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This paper describes a method for performing nonrigid point set registration on data with different kinds of degradation (deformation, occlusion, noise, and outliers). We formulate the registration problem as a mixture model estimation problem by employing two topologically complementary constraints in a Gaussian mixture model (GMM)-based learning framework. The first constraint is Tikhonov-based regularization, which maintains the overall spatial connectivity by moving the point set collectively and coherently. The second constraint is graph-Laplacian-based regularization embedding, which preserves the intrinsic topological characteristics of the marginal space during registration. Hence, the proposed method is named coregularized least squares (Co-RLS). Our method iteratively estimates the correspondences and nonrigid transformation between two given sets of points. First, the correspondences are established subject to the ordering information of the contour points using feature descriptors, i.e., the shape context. Then, the transformation is recovered by minimizing the Co-RLS function, and the expectation maximization method is used to update the transformation parameters and outlier ratios. Experimental results on various types of synthetic and real data show the superior effectiveness and robustness of the proposed method compared with other state-of-the-art methods.

A Unified Framework for Nonrigid Point Set Registration via Coregularized Least Squares