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reverse projection transformation is required to map the image to world coordinates so that the interface location is determined in physical dimensions.

    For this purpose, a calibration image is obtained with the camera. In the calibration image, the world coordinates of specific points in the image are known. In this case, the calibration image is a series of squares whose vertices are known in world coordinates. The lines of the square that are captured by the camera are at least 5 pixels thick. Projection transformation (camera view) of these squares will transform parallel lines into lines that intersect at some point within or outside the image. The "n" number of intersection points defines the projection transformation as an "n" point projection. Since the image is of a plane as a pixel map in this case, the projection is a two-point projection. The camera view (transformed) and the reverse projection transformation of the calibration image are shown in Figure 4-9. The transformation is achieved by means of trial and error by ensuring the quadrilaterals are mapped to rectangles whose vertices have a pixel difference of less than 1.


    150                                      150
    U)                                     U)
    a)                                     a)
    .x250                                  x250

    350                                      350
       300   400   500   600   700    800      300   400   500   600    700   800
                    X pixels                                Xpixels

    Figure 4-9 Projection transformation and reverse projection transformation of the calibration image.

    The following transformation matrix achieves the desired result: