Some commonly used color models have their associated cylindrical representations that severely deform the RGB color cube. In this paper, color image processing techniques are studied under a color model that uses the distance from a color point to the gray diagonal of the RGB color cube as a component, thereby forming a cylindrical model that does not deform the color cube. This distance component is closely related to color vividness and can be used as a color processing channel by itself. The space of this cylindrical model is larger than the RGB color cube, so the gamut problem may occur when color processing is not well controlled. This paper introduces a method to solve the gamut problem by compressing color overflow near the boundary of the color cube. This allows free application of conventional processing methods of redistributing the values of a component. With the proposed compressing method, the usual techniques of adjusting the distribution can be used in two components including the intensity component and the distance component without worrying about the gamut problem, providing an effect that is difficult to achieve by other pseudo cylindrical models geometrically deforming the RGB color cube.