A regulated black colorant amount calculating section calculates a corresponding regulated black colorant amount from the L*a*b* of a plurality of typical color signals in a partial color gamut, which can be represented by three colors excluding black. An optimum black colorant amount modeling section performs color prediction modeling to predict an optimum black colorant amount in a whole color gamut from plural sets of the typical color signal and the regulated black colorant amount. At this time, an extrapolation prediction from a color in a partial color gamut to a whole color gamut is performed to predict the optimum black colorant amount in which a natural color reproduction. By using the color prediction modeling, the optimum black colorant amount determining section determines a corresponding optimum black colorant amount from the L*a*b* of an input lattice point. a YMCK signal calculating section determines residual YMC and outputs a YMCK signal.