Point set registration through minimization of the L₂ distance between 3D-NDT models

Point set registration - the task of finding the best fitting alignment between two sets of point samples, is an important problem in mobile robotics. This article proposes a novel registration algorithm, based on the distance between Three-Dimensional Normal Distributions Transforms. 3D-NDT models - a sub-class of Gaussian Mixture Models with uniformly weighted, largely disjoint components, can be quickly computed from range point data. The proposed algorithm constructs 3D-NDT representations of the input point sets and then formulates an objective function based on the L₂ distance between the considered models. Analytic first and second order derivatives of the objective function are computed and used in a standard Newton method optimization scheme, to obtain the best-fitting transformation. The proposed algorithm is evaluated and shown to be more accurate and faster, compared to a state of the art implementation of the Iterative Closest Point and 3D-NDT Point-to-Distribution algorithms.