提出基于SDF的不确定性估计方法，提升3D几何建模可靠性。
BayesSDF: Surface-Based Laplacian Uncertainty Estimation for 3D Geometry with Neural Signed Distance Fields
- 用拉普拉斯近似对SDF权重建模不确定性
- 通过海森矩阵度量局部几何不稳定性，与重建误差强相关
- 适合需要可解释性3D感知的科研与工业应用
准确的表面估计对科学模拟等下游任务至关重要，但隐式神经3D表示中的不确定性量化仍面临计算效率低、可扩展性差和几何不一致等挑战。现有神经隐式表面模型缺乏系统性的不确定性量化方法，限制了其在真实场景中的可靠性。受概率渲染启发，我们提出BayesSDF，一种新型概率框架用于神经隐式3D表示的不确定性估计。与基于辐射率的NeRF或3D高斯泼溅不同，有符号距离函数（SDF）提供连续可微的表面表示，更适用于不确定性建模。BayesSDF在SDF权重上应用拉普拉斯近似，并推导出基于海森矩阵的度量以估计局部几何不稳定性。我们在合成与真实世界基准上实证表明，这些不确定性估计与表面重建误差高度相关。通过实现面向表面的不确定性量化，BayesSDF为更鲁棒、可解释且可操作的3D感知系统奠定基础。
原文摘要 · Abstract (English)
Accurate surface estimation is critical for downstream tasks in scientific simulation, and quantifying uncertainty in implicit neural 3D representations still remains a substantial challenge due to computational inefficiencies, scalability issues, and geometric inconsistencies. However, current neural implicit surface models do not offer a principled way to quantify uncertainty, limiting their reliability in real-world applications. Inspired by recent probabilistic rendering approaches, we introduce BayesSDF, a novel probabilistic framework for uncertainty estimation in neural implicit 3D representations. Unlike radiance-based models such as Neural Radiance Fields (NeRF) or 3D Gaussian Splatting, Signed Distance Functions (SDFs) provide continuous, differentiable surface representations, making them especially well-suited for uncertainty-aware modeling. BayesSDF applies a Laplace approximation over SDF weights and derives Hessian-based metrics to estimate local geometric instability. We empirically demonstrate that these uncertainty estimates correlate strongly with surface reconstruction error across both synthetic and real-world benchmarks. By enabling surface-aware uncertainty quantification, BayesSDF lays the groundwork for more robust, interpretable, and actionable 3D perception systems.
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