the same as the one used in the vertical direction the two matrices could be different due to the presence of anisotropy in the image and the fact that the aspect ratio is not 1 1 the zone of influence of a pixel is defined as the minimum distance needed so that pixels with distance greater to this minimum distance are not correlated with the pixel the dimension of the transformation matrix is selected to be such that the auto correlation function between two pixels with distance equal to the dimension is greater than or equal to r where r is less than 1 and greater than 0 5 if the horizontal transformation matrix is h then coefficients of the matrix h are computed so that the matrix h is stochastically orthonormal under the assumption of wide sense stationarity the expected value of all bands except for the low band is equal to zero the object is to find the parameters a ij ij 1 2 3 n j 1 2 3 n which maximizes the variance of the low band minimizes the variance of all other bands and satisfies the above constraints a similar approach is used for the vertical transformation this approach is used for each one of the color channels the quantization matrix is designed to give one of two options the.