1. An image processing method for correcting, on a pixel-by-pixel basis, brightness of an original image which includes pixels having pixel values each related to brightness, the image processing method comprising: (a) generating coefficients corresponding to pixels of a reduced image of the original image, using a predetermined relation for a pixel value of a current pixel to be processed, a brightness state related to brightness of a portion surrounding the current pixel, and a coefficient for correcting the pixel value of the current pixel; and (b) generating coefficients corresponding to the pixels of the original image from the coefficients corresponding to the pixels of the reduced image, to expand the coefficients corresponding to the pixels of the reduced image to the coefficients corresponding to the pixels of the original image, and correcting the pixel values of the pixels of the original image using the coefficients corresponding to the pixels of the original image, wherein in step (b), the coefficients corresponding to the pixels of the reduced image are expanded to the coefficients corresponding to the pixels of the original image by performing, on the coefficients corresponding to the pixels of the reduced image one or more times, expansion processing of expanding coefficients from coefficients corresponding to pixels of a first image to coefficients corresponding to pixels of a second image larger than the first image, and step (b) further includes limiting, to a limit range according to the predetermined relation, at least one of (i) a coefficient corresponding to a pixel of the pixels of the second image in at least one of the one or more times the expansion processing is performed or (ii) a corrected pixel value of the corrected pixel values of the pixels of the original image.