1. An image processing apparatus comprising: means for calculating luminance domain information representing a width of a luminance distribution of a first frame of an image; means for smoothing the luminance domain information by using a predetermined weight, a multiplication operation, and a summing operation on the luminance domain information of the first frame to be smoothed and the luminance domain information of a plurality of frames of the image having a time-sequence relationship with the first frame to calculate a smoothed luminance domain information, and outputting the smoothed luminance domain information; and means for normalizing luminance of the image in accordance with a luminance range of a display displaying the image, based on the smoothed luminance domain information.