Bayesian Heuristics for Robust Spatial Perception

TL;DR

This work tackles robust spatial perception under measurement outliers in nonlinear estimation. It develops three Bayesian heuristics—EROR, ESOR, and ASOR—built on variational Bayes and an EM interpretation to repurpose existing non-minimal solvers for robust estimation. The authors analyze standard ROR and SOR methods, extend them to adapt hyperparameters during inference, and demonstrate competitive accuracy with clear computational benefits across 3D point-cloud registration, mesh registration, and pose-graph optimization. The results suggest these Bayesian heuristics offer practical, efficient alternatives to state-of-the-art robust solvers, with potential for integration into hybrid or certifiable pipelines in robotic perception tasks.

Abstract

Spatial perception is a key task in several machine intelligence applications such as robotics and computer vision. In general, it involves the nonlinear estimation of hidden variables that represent the system's state. However, in the presence of measurement outliers, the standard nonlinear least squared formulation results in poor estimates. Several methods have been considered in the literature to improve the reliability of the estimation process. Most methods are based on heuristics since guaranteed global robust estimation is not generally practical due to high computational costs. Recently general purpose robust estimation heuristics have been proposed that leverage existing non-minimal solvers available for the outlier-free formulations without the need for an initial guess. In this work, we propose three Bayesian heuristics that have similar structures. We evaluate these heuristics in practical scenarios to demonstrate their merits in different applications including 3D point cloud registration, mesh registration and pose graph optimization. The general computational advantages our proposals offer make them attractive candidates for spatial perception tasks.

Figures (8)

• Figure 1: $w_i$ vs ${\hat{r}_{i}^{2}}/\mu$ in ROR.
• Figure 2: $w_i$ vs ${\hat{r}_{i}^{2}}-\rho^2$ in SOR.
• Figure 3: Point clouds with correspondences in 3D point cloud registration for the Bunny dataset curless1996volumetric.
• Figure 4: Performance of robust estimators for 3D point cloud registration considering the Bunny dataset curless1996volumetric.
• Figure 5: Performance of robust estimators for mesh registration considering the motorbike model 6836101.