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This letter proposes a novel algorithm for affine registration of point sets in the way of incorporating an affine transformation into the iterative closest point (ICP) algorithm. At each iterative step of this algorithm, a closed-form solution of the affine transformation is derived. Similar to the ICP algorithm, this new algorithm converges monotonically to a local minimum from any given initial parameters. To get the best affine registration result, good initial parameters are required which are successfully estimated by using independent component analysis (ICA). Experimental results demonstrate the robustness and high accuracy of this algorithm.