Non‐metamerism of boundary colors in multi‐primary displays

Abstract— A control sequence gives the intensities of the primaries for a pixel of a display device. The display gamut, i.e., the set of all the colors that a display can produce, is a zonohedral subset of CIE XYZ space and contains both boundary and interior colors. Displays with four primaries or more exhibit metamerism, in which different control sequences produce colors that appear identical to an observer. This paper shows mathematically that, provided no three primaries are linearly dependent, metamerism can only occur for interior colors. When there are four or more primaries, metamers can always be found for interior colors. A color on the gamut boundary, by contrast, is only produced by a unique control sequence. The proof used for displays can be extended to object‐color solids, to show that optimal colors, which are on the boundary of an object‐color solid, have unique reflectance functions.