1. An image processing apparatus comprising: a calculating unit that sequentially selects pixels as a target pixel, on binary image data composed of a plurality of color plates for each printing color after having been subjected to halftone-dot processing, and calculates a characteristic amount in each of a plurality of preset areas around the selected target pixel on the basis of states of pixels in the areas; a determination unit that determines, on the basis of the characteristic amount in each of the areas calculated by the calculating unit, whether or not the target pixel is a pixel to be subjected to overlay processing; a decision unit that decides, for each of the color plates, a position of a pixel to be referred to when changing a pixel value of the target pixel, on the basis of a halftone-dot processing attribute for each of the color plates; and a changing unit that, if it is determined by the determination unit that the target pixel is the pixel to be subjected to the overlay processing, changes the pixel value of the target pixel of the image data of the color plate for a printing color to be changed in pixel value in the overlay processing, to a pixel value at the position decided by the decision unit.