1. A method for processing an image, the method comprising: selecting, by an image mapper of an image processing circuit, a gamma curve with a first image having a high dynamic range (HDR) and cumulative minimum luminance error among a plurality of gamma curves corresponding to a display device having a standard dynamic range (SDR) in order to display the first image in the display device by: mapping the first image to each of the gamma curves with different maximum luminance to calculate luminance error for each frame, accumulating the calculated luminance error, and detecting cumulative luminance error for each of the gamma curves; selecting the gamma curve with the cumulative minimum luminance error among the cumulative luminance error of each of the gamma curves; and determining a maximum luminance of the selected gamma curve; and converting, by the image mapper, the first image into a second image having the SDR according to the selected gamma curve by: selecting a look-up table (LUT) corresponding to the determined maximum luminance among preset HDR-to-SDR converting LUTs corresponding to each of the gamma curves; and mapping the first image to the second image using the selected LUT.