Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC

TL;DR

This paper presents TG-MCMC, a novel algorithm that combines global non-convex optimization and posterior sampling on quaternion manifolds to improve pose graph initialization, providing reliable solutions and uncertainty estimates.

Contribution

The introduction of TG-MCMC, uniting optimization and sampling on spherical manifolds with theoretical guarantees, is a novel approach for pose graph problems.

Findings

Robust to missing data and noise

Provides meaningful uncertainty estimates

Achieves reliable initial pose solutions

Abstract

We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites asymptotically global non-convex optimization on the spherical manifold of quaternions with posterior sampling, in order to provide both reliable initial poses and uncertainty estimates that are informative about the quality of individual solutions. We devise rigorous theoretical convergence guarantees for our method and extensively evaluate it on synthetic and real benchmark datasets. Besides its elegance in formulation and theory, we show that our method is robust to missing data, noise and the estimated uncertainties capture intuitive properties of the data.