New Orientation Procedures

Orientation procedures are preceived as the central part of photogrammetry. During the last decade the problem of determining the interior and the exterior orientation of one or more cameras has found high attraction in Computer Vision. The problem was formulated newly within a projective framework for several reasons: (1) often, the calibration of the cameras in use was not known, nor could be determined; (2) often, no approximate values for the orientation and calibration parameters were available; (3) often, self-calibration turned out to be instable, especially in case of image sequences or of variable focal length; (4) special boundary conditions, such as planar objects or the coplanarity of the projection centres allowed orientation and calibration with less corresponding points; (5) generating new views from given ones turned out ot be possible without calibration; (6) using more than two cameras with the same interior orientation was proven to allow selfcalibration, after projective reconstruction; (7) the epipolar constraint for image pairs turned out to be not sufficient for image triplets in practically relevant cases; last but not least: (8) orientation procedures were not documented for non-photogrammetrists in photogrammetric literature. A set of new orientation and calibration procedures has evolved. The imaging process is described in a projective framework (SEMPLE & KNEEBONE 1952), explicitely interpreting the 11 parameters of the direct linear transformation, being the basis for a direct determination of the 6 parameters of the exterior and 5 parameters of the interior orientation. These 5 parameters guarantee the projection to map straight lines into straight lines. Cameras with some of these 5 parameters unknown are called uncalibrated. The relative orientation of two cameras with unknown calibration can be achieved by a direct solution from corresponding points, leading to the fundamental matrix F, having 7 degrees of freedom, establishing the coplanarity or epipolar constraint as matching constraint, and which can be used to determine the two principle distances. Restriction to calibrated cameras, F reduces to the essential matrix E with 5 degrees of freedom, already known in photogrammetry. The relative orientation of three cameras with unknown calibration can also be achieved by a direct solution, in this case from corresponding points and lines, leading to the trifocal tensor T, having 18 degrees of freedom. It establishes matching constraints for points and straight lines, and can be used to determine a part of the calibration parameters of the three cameras. Restriction to calibrated cameras reduces to a metrical parametrization of the trifocal tensor, with 11 degrees of freedom, combining relative orientation of the first two cameras and spatial resection of the third. The paper presents solutions to these problems useful for photogrammetric applications.