Provided is an image processing method and a apparatus of converting a color input image or a partial region thereof in accordance with a color gamut of a color image output apparatus is provided. The method and apparatus is characterized in that only the region requiring color gamut compression can be put to color gamut compression depending on the distribution of an input image, that the direction of the color gamut compression can be controlled continuously for each of the regions; the amount of the color gamut compression can be controlled continuously including clipping, that when color gamut compression is conducted by a color converter of a multi-dimensional DLUT interpolating calculation type, an excessively unnecessary color gamut compression can be avoided particularly upon clipping, and that there is enabled correction for visual bending in iso-hue lines caused by distortion of a color space in each of the regions of the color space.