建失真与训练不稳问题。
HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition
- 基于屏蔽泊松方程解设计损失函数，确保收敛到真实距离函数。
- 在2D/3D数据集上重建精度更高，距离估计误差更小。
- 适合需要高保真几何重建的场景，如3D建模与逆向工程。
我们提出一种名为HotSpot的方法，用于优化神经符号距离函数。现有损失（如eikonal损失）仅为必要但不充分约束，无法保证恢复的隐式函数为真实距离函数，即使输出几乎处处最小化这些损失。此外，eikonal损失在优化中存在稳定性问题。传统方法中的正则化损失会扭曲表面面积，影响重建质量。我们通过求解屏蔽泊松方程设计新损失函数，该损失在最小化时可提供渐近充分条件，确保输出收敛至真实距离函数。该损失还带来稳定优化，并自然惩罚过大的表面面积。我们在具有挑战性的2D和3D数据集上进行了理论分析与实验，结果表明本方法在表面重建和距离近似方面表现更优。
原文摘要 · Abstract (English)
We propose a method, HotSpot, for optimizing neural signed distance functions. Existing losses, such as the eikonal loss, act as necessary but insufficient constraints and cannot guarantee that the recovered implicit function represents a true distance function, even if the output minimizes these losses almost everywhere. Furthermore, the eikonal loss suffers from stability issues in optimization. Finally, in conventional methods, regularization losses that penalize surface area distort the reconstructed signed distance function. We address these challenges by designing a loss function using the solution of a screened Poisson equation. Our loss, when minimized, provides an asymptotically sufficient condition to ensure the output converges to a true distance function. Our loss also leads to stable optimization and naturally penalizes large surface areas. We present theoretical analysis and experiments on both challenging 2D and 3D datasets and show that our method provides better surface reconstruction and a more accurate distance approximation.
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