BayesSDF: Surface-Based Laplacian Uncertainty Estimation for 3D Geometry with Neural Signed Distance Fields

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.