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This paper presents a theoretically simple, yet efficient approach for the problem of matching the 2-D point sets under rigid motion, where jitter is allowed. It is a fundamental problem in pattern recognition, having applications ranging from robotics to astronautics. Commonly, the previous methods tend to use symbolic arithmetic to solve this problem. However, they are always complex and limited by computational cost. In this paper, we present a visual analysis for the point set matching problem and develop a geometrical arithmetic which is proven to yield equivalent results to the symbolic arithmetic. This allows us to view the problem as one of shape matching and obtain an algorithm that firstly generates a probabilistic shape descriptor (PSD) to describe the local geometric property of each point in the point sets, then acquires the local correspondence from the Euclidean distance matrix of the descriptors, and validates the global transformation finally. Experimental results demonstrate that our simple algorithm with a lower computation complexity effectively improves accuracy over current method, particularly when matching equal-size patterns under varying jitter.