While the RGB color model refers to the biological processing of colors in the human visual system, the HSV color model corresponds to the human perception of color similarity. In this paper we formulate a projection of RGB vectors within the RGB color space, which separates achromatic from chromatic information. The projection is the mathematical equivalent to Hue and Saturation of the HSV color space in the RGB space. It integrates the psycho-visual concept of human differentiation between colors of the HSV space into the physiological-visual based concept of the RGB space. With the projection it is, contrary to the prevailing opinion, possible to differentiate between colors based on human perception in the linear geometry of the RGB color space. This opens new possibilities in many fields of color image processing, especially in the domain of color image segmentation, where color similarity plays a major role.