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The problem of partial registration of isotropic scaling point sets with outliers including noises and missing data is discussed. To solve this problem, a novel objective function based on bidirectional distance is proposed by introducing an overlapping percentage and a scale factor. Furthermore, a novel isotropic scaling iterative closest point (ICP) algorithm is proposed which can compute the scale transformation, the correspondence and the overlapping percentage automatically at each iterative step. Experimental results demonstrate that the algorithm is more robust and precise than the traditional ICP and the state-of-the-art algorithms.