PURPOSE: To attain excellent gradation for a compression result by applying color space compression processing to input image data with a nonlinear and consecutive mapping relation within a desired range so as to eliminate a discontinuous part.

CONSTITUTION: An input color signal at the outside of a mapping border including an input color signal at the outside of a device color reproduction range is mapped with a signal within the mapping border and within the device color reproduction range while keeping the luminance. In this case, the signal is reproduced in the mapping border with fidelity on a equi-luminance plane and mapped nonlinearly so as to be more dense toward the device color reproduction range. Thus, a discontinuous point in gradation is eliminated and the signal is reproduced with excellent gradation over the entire gradation. Furthermore, the gradation at the outside of the device color reproduction range is reproduced excellently. Since the image is reproduced with fidelity in the mapping border, the environment of the input image is maintained.