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

• URL: http://arxiv.org/abs/2507.06269v3
• Date: Thu, 04 Sep 2025 18:52:33 GMT
• Title: BayesSDF: Surface-Based Laplacian Uncertainty Estimation for 3D Geometry with Neural Signed Distance Fields
• Authors: Rushil Desai,
• Abstract summary: BayesSDF is a novel probabilistic framework for uncertainty estimation in neural implicit 3D representations.<n>By enabling surface-aware uncertainty quantification, BayesSDF lays the groundwork for more robust, interpretable, and actionable 3D perception systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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