Image resituation: initial theory

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Abstract
An important step in many photogrammetry problems is to determine the intrinsic and extrinsic parameters associated with image formation, a process we shall term image resituation. An ideal photogrammetric system would be able to compute these parameters for an arbitrary nubmer of images using only the automatically determined coordinates of homologous points. While such a system has yet to be developed, this paper formulates a relatively general image resituation problem and presents some new solutions in the two-image case. The approach recasts the stereo coplanarity equation, including unknown intrinsic parameters, into a quandratic form defining a general coplanarity matrix. This leads to a system from which up to seven free imaging parameters can be determined. We consider the situation in which two images are captured using adaptive cameras, where the focal length and principal point may differ in each image, but are always in a known relationship to each other. We show that the unknown two focal lengths and five relative orientation parameters can be derived in closed-form from the general coplanarity matrix. A numerial example is provided to illustrate the approach. These results contibute to the long-term goal of developing a photogrammetric system able to operate in the absence of object-space control information. A companion paper describes more detailed algorithms and experiments.

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