1. An image processing apparatus comprising: means for calculating luminance domain information representing a width of a luminance distribution of an image; means for smoothing in time sequence the luminance domain information calculated by the luminance domain information calculating means to output 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 outputted from the luminance domain information smoothing means.