Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC

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.

arXiv commentPublished at NeurIPS 2018, 25 pages with supplements

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• Quaternion Equivariant Capsule Networks for 3D Point Clouds
• Learning to Communicate and Correct Pose Errors
• Adversarial Networks for Camera Pose Regression and Refinement
• 6D Camera Relocalization in Ambiguous Scenes via Continuous Multimodal Inference
• Improved Pose Graph Optimization for Planar Motions Using Riemannian Geometry on the Manifold of Dual Quaternions