1. An image processing apparatus which reduces a tile distortion when an image is compressed or expanded on a tile-by-tile basis, the tile distortion being a distortion that occurs at a tile boundary, the apparatus comprising: a tone jump detecting section calculating differences between values of pixels located on both sides of the tile boundary and detecting a tone jump in the tile distortion according to the differences; a slope calculating section calculating slope-like correction values to be used for causing a value of the tone jump to approach zero in a prescribed length, the prescribed length<tile length; and a slope correcting section correcting the tone jump in the tile distortion into a gentle slope-like variation by correcting values of pixels near the tile boundary using the slope-like correction values.