1. An image processing system comprising: distortion correction means for correcting image signals to adjust the distortion in an image; image projection means including a lens unit which has a focus adjustment function, the lens unit projecting an image based on the corrected image signals; drive control means for controlling driving of the lens unit so that a focal length of the lens unit to an image projection area changes; sensing means for sensing the projected image; and distortion correction amount deriving means for deriving the focal length to a center of the image projection area and deriving an amount of distortion correction for the distortion correction means, based on sensing information from the sensing means, wherein the distortion correction amount deriving means determines an optimum focal length to each of a plurality of boundary points in the image projection area, based on a change of luminance in a sensed image according to the sensing information; derives the focal length to the center of the image projection area, based on the optimum focal length to each of the boundary points; derives coordinates of the boundary points in a three-dimensional space, based on the optimum focal length to each of the boundary points and horizontal and vertical half angle-of-views in the image projection means; and derives the amount of distortion correction, based on the coordinates in the three-dimensional space, wherein the distortion correction means corrects the image signals, based on the derived amount of distortion correction, and wherein the drive control means controls the driving of the lens unit so that the focal length of the lens unit becomes the focal length to the center of the image projection area derived by the distortion correction amount deriving means.