Reviews: Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC

This paper presents a stochastic gradient Monte Carlo approach defined on a Cartesian product of SE(3), a domain commonly used to characterize problems in structure-from-motion (SFM) among other areas. The algorithm is parameterized by an inverse temperature such that when the value goes to inifinity, the algorithm is implicitly operating on a delta function with it's peak at the maximum of the base distribution. The proposed algorithm is formulated as a SDE and a splitting scheme is proposed to integrate it. A theoretical analysis on the SDE and its discretization is explored, showing that 1) the resulting Markov process has the appropriate invariant distribution and 2) the sampler will draw samples close to the maximum of the posterior (in terms of expectation of the unnormalized log posterior). Along with the algorithm, a model is defined using the Bingham distribution to characterize typical SFM posteriors which is then used to perform experiments with the algorithm.