1. An image processing system comprising: a processor; and a memory; the processor configured to carry out instructions comprising: a first calculating that calculates a contour intensity of a color component of an input color image and calculates an enhancement degree for a color contour, based on the contour intensity of the color component; and a color contour enhancing that performs an enhance process for a lightness component of the color image in accordance with the enhancement degree for the color contour calculated by the first calculating, wherein the first calculating calculates a contour intensity of the lightness component of the color image, and calculates the enhancement degree for the color contour based on the contour intensity of the color component and the contour intensity of the lightness component, the instructions further comprising; a second calculating that calculates an enhancement degree for a lightness contour based on the contour intensity of the color component and the contour intensity of the lightness component calculated by the first calculating; and an enhancing that performs an enhance process for the lightness component of the color image in accordance with the enhancement degree for the lightness contour calculated by the second calculating.