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In this paper, we are concerned with the registration of two 3D data sets with large-scale stretches and noises. First, by incorporating a scale factor into the standard iterative closest point (ICP) algorithm, we formulate the registration into a constraint optimization problem over a 7D nonlinear space. Then, we apply the singular value decomposition (SVD) approach to iteratively solving such optimization problem. Finally, we establish a new ICP algorithm, named Scale-ICP algorithm, for registration of the data sets with isotropic stretches. In order to achieve global convergence for the proposed algorithm, we propose a way to select the initial registrations. To demonstrate the performance and efficiency of the proposed algorithm, we give several comparative experiments between Scale-ICP algorithm and the standard ICP algorithm.