GOGMA: Globally-Optimal Gaussian Mixture Alignment

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and Pattern Recognitio

Contour Context: Abstract Structural Distribution for 3D LiDAR Loop Detection and Metric Pose Estimation

This paper proposes \textit{Contour Context}, a simple, effective, and efficient topological loop closure detection pipeline with accurate 3-DoF metric pose estimation, targeting the urban utonomous driving scenario. We interpret the Cartesian birds' eye view (BEV) image projected from 3D LiDAR points as layered distribution of structures. To recover elevation information from BEVs, we slice them at different heights, and connected pixels at each level will form contours. Each contour is parameterized by abstract information, e.g., pixel count, center position, covariance, and mean height. The similarity of two BEVs is calculated in sequential discrete and continuous steps. The first step considers the geometric consensus of graph-like constellations formed by contours in particular localities. The second step models the majority of contours as a 2.5D Gaussian mixture model, which is used to calculate correlation and optimize relative transform in continuous space. A retrieval key is designed to accelerate the search of a database indexed by layered KD-trees. We validate the efficacy of our method by comparing it with recent works on public datasets.Comment: 7 pages, 7 figures, accepted by ICRA 202