1. An image processor comprising: a detection unit for sequentially scanning pixel lines of an image signal that is received as input to detect linear interpolation application regions, which are regions in which gray-level changes are to be smoothed for each line of said image signal; an extension-correction unit for carrying out a gray-level extension process upon said linear interpolation application regions that have been detected in said detection unit; and a gray-level-change limitation unit for limiting, to within prescribed values, gray-level changes in a second direction that differs from the direction in which said detection unit carried out the detection process for regions in which said gray-level extension process has been implemented.