1. A method for modifying an input digital image having one or more color channels, each color channel having an (x,y) array of image pixel values, to form a modified digital image comprising the steps for: a) computing a transformed digital image responsive to the input digital image, wherein the transformed digital image contains at least a black color channel and one or more additional color channels, each such channel having pixel values; b) computing a color dependent scale factor channel responsive to the image pixel values of the transformed digital image to produce color dependent scale factor image pixel values; c) computing a filtered black color channel from the black color channel using a convolution operation to produce filtered black image pixel values; and d) forming the modified digital image by modifying image pixel values in one or more of the additional color channels of the transformed digital image in response to the corresponding color dependent scale factor image pixel values and the corresponding filtered black image pixel values, so that when the modified digital image is used to produce a printed image on an inkjet printer, there are reduced ink bleed artifacts, wherein the process of forming the modified digital image includes: i) determining pixel-dependent scale factor(s) for the one or more additional color channels in response to the corresnonding filtered black image pixel values and the color dependent scale factor; and ii) scaling the image pixel values for the one or more additional color channels using the pixel-dependent scale factor(s) to determine the modified image pixel values.