1. An image processing device comprising: an extraction unit that extracts low-intensity pixels, which have intensity equal to or less than a specified intensity, from a digital image of an eye; an assignment unit that sequentially selects the low-intensity pixels that were extracted by the extraction unit, and sequentially assigns specified values to each pixel that is within a specified distance from the selected low-intensity pixels; and a setting unit that, based on a value that is totaled for each pixel of values that are assigned to the pixels, sets a reference pixel that corresponds to the center of the pupil of the eye.