The relation between dither matrix and a pair of orthogonal generalized Latin squares

The dither matrix has been extensively applied in image processing, color matching and other aspects. In the paper, a new concept is put forward about the generalized Latin square and a mathematical description of the dither matrix, the counting formula of the generalized Latin square and a pair of orthogonal generalized Latin squares are given. The necessary and sufficient conditions of two orthogonal generalized Latin squares are presented and one-to-one correspondence relation of two sets between dither matrix and a pair of orthogonal generalized Latin squares are established by studying the generalized Latin squares. So the study of dither matrix can be transformed to that of a pair of orthogonal generalized Latin squares.