Feature preserving non-rigid iterative weighted closest point and semi-curvature registration

Abstract

Preserving features of a surface as characteristic local shape properties captured e.g. by curvature, during non-rigid registration is always difficult where finding meaningful correspondences, assuring the robustness and the convergence of the algorithm while maintaining the quality of mesh are often challenges due to the high degrees of freedom and the sensitivity to features of the source surface. In this paper, we present a non-rigid registration method utilizing a newly defined semi-curvature, which is inspired by the definition of the Gaussian curvature. In the procedure of establishing the correspondences, for each point on the source surface, a corresponding point on the target surface is selected using a dynamic weighted criterion defined on the distance and the semi-curvature. We reformulate the cost function as a combination of the semi-curvature, the stiffness, and the distance terms, and ensure to penalize errors of both the distance and the semi-curvature terms in a guaranteed stable region. For a robust and efficient optimization process, we linearize the semi-curvature term, where the region of attraction is defined and the stability of the approach is proven. Experimental results show that features of the local areas on the original surface with higher curvature values are better preserved in comparison with the conventional methods. In comparison with the other methods, this leads to, on average, 75\%, 8\% and 82\% improvement in terms of quality of correspondences selection, quality of surface after registration, and time spent of the convergence process respectively, mainly due to that the semi-curvature term logically increases the constraints and dependency of each point on the neighboring vertices based on the point's degree of curvature.