Determination of three-dimensional positions of known sparse objects from a single projection

A new technique is developed for accurate determination of the three-dimensional position and orientation of known sparse objects, e.g., a configuration of points, from a single-perspective projection. In this technique, a computer model of the known object is translated and rotated so as to align it optimally in a least-squares sense with the projection lines connecting the image points with the focal spot by using a modification of the projection-Procrustes technique. The translational and rotational adjustments are repeated iteratively until the angular change between iterations is less than 0.25 degree. Simulations indicate that, for rms input image errors of 0.03 cm, the three-dimensional positions and orientations can be determined to within approximately 0.2 cm and 0.3 degree for a wide range of initially guessed positions and orientations, and positions can be determined with an accuracy of approximately 0.3 cm for objects having as few as four points. In phantom experiments, three-dimensional positions and orientations of a cube phantom were reproducibly determined to within 0.23 cm and 0.13 degree. The entire calculation requires only 10 s on a VAX 3500 to converge to the solution. The accuracy, precision, and speed of the technique indicate that it will be a useful tool for determination of three-dimensional positions and orientations of known sparse objects.