1. An image processing apparatus comprising: a processor configured to, project an image; capture the projected image to generate a captured image; identify a high-lightness area and a low-lightness area of the captured image; correct a lightness of the projected image in an iterative process by, determining a first lightness of the low-lightness area of the captured image, adjusting a lightness of the captured image, projecting another image with the adjusted lightness, capturing the other projected image with the adjusted lightness, determining a second lightness of the high-lightness area of the captured other projected image, and correcting the lightness of the projected image based on the determined first lightness and the determined second lightness such that upon completion of the iterative process the second lightness of the high-lightness area is adjusted to correspond to the first lightness of the low-lightness area, and project the projected image having the corrected lightness and an image to prompt a user to provide an input indicating whether the changed lightness of the projected image is acceptable or not.