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The ICP algorithm is accurate and fast for registration between two point sets in a same scale, but it doesn't handle the case with different scales. This paper instead introduces a novel approach named the scaling iterative closest point (SICP) algorithm which integrates a scale matrix with boundaries into the original ICP algorithm for scaling registration. This method uses a simple iterative algorithm with the SVD algorithm and the properties of parabola incorporated to compute the translation, rotation and scale transformations at each iterative step, and its convergence is rapid with only a few iterations. The SICP algorithm is independent of shape representation and feature extraction; thereby it is general for scaling registration. Experimental results demonstrate its robustness and fast speed compared with the standard ICP algorithm.