SCM: Spatially Coherent Matching With Gaussian Field Learning for Nonrigid Point Set Registration.

While point set registration has been studied in many areas of computer vision for decades, registering points encountering different degradations remains a challenging problem. In this article, we introduce a robust point pattern matching method, termed spatially coherent matching (SCM). The SCM algorithm consists of recovering correspondences and learning nonrigid transformations between the given model and scene point sets while preserving the local neighborhood structure. Precisely, the proposed SCM starts with the initial matches that are contaminated by degradations (e.g., deformation, noise, occlusion, rotation, multiview, and outliers), and the main task is to recover the underlying correspondences and learn the nonrigid transformation alternately. Based on unsupervised manifold learning, the challenging problem of point set registration can be formulated by the Gaussian fields criterion under a local preserving constraint, where the neighborhood structure could be preserved in each transforming. Moreover, the nonrigid transformation is modeled in a reproducing kernel Hilbert space, and we use a kernel approximation strategy to boost efficiency. Experimental results demonstrate that the proposed approach robustly rejecting mismatches and registers complex point set pairs containing large degradations.