GOGMA: Globally-Optimal Gaussian Mixture Alignment
This addresses the robustness issue in point-set registration for applications like robotics and computer vision, though it is incremental as it extends existing alignment methods with global optimality.
The paper tackled the problem of 3D rigid Gaussian mixture alignment, which previously relied on local optimization prone to local minima, by presenting the first globally-optimal solution under the L2 distance, guaranteeing optimality regardless of initialization and showing improved robustness on challenging datasets.
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.