1. An image processing apparatus comprising: a gradient detection unit configured to detect a gradient value from an image; a suppression coefficient calculation unit configured to calculate a suppression coefficient based on the gradient value; a suppression unit configured to perform image processing to suppress color blur in a suppression target area in the image based on the suppression coefficient; and a gamma correction unit configured to perform gamma correction according to gamma correction characteristics set for the image, wherein the gamma correction characteristics are set such that a ratio of a change width of an output signal to a change width of an input signal when a brightness signal level is in a first range is larger than a ratio of a change width of an output signal to a change width of an input signal when the brightness signal level is in a second range, and the suppression coefficient calculation unit calculates the suppression coefficient so as to cause color blur only in the suppression target area to be suppressed when the gradient value exceeds a threshold value, and sets the threshold value such that a range of the gradient value required to suppress color blur in an area where the brightness signal level is included in the second range in the image is narrower than a range of the gradient value required to suppress color blur in an area where the brightness signal level is included in the first range in the image.