1. An image processing apparatus comprising: a face detection unit that detects a face region in an image; an eye detection unit that detects an eye region in the image; an evaluation value computation unit that computes an evaluation value for pixels included in the eye region, the evaluation value increased with increase in the redness of a pixel and with decrease in the luminance of a pixel; a luminance computation unit that computes a luminance value for a surrounding region around the eye region in the image and a luminance value for the face region; and a correction unit that corrects a color saturation value for pixels included in the eye region with the use of the evaluation value and the luminance values, wherein the correction unit determines to correct the color saturation value for the pixels included in the eye region when an absolute value of the difference between the luminance value for the surrounding region and the luminance value for the face region is not more than a predetermined value, and determines not to correct the color saturation value for the pixels included in the eye region when the absolute value is more than the predetermined value.