An image processing apparatus reduces a distortion that occurs at a tile boundary (tile distortion) when an image is compressed or expanded on a tile-by-tile basis. It is equipped with a tone jump detecting section, a slope calculating section, and a slope correcting section. The tone jump detecting section calculates differences between the values of pixels on both sides of the tile boundary and detects a tone jump in the tile distortion according to the differences. The slope calculating section calculates slope-like correction values to be used for causing the tone jump to approach zero in a prescribed length ((prescribed length)<(tile length)), and adds the slope-like correction values to the values of pixels near the tile boundary. As a result, the steep tone jump due to the tile distortion is corrected into a gentle slope-like variation. Tile distortions are reduced properly by this processing.