1. An image processing method for correcting, on a pixel-by-pixel basis, brightness of an original image which includes pixels that have greater pixel values when the pixels have higher brightness, the image processing method comprising: (a) generating coefficients corresponding to pixels of a reduced image of the original image by generating a greater coefficient for each of the pixels of the reduced image when a portion surrounding the pixel of the reduced image is darker; (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 (c) multiplying, for each of the pixels of the original image, a pixel value of the pixel of the original image by one of the coefficients corresponding to the pixel of the original image, to correct the pixel values of the pixels of the original image, wherein: in step (b), the coefficients corresponding to the pixels of the original image are generated such that a spatial change of the coefficients corresponding to the pixels of the original image is caused according to a boundary between a bright portion and a dark portion included in the original image, the spatial change occurring on an area having a center located on a dark side of the boundary, 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 in at least one of the one or more times the expansion processing is performed, (i) two or more weights are assigned to two or more of the pixels of the first image by assigning a weight to each of the two or more of the pixels of the first image such that the smaller a difference between a pixel value of the pixel of the first image and a pixel value obtained by increasing a pixel value of one of the pixels of the second image is, the greater the weight is, and (ii) among the coefficients corresponding to the pixels of the second image, a coefficient corresponding to the one of the pixels of the second image is generated from two or more coefficients corresponding to the two or more of the pixels of the first image among the coefficients corresponding to the pixels of the first image, using the two or more weights assigned to the two or more of the pixels of the first image.