1. A color conversion apparatus for converting first image data to second image data, the first and second image data both describing an image with a plurality of picture elements (pixels), the first image data having first color data with three values per pixel, the three values expressing, respectively, red, green, and blue components of the pixel, the second image data having second color data with at least four values per pixel, the color conversion apparatus comprising: means for calculating characteristic information of the first color data; means for calculating, from the first color data, a plurality of first hue region data values valid in respective hue regions surrounding certain predetermined hues; means for using the characteristic information to adjust magnitudes of the plurality of the first hue region data values to obtain, for at least some of the hue regions, second to N-th hue region data values, wherein N is an integer equal to or greater than three; coefficient generating means for generating prescribed matrix coefficients for the second to N-th hue region data values; and matrix operation means for calculating the second color data by performing a matrix operation including multiplication of the second to N-th hue region data values by the matrix coefficients.