By sequentially scanning pixel lines of an image signal that has been received as input linear interpolation application regions, which are regions in which gray-level changes are to be smoothed, are detected for each line of the input signal, and the detected linear interpolation application regions are then subjected to an gray-level extension process. The regions that have been subjected to the gray-level extension process are further subjected to a process of limiting, to within prescribed values, gray-level changes in a second direction that differs from the direction in which the linear interpolation application region detection process was carried out.