Feature matching is a key method of feature-based image registration, which refers to establishing reliable correspondence between feature points extracted from two images. In order to eliminate false matchings from the initial matchings, we propose a simple and efficient method. The key principle of our method is to maintain the topological and affine transformation consistency among the neighborhood matches. We formulate this problem as a mathematical model and derive a closed solution with linear time and space complexity. More specifically, our method can remove mismatches from thousands of hypothetical correspondences within a few milliseconds. We conduct qualitative and quantitative experiments on our method on different types of remote-sensing datasets. The experimental results show that our method is general, and it can deal with all kinds of remote-sensing image pairs, whether rigid or non-rigid image deformation or image pairs with various shadow, projection distortion, noise, and geometric distortion. Furthermore, it is two orders of magnitude faster and more accurate than state-of-the-art methods and can be used for real-time applications.