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This paper presents a relaxation labeling technique with newly defined compatibility measures for solving a general non-rigid point matching problem. In the literature, there exists a point matching method using relaxation labeling, however, the compatibility coefficients always take a binary value zero or one depending on whether a point and a neighboring point have corresponding points. Our approach generalizes this relaxation labeling approach. The compatibility coefficients take n-discrete values which measures the correlation between edges. We use log-polar diagram to compute correlations. Through simulations, we show that this topology preserving relaxation method improves the matching performance significantly compared to other state-of-the-art algorithms such as shape context, thin plate spline-robust point matching, robust point matching by preserving local neighborhood structures and coherent point drift.