An image processor is provided with the high-frequency component detecting unit that calculates a convolution for each of regions of interest in part of an image region of input image data, to output the high-frequency component detection result for each pixel of interest; the smoothing unit that smoothes the image data, to output the smoothed image data; and the image data processing unit that combines based on the high-frequency component detection result the image data with the smoothed image data, to output the combined image data; wherein the image data processing unit varies the combination rate for the smoothed image data, based on the high-frequency component detection result. Thereby, even when a region in the image data contains such high frequency components as a checkered pattern has, an image resistant to moiré that would be generated in magnifying or reducing of the image on a region basis can be displayed without deterioration of image quality.