1. An image processing apparatus comprising: an image input device for accepting input of applied image data; a color bleed determining device for determining whether a pixel of interest in the image data exhibits color bleed; a luminance monotonic decrease direction discriminating device for discriminating, in a case where said color bleed determining device has determined that the pixel of interest exhibits color bleed, a direction in which luminance is monotonically decreasing, using the pixel of interest as a starting point, in the neighborhood of the pixel of interest; a luminance monotonic decrease end pixel search device for finding a pixel, at which the monotonic decrease in luminance ends, in the direction in which luminance is monotonically decreasing discriminated by said luminance monotonic decrease direction discriminating device; a target pixel deciding device for deciding upon the luminance monotonic decrease end pixel, which has been found by said luminance monotonic decrease end pixel search device, as a target pixel; a color correction value calculating device for calculating a correction value that corrects color of the pixel of interest to the color of the target pixel decided by said target pixel deciding device a color correcting device for correcting the color of the pixel of interest using the color correction value calculated by said color correction value calculating device; and a distance calculating device for calculating, in a case where a plurality of directions of luminance monotonic decrease have been discriminated by said luminance monotonic decrease direction discriminating device, distances between the pixel of interest and a plurality of luminance monotonic decrease end pixels found in every direction of luminance monotonic decrease by said luminance monotonic decrease end pixel search device; wherein said target pixel deciding device decides, in accordance with the distances calculated by said distance calculating device, that a luminance monotonic decrease end pixel closest to the pixel of interest is the target pixel from among the plurality of luminance monotonic decrease end pixels found by said luminance monotonic decrease end pixel search device.