In an image processing method for reducing an input image while preventing moire without deterioration of image quality, presence/absence of periodicity is detected for each pixel on the input image, and if there is periodicity, an image period is detected (S4). Sample points are sequentially extracted from the input image at prescribed sampling intervals (S5). A value is obtained by multiplying the image period by n (n is a natural number) that exceeds the sampling interval, to set a smoothing area. Pixels around a sample point is smoothed in the set smoothing area. The pixel value for a reduced image is obtained (S6). If there is an unprocessed sample point (NO at S8), the step goes back to S6, and the next sample point is subjected to a similar process. If the process is terminated for all the sample points (YES at S8), the reduced image is output.