1. A color image processing method comprising the steps of: edge-detection of a digital color original image obtained by digitally inputting a single side of a document color-printed on both sides of paper; estimating background color of said paper or background color image on said single side with respect to a portion with low intensity of said detected edge; performing color threshold processing in which said portion with the low edge intensity as a component corresponding to the show-through is replaced with said estimated background color or background color image in said original image; and generating a show-through removed image as an image from which the component corresponding to the show-through has been removed.