1. An image processing apparatus that processes a color image composed of color signals of a plurality of colors, the apparatus comprising a hardware processor which performs functions of: a tone correcting section that performs different tone corrections on pixels at different positions in the color image; a false contour detecting section that calculates a degree of false contour occurrence for the color image based on a difference in signal saturation level between the color signals; and a controlling section that controls characteristics of the tone corrections based on a result of the calculation by the false contour detecting section such that a tone correction curve that determines the tone correction characteristics for each pixel varies moderately in a saturated area.