Estimating transformations from degraded point sets is necessary for many computer vision and pattern recognition applications. In this paper, we propose a robust non-rigid point set registration method based on spatially constrained context-aware Gaussian fields. We first construct a context-aware representation (e.g., shape context) for assignment initialization. Then, we use a graph Laplacian regularized Gaussian fields to estimate the underlying transformation from the likely correspondences. On the one hand, the intrinsic manifold is considered and used to preserve the geometrical structure, and a priori knowledge of the point set is extracted. On the other hand, by using the deterministic annealing, the presented method is extended to a projected high-dimensional feature space, i.e., reproducing kernel Hilbert space through a kernel trick to solve the transformation, in which the local structure is propagated by the coarse-to-fine scaling strategy. In this way, the proposed method gradually recovers much more correct correspondences, and then estimates the transformation parameters accurately and robustly when facing degradations. Experimental results on 2D and 3D synthetic and real data (point sets) demonstrate that the proposed method reaches better performance than the state-of-the-art algorithms.

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.

The main problems in point registration involve recovering correspondences and estimating transformations, especially in a fully unsupervised way without any feature descriptors. In this work, we propose a robust point matching method using discrete optimal transport (OT), which is a natural and useful approach for assignment tasks, to recover the underlying correspondences and improve the nonrigid registration in the presence of unknown global transformations. Specifically, we cast the registration problem as a joint estimation over local transport couplings and global transformations, observing that the local neighborhood topology structures should be preserved strongly and stably for nonrigid transformations. By solving the Gromov–Wasserstein discrepancy, a smooth assignment matrix from one point set to another can be recovered in a fully unsupervised way. Registration performance can be improved by applying an unsupervised map to guide the transformation estimate under the alternating optimization. Experimental results on several datasets reveal how the presented method is superior to the state-of-the-art methods when facing large data degradations.