Images are an essential element in the growing domain of worldwide “Multimedia networking”. Several image-related problems arise which apply to this domain. For instance, when one or more images is inserted in a document, adjustments of the tone of color, enhancement, halftoning, gauzying, transforming low key or high key images and removal of staircasing shaped distortion along contours will be necessary. Especially the staircasing shaped distortion should be more strictly removed in the display of rotating 3D objects.In such complicated image processing as described above, it is necessary that humans perceive the deterioration of color directly, and consequently that image processing should be handled in a color space which directly represents the three attribute of human color perception: hue, value and chroma. It is also necessary that processing is monitored by the color difference or a function of color difference between the original and the processed image. The function of the color difference we define to be the “Picture Quality Scale” (PQS).In order for the measured color difference to be proportional to the perceived color difference, we have introduced the ULCS (Uniform Lightness-Chromaticness Scale system). In ULCS a color difference is defined by the Euclidean distance in the color space. As a representative of ULCS we have selected the Munsell Renotation System [Figure 1]. The transformation from an RGB image to an HVC image in the Munsell Renotation System depends on the look up table and which have a corresponding mathematical formula as is shown in the L*a*b*. However we have developed a mathematical transformation from an R,G,B color to the corresponding H,V,C (Hue, Value, Chroma) color which closely approximates the color of the Munsell Renotation System. We have named the new mathematical transformation MTM (a Mathematical Transform to Munsell Renotation System). The maximum approximation error of the color space transformed by MTM to the Munsell Renotation System is 0.59 in National Bureau of Standards unit (NBS).Using MTM we have shown the quantization precision; the quantization accuracy of R, G and B signals should be not less than 14, 16 and 12 bits for linear quantization and 10, 12 and 9 bits for non-linear quantization (gamma = 3.0) respectively in order to keep the color difference of quantization errors smaller than 1NBS unit. MTM is applicable to many kinds of color image processing and is especially effective in the discussion of device independent color image processing.