1. An image processing device comprising: a color space data storage section storing chromaticity surface division data concerning a method of dividing a chromaticity surface for any brightness in a device independent color space; a color conversion LUT storage section storing a plurality of color conversion LUTs, each of which combines a plurality of color zones, those into which the chromaticity surface is divided, and a printing order of a plurality of ink colors used for multicolor-printing a multicolor original image with a compliance relationship between multivalued pixel values in an original color space associated with the multicolor original image and multivalued pixel values in an ink color space associated with the plurality of ink colors; a controller obtaining chromaticities of the plurality of ink colors from a printer; a color conversion LUT selector discriminating which of the plurality of color zones the obtained chromaticities belong to, and selecting a color conversion LUT corresponding to a combination of the discriminated color zones and the printing order of the plurality of ink colors from among the plurality of color conversion LUTs; a color converter converting multivalued pixel values of the multicolor original image in the original color space into multivalued pixel values in the ink color space, based on the selected color conversion LUT.