1. An image processing apparatus configured to correct at least part of a face image, comprising: an image acquisition unit that acquires an input image; a region extraction unit that extracts a pupil region, which is a region corresponding to an eye of a person, from the input image; a pixel extraction unit that extracts a pixel from the pupil region whose brightness value is higher than a threshold value; a determination unit that determines, based on the result of extraction performed by the pixel extraction unit, whether or not halation has occurred in the pupil region; and a correction unit that performs, based on the result of determination performed by the determination unit, processing for correcting halation on the pupil region, wherein the pixel extraction unit sets the threshold value based on a bias of a brightness distribution of the pixels included in the pupil region, wherein the threshold value is a value according to which the brightness distribution of the pixels included in the pupil region is separated into a high brightness class and a low brightness class, wherein the determination unit calculates a degree of separation, which is a ratio between an intra-class variance and an inter-class variance in the brightness distribution of the pixels included in the pupil region and sets the threshold value to a value according to which the degree of separation is maximized, and wherein, if the degree of separation is less than or equal to a predetermined value and the average of the brightness values of the pixels included in the pupil region is greater than or equal to the predetermined value, the correction unit performs halation correction processing regardless of the result of the determination performed by the determination unit.