Method and apparatus for calibrating projector-camera system

An automatic calibration system comprising:

• a camera with a camera image frame and a camera field of view;
• a projector with a source image frame and a projector field of projection;
• a projection surface with a projection image frame;
• a means for performing a feature extraction algorithm;
• and
• a means for mapping parameters utilizing techniques of linear algebra,
• wherein the camera and the projector are arbitrarily placed, a camera field of view of the camera intersects a projector field of projection of the projector on the projection surface, the projector projects an image of a calibration pattern with a plurality of calibration pattern feature points onto the projection surface, the camera captures the image of the calibration pattern, the locations of calibration pattern feature points in the camera image frame of the captured image are identified using the feature extraction algorithm, and the parameters for mapping are obtained, given a location of a calibration pattern feature point in the source image frame and a corresponding location of the calibration pattern feature point in the camera image frame;
• wherein the location of the calibration pattern feature point, i, in the camera image frame is (Xi, Yi), the corresponding location of the calibration pattern feature point in the source image frame is (xi,yi), A i = ( X i Y i 1 0 0 0 - X i ⁢ x i - Y i ⁢ x i - x i 0 0 0 X i Y i 1 - X i ⁢ y i - Y i ⁢ y i - y i ) B = ∑ i ⁢ A i τ ⁢ A i
• the parameters of the mapping are represented by {overscore (p)}=(p1. . . p9), {overscore (p)} is a unit vector resulting in eight degrees of freedom, the {overscore (p)} that best maps the calibration pattern feature point from the camera image frame to the source image frame is given by the eigenvector corresponding to the smallest eigenvalue of the matrix B, and given the mapping {overscore (p)}, any given point (X, Y) in the camera image frame is transformable to its corresponding point (x,y) in the source image frame by the following equation, ( x , y ) = ( p 1 ⁢ X + p 2 ⁢ Y + p 3 p 7 ⁢ X + p 8 ⁢ Y + p 9 , p 4 ⁢ X + p 5 ⁢ Y + p 6 p 7 ⁢ X + p 8 ⁢ Y + p 9 ) .