NEW ORIENTATION PROCEDURES

Orientation procedures are preceived as the central part of ph togrammetry. During the last decade the problem of deter mining the interior and the exterior orientation of one or mo re cameras has found high attraction in Computer Vision. The problem was formulated newly within a projective framew ork 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-ca libr tion turned out to be instable, especially in case of im age 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 l ess corresponding points; (5) generating new views from giv en ones turned out ot be possible without calibration; (6) usin g more than two cameras with the same interior orientation was proven to allow selfcalibration, after projective reco nstruction; (7) the epipolar constraint for image pairs tur ned out to be not sufficient for image triplets in practically releva nt cases; last but not least: (8) orientation procedures wer e not documented for non-photogrammetrists in photogrammetric literature. A set of new orientation and calibration procedures has evol v d. The imaging process is described in a projective framework ( SEMPLE & K NEEBONE 1952), explicitely interpreting the 11 parameters of the direct linear transformation, bein g the basis for a direct determination of the 6 parameters of t he exterior and 5 parameters of the interior orientation. Thes e 5 parameters guarantee the projection to map straight line s into straight lines. Cameras with some of these 5 parameters unknown are called uncalibrated. The relative orientation of two cameras with unknown calibr ation can be achieved by a direct solution from corresponding points, leading to the fundamental matrix F, having 7 degrees of freedom, establishing the coplanarity o epipolar constraint as matching constraint, and which can b e used to determine the two principle distances. Restrictio n 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 cali br tion can also be achieved by a direct solution, in this case from corresponding points and lines, leading to the tri focal tensorT, 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 reduc es to a metrical parametrization of the trifocal tensor, wit h 11 degrees of freedom, combining relative orientation of the fi rst two cameras and spatial resection of the third. The paper presents solutions to these problems useful for ph otogrammetric applications.