Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC
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.
Code (0)
등록된 구현이 없습니다.
Tasks
Simultaneous Localization and MappingSimilar Papers 제목 키워드 기반
Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant
This paper proposes an efficient numerical integration formula to compute the normalizing constant of Fisher--Bingham distributions. This formula uses a numerical integration formula with the continuous Euler transform t…
Numerical IntegrationFisher-Bingham-like normalizing flows on the sphere
A generic D-dimensional Gaussian can be conditioned or projected onto the D-1 unit sphere, thereby leading to the well-known Fisher-Bingham (FB) or Angular Gaussian (AG) distribution families, respectively. These are som…
Density EstimationDeep Bingham Networks: Dealing with Uncertainty and Ambiguity in Pose Estimation
In this work, we introduce Deep Bingham Networks (DBN), a generic framework that can naturally handle pose-related uncertainties and ambiguities arising in almost all real life applications concerning 3D data. While exis…
Camera RelocalizationPose EstimationProbabilistic Rotation Representation With an Efficiently Computable Bingham Loss Function and Its Application to Pose Estimation
In recent years, a deep learning framework has been widely used for object pose estimation. While quaternion is a common choice for rotation representation of 6D pose, it cannot represent an uncertainty of the observatio…
Pose EstimationOn Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods
A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means…
Bayesian Inference