A robust non-rigid point set registration algorithm using both local and global constraints

The goal of non-rigid point set registration is to estimate the optimal correspondence between points, and then recover the non-rigid deformation between point sets in a specific way, typically by using a set of complex interpolation functions. Many non-rigid matching algorithms have been studied, but only a few algorithms fully exploit the local structure between point sets. To improve the accuracy of point set registration, this paper proposes a new non-rigid registration algorithm that uses both the global structure and the stable local structure of a non-rigid shape to constrain the registration. Specifically, we consider the point set registration problem as a probability assignment problem, with the probability determined by the Gaussian mixture model and the local structure of the point set. In particular, the Hausdorff distance can effectively measure the similarity of the local structure of the point set in the proposed algorithm. The transformation between the two-point sets is determined by the reproducing kernel Hilbert space based on the motion coherence theory once the correspondence is determined. A significant number of experiments show that the proposed technique has higher registration accuracy than several other state-of-the-art algorithms when dealing with non-rigid registration problems, especially when the point set contains outliers and severely missing points.