RESUMEN
Preserving features or local shape characteristics of a mesh using conventional non-rigid registration methods is always difficult, as the preservation and deformation are competing with each other. The challenge is to find a balance between these two terms in the process of the registration, especially in presence of artefacts in the mesh. We present a non-rigid Iterative Closest Points (ICP) algorithm which addresses the challenge as a control problem. An adaptive feedback control scheme with global asymptotic stability is derived to control the stiffness ratio for maximum feature preservation and minimum mesh quality loss during the registration process. A cost function is formulated with the distance term and the stiffness term where the initial stiffness ratio value is defined by an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictor regarding the source mesh and the target mesh topology, and the distance between the correspondences. During the registration process, the stiffness ratio of each vertex is continuously adjusted by the intrinsic information, represented by shape descriptors, of the surrounding surface as well as the steps in the registration process. Besides, the estimated process-dependent stiffness ratios are used as dynamic weights for establishing the correspondences in each step of the registration. Experiments on simple geometric shapes as well as 3D scanning datasets indicated that the proposed approach outperforms current methodologies, especially for the regions where features are not eminent and/or there exist interferences between/among features, due to its ability to embed the inherent properties of the surface in the process of the mesh registration.
RESUMEN
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.
