1. An apparatus for converting X,Y,Z; L*a*b*; or L*u*v* colorimetric values of an original color image to R,G,B; C,M,Y; or C,M,Y,K, color separation values, the apparatus comprising: a plurality of converting means for converting the colorimetric values of the original color image which has been obtained under a specific illuminant to the color separation values under a plurality of observation illuminants differing in types; means for selecting one of said plurality of converting means; and means for outputting the color image based on the color separation value obtained by said converting means selected by said selecting means, each of said plurality of converting means converting colorimetric values such that observed colors of the color image output by said outputting means under the corresponding illuminant match with colors of the original color image.