1. An image processor comprising: a detection unit that sequentially scans 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 that carries 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 that limits, 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, wherein said gray-level-change limitation unit, as a process for limiting said gray-level changes to within prescribed values, carries out a spatial averaging process that takes, as the gray-level value of the pixel of interest, the average value of the gray-level value of the pixel that is the object of processing and the gray-level values of pixels that are adjacent in said second direction.