Nonrigid point set registration with robust transformation learning under manifold regularization

This paper solves the problem of nonrigid point set registration by designing a robust transformation learning scheme. The principle is to iteratively establish point correspondences and learn the nonrigid transformation between two given sets of points. In particular, the local feature descriptors are used to search the correspondences and some unknown outliers will be inevitably introduced. To precisely learn the underlying transformation from noisy correspondences, we cast the point set registration into a semisupervised learning problem, where a set of indicator variables is adopted to help distinguish outliers in a mixture model. To exploit the intrinsic structure of a point set, we constrain the transformation with manifold regularization which plays a role of prior knowledge. Moreover, the transformation is modeled in the reproducing kernel Hilbert space, and a sparsity-induced approximation is utilized to boost efficiency. We apply the proposed method to learning motion flows between image pairs of similar scenes for visual homing, which is a specific type of mobile robot navigation. Extensive experiments on several publicly available data sets reveal the superiority of the proposed method over state-of-the-art competitors, particularly in the context of the degenerated data.