BayesFusion-SDF: Probabilistic Signed Distance Fusion with View Planning on CPU

TL;DR

BayesFusion-SDF introduces a CPU-based probabilistic 3D reconstruction method that models geometry as a Gaussian random field, providing accurate results and uncertainty estimates for view planning, offering an interpretable alternative to neural methods.

Contribution

It presents a novel probabilistic SDF fusion framework that uses Bayesian formulation and sparse linear algebra, enabling uncertainty-aware 3D reconstruction on CPU.

Findings

More accurate than TSDF baselines in geometry reconstruction

Provides useful uncertainty estimates for active sensing

Operates efficiently on CPU without GPU dependence

Abstract

Key part of robotics, augmented reality, and digital inspection is dense 3D reconstruction from depth observations. Traditional volumetric fusion techniques, including truncated signed distance functions (TSDF), enable efficient and deterministic geometry reconstruction; however, they depend on heuristic weighting and fail to transparently convey uncertainty in a systematic way. Recent neural implicit methods, on the other hand, get very high fidelity but usually need a lot of GPU power for optimization and aren't very easy to understand for making decisions later on. This work presents BayesFusion-SDF, a CPU-centric probabilistic signed distance fusion framework that conceptualizes geometry as a sparse Gaussian random field with a defined posterior distribution over voxel distances. First, a rough TSDF reconstruction is used to create an adaptive narrow-band domain. Then, depth observations are combined using a heteroscedastic Bayesian formulation that is solved using sparse linear algebra and preconditioned conjugate gradients. Randomized diagonal estimators are a quick way to get an idea of posterior uncertainty. This makes it possible to extract surfaces and plan the next best view while taking into account uncertainty. Tests on a controlled ablation scene and a CO3D object sequence show that the new method is more accurate geometrically than TSDF baselines and gives useful estimates of uncertainty for active sensing. The proposed formulation provides a clear and easy-to-use alternative to GPU-heavy neural reconstruction methods while still being able to be understood in a probabilistic way and acting in a predictable way. GitHub: https://mazumdarsoumya.github.io/BayesFusionSDF