1. An image processing apparatus comprising: a projecting unit configured to project an image; an image capturing unit configured to capture the projected image to generate a captured image; an area identifying unit configured to identify a high-lightness area and a low-lightness area of the captured image; and a correcting unit configured to correct a lightness of the projected image in a manner that gradually changes the lightness of the high-lightness area of the captured image obtained by projecting a white image to the lightness of the low-lightness area of the captured image and sets the lightness thus changed as the lightness of the projected image, wherein the projecting unit projects the projected image having the corrected lightness and an image to prompt a user for a response to the change in the lightness of the projected image.