Learning coherent vector fields for robust point matching under manifold regularization

In this paper, we propose a robust method for coherent vector field learning with outliers (mismatches) using manifold regularization, called manifold regularized coherent vector field (MRCVF). The method could remove outliers from inliers (correct matches) and learn coherent vector fields fitting for the inliers with graph Laplacian constraint. In the proposed method, we first formulate the point matching problem as learning a corresponding vector field based on a mixture model (MM). Manifold regularization term is added to preserve the intrinsic geometry of the mapped point set of vector fields. More specially, the optimal mapping function is obtained by solving a weighted Laplacian regularized least squares (LapRLS) in a reproducing kernel Hilbert space (RKHS) with a matrix-valued kernel. Moreover, we use the Expectation Maximization (EM) optimization algorithm to update the unknown parameters in each iteration. The experimental results on the synthetic data set, real image data sets, and non-rigid images quantitatively demonstrate that our proposed method is robust to outliers, and it outperforms several state-of-the-art methods in most scenarios.