Non-rigid surface registration using cover tree based clustering and nearest neighbor search

We propose a novel non-rigid registration method that computes the correspondences of two deformable surfaces using the cover tree. The aim is to find the correct correspondences without landmark selection and to reduce the computational complexity. The source surface S is initially aligned to the target surface T to generate a cover tree from the densely distributed surface points. The cover tree is constructed by taking into account the positions and normal vectors of the points and used for hierarchical clustering and nearest neighbor search. The cover tree based clustering divides the two surfaces into several clusters based on the geometric features, and each cluster on the source surface is transformed to its corresponding cluster on the target. The nearest neighbor search from the cover tree reduces the search space for correspondence computation, and the source surface is deformed to the target by optimizing the point pairs. The correct correspondence of a given source point is determined by choosing one target point with the best correspondence measure from the k nearest neighbors. The proposed energy function with Jacobian penalty allows deforming the surface accurately and with less deformation folding.