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This paper proposes a method for the registration of range and color (or intensity) images, based on the range intensity image that is simultaneously acquired with a range image. The gradient constraint between the range intensity image and the color image is introduced, and a linear equation for the registration parameters is derived, which combines displacement estimations for extrinsic and intrinsic parameters. By using the equation, precise automatic registration without explicit detection of correspondences is achieved. Experimental results illustrate the proposed method.