Point Set Registration via Particle Filtering and Stochastic Dynamics

In this paper, we propose a particle filtering approach for the problem of registering two point sets that differ by a rigid body transformation. Typically, registration algorithms compute the transformation parameters by maximizing a metric given an estimate of the correspondence between points across the two sets of interest. This can be viewed as a posterior estimation problem, in which the corresponding distribution can naturally be estimated using a particle filter. In this work, we treat motion as a local variation in pose parameters obtained by running a few iterations of a certain local optimizer. Employing this idea, we introduce stochastic motion dynamics to widen the narrow band of convergence often found in local optimizer approaches for registration. Thus, the novelty of our method is threefold: First, we employ a particle filtering scheme to drive the point set registration process. Second, we present a local optimizer that is motivated by the correlation measure. Third, we increase the robustness of the registration performance by introducing a dynamic model of uncertainty for the transformation parameters. In contrast with other techniques, our approach requires no annealing schedule, which results in a reduction in computational complexity (with respect to particle size) as well as maintains the temporal coherency of the state (no loss of information). Also unlike some alternative approaches for point set registration, we make no geometric assumptions on the two data sets. Experimental results are provided that demonstrate the robustness of the algorithm to initialization, noise, missing structures, and/or differing point densities in each set, on several challenging 2D and 3D registration scenarios.