The problem of registering nonrigid point sets, with the aim of estimating the correspondences and learning the transformation between two given sets of points, often arises in computer vision tasks. This paper proposes a novel method for performing nonrigid point set registration on data with various types of degradation, in which the registration problem is formulated as a Gaussian mixture model (GMM)-based density estimation problem. Specifically, two complementary constraints are jointly considered for optimization in a GMM probabilistic framework. The first is a thin-plate spline-based regularization constraint that maintains global spatial motion consistency, and the second is a spectral graph-based regularization constraint that preserves the intrinsic structure of a point set. Moreover, the correspondences and the transformation are alternately optimized using the expectation maximization algorithm to obtain a closed-form solution. We first utilize local descriptors to construct the initial correspondences and then estimate the underlying transformation under the GMM-based framework. Experimental results on contour images and real images show the effectiveness and robustness of the proposed method.