Point set registration (PSR) is a crucial problem in computer vision and pattern recognition. Existing PSR methods cannot align point sets robustly due to degradations, such as deformation, noise, occlusion, outlier, and multi-view changes. In this paper, we present a self-selected regularized Gaussian fields criterion for nonrigid point matching. Unlike most existing methods, we formulate the registration problem as a sparse approximation task with low rank constraint in reproducing kernel Hilbert space (RKHS). A self-selected mechanism is used to dynamically assign real-valued label for each point in an accuracy-aware weighting manner, which makes the model focus more on the reliable points in position. Based on the label, an equivalent matching number optimization is embedded into the non-rigid criterion to enhance the reliability of the approximation. Experimental results show that the proposed method can achieve a better result in both registration accuracy and correct matches compared to state-of-the-art approaches.