Fuzzy correspondences guided Gaussian mixture model for point set registration

Recovering correspondences and estimating transformations are challenging to solve in the presence of outliers and other degradations for non-rigid point set registration. In this paper, we propose a new methodology based on fuzzy correspondences guided Gaussian Mixture Model (GMM) to solve the registration problem between two or more feature point sets. We first construct a mixture model to represent the moving point set, where inliers are formulated as a mixture of Gaussian, and outliers are formulated as an additional uniform distribution. Then we use the context-aware shape descriptor to assign the points and obtain the fuzzy correspondences. On the one hand, the soft-assignment is used to classify the weight of inliers and outliers. On the other hand, by using the fuzzy correspondences, the Gaussian elements in the mixture model can be estimated to increase the registration accuracy efficiently. In this way, the optimal transformation between two point sets can be expressed by representation theorem and solved by EM algorithm iteratively in a high-dimensional feature space (i.e., reproducing kernel Hilbert space, RKHS). Extensive experiments on synthesized and real datasets demonstrate the proposed method performs favorably against the state-of-the-art methods in most tested scenarios.