1. An image projection system for projecting a single image on an image projection region by projecting images on different sub-regions within the image projection region from a plurality of image projection sections, the system comprising: an image-taking section configured to take, via a lens, an image of a checkered sheet placed in the image projection region; a correction section configured to correct lens-induced distortion of the taken checkered sheet image by using an internal parameter of the image-taking section; a checker intersection coordinate detection section configured to detect, with sub-pixel precision, checker intersection coordinates in the corrected checkered sheet image; a first transformation matrix calculation section configured to calculate a first projective transformation matrix for projective transformation of the detected checker intersection coordinates into checker intersection coordinates located at equal or substantially equal intervals in the image projection region; a generation section configured to correct, when first positive images and first negative images of an 8-bit vertical Gray code pattern projected on a first sub-region of the image projection region from a given one of the image projection sections are taken by the image-taking section, lens-induced distortion of the taken first positive images and first negative images by using the internal parameter of the image-taking section, and generate a first spatial code image whose code value changes in a lateral direction based on the corrected first positive images and first negative images, and to correct, when second positive images and second negative images of an 8-bit horizontal Gray code pattern projected on the first sub-region from the given image projection section are taken by the image-taking section, lens-induced distortion of the taken second positive images and second negative images by using the internal parameter of the image-taking section, and generate a second spatial code image whose code value changes in a longitudinal direction based on the corrected second positive images and second negative images; a boundary coordinate acquisition section configured to obtain, with sub-pixel precision, an intersection of brightness profiles in the corrected first positive images and first negative images, and obtain, with sub-pixel precision, an intersection of brightness profiles in the corrected second positive images and second negative images, thus acquiring the obtained intersections as boundary coordinates; an intersection acquisition section configured to acquire, based on the acquired boundary coordinates, a first boundary line connecting the boundary coordinates of the same code value in the first spatial code image, acquire, based on the acquired boundary coordinates, a second boundary line connecting the boundary coordinates of the same code value in the second spatial code image, and combine the first and second spatial code images, thus acquiring first intersection coordinates of the first and second boundary lines; a second transformation matrix calculation section configured to transform the acquired first intersection coordinates by using the first projective transformation matrix, and calculate a second projective transformation matrix for projective transformation of the transformed first intersection coordinates into second intersection coordinates distributed over the entire first sub-region; and an image data correction section configured to transform, using the second projective transformation matrix, image data to be outputted to the given image projection section, thus correcting the image data; wherein the second transformation matrix calculation section is configured to transform the first intersection coordinates transformed by using the first projective transformation matrix and the second intersection coordinates to be distributed over the entire first sub-region into coordinates of a local coordinate system specific to the given image projection section, and then calculate the second projective transformation matrix.