Image registration involves estimating how one set of n-dimensional points is rotated, scaled, and translated into another set of n-dimensional points. As the rigid invariants, the matching point pairs preserve geometric topological relationship while mapping. Thus we propose a novel method for two-dimensional rigid registration problem, dubbed Geometric Topological Inference algorithm (GTI). Given a basic triplet point pairs, GTI can discover a complete matching point set without computing the transformation matrix. The method has been tested on synthetic data sets and real SAR images and performs well.