Convex hull indexed Gaussian mixture model (CH-GMM) for 3D point set registration

Abstract

To solve the problem of rigid/non-rigid 3D point set registration, a novel convex hull indexed Gaussian mixture model (CH-GMM) is proposed in this paper. The model works by computing a weighted Gaussian mixture model (GMM) response over the convex hull of each point set. Three conditions, proximity, area conservation and projection consistency, are incorporated into the model so as to improve its performance. Given that the convex hull is the tightest convex set of a point set, the combination of Gaussian mixture and convex hull can effectively preserve the topological structure of a point set. Furthermore, computational complexity can be significantly reduced since only the GMM of the convex hull (instead of the whole point set) needs to be calculated. Rigid registration is achieved by seeking the best rigid transformation parameters yielding the most similar CH-GMM responses. Non-rigid deformation is realized by optimizing the coordinates of the control points used by the thin-plate spline model for interpolating the entire point set. Experiments are designed to evaluate a method׳s robustness to rotational changes between two point sets, positional noise, differences in density and partial overlap. The results demonstrated better robustness and registration accuracy of CH-GMM based method over state-of-the-art methods including iterative closest point, coherent point drift and the GMM method. Besides, the computation of CH-GMM is efficient.