1. An image correction apparatus comprising: a processor configured to: generate a reduced image which is smaller in number of pixels than an input image; generate a first smoothed image by setting, for each pixel of the reduced image, a filter area including the pixel and performing smoothing without making reference to each reference pixel, in which a difference obtained by subtracting a luminance value of the pixel from a luminance value of the reference pixel becomes greater than or equal to a first predetermined value, among a plurality of reference pixels included in the filter area and by using a luminance value of each of other reference pixels of the plurality of reference pixels; generate a second smoothed image by setting the filter area for each pixel of the reduced image and performing smoothing without making reference to each reference pixel, in which the difference obtained by subtracting the luminance value of the reference pixel from the luminance value of the pixel becomes greater than or equal to a second predetermined value, among the plurality of reference pixels included in the filter area and by using the luminance value of each of other reference pixels of the plurality of reference pixels; generate a smoothed image by calculating, for each pixel of the input image and for each of at least one first pixel of the first smoothed image located surrounding the pixel, a first reference value by making a weight for a higher one of the luminance value of the pixel and the luminance value of the first pixel greater than a weight for other one and performing a weighted addition of the luminance value of the pixel and the luminance value of the first pixel, calculating a second reference value by making a weight for a lower one of a luminance value of a second pixel of the second smoothed image corresponding to the first pixel and the luminance value of the pixel greater than a weight for other one and performing a weighted addition of the luminance value of the pixel and the luminance value of the second pixel, calculating an average of the first reference value and the second reference value as a combined reference value and setting a luminance value obtained by an interpolation using the combined reference value in each of the at least one first pixel as the luminance value of the pixel of the smoothed image corresponding to the pixel of the input image; and generate a corrected image by calculating, for each pixel of the corrected image, the luminance value of the pixel as a value based on a ratio of a luminance value of a corresponding pixel of the input image to a luminance value of a corresponding pixel of the smoothed image.