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This paper presents a relaxation labeling process with the newly defined compatibility measure for solving a general nonrigid point matching problem. In the literature, there exists a point matching method using relaxation labeling; however, the compatibility coefficient takes a binary value of zero or one depending on whether a point and a neighbor have corresponding points. Our approach generalizes this relaxation labeling method. The compatibility coefficient takes n-discrete values which measure the correlation between point pairs. In order to improve the speed of the algorithm, we use a diagram of log distance and polar angle bins to compute the correlation. The extensive experiments show that the proposed topology preserving relaxation algorithm significantly improves the matching performance compared to other state-of-the-art point matching algorithms.