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Journal for Geometry and Graphics 13 (2009), No. 1, 091--099
Copyright Heldermann Verlag 2009

Orientation Parameters and Reconstruction of Space Models from a Single Photo

Mohammed Elshafei Abdel-Latif
Civil Engineering Department, Faculty of Engineering, Assiut University, Assiut, Egypt

Ahmed A. Elsonbaty
Civil Engineering Department, Faculty of Engineering, Assiut University, Assiut, Egypt

Precise measurements in photogrammetry require the use of metric cameras. But they are too expensive and are not always available. Non-metric cameras are always at hand and have flexibility in focusing range. However, a non-metric camera needs to be calibrated. The determination of its orientation parameters (camera position, image plane, principle point in photo and camera focal length) allows the use of the camera in many fields of photogrammetry. Previous methods used to determine the orientation parameters require at least five control points, and the solution is complicated unless the equations are linearized. Moreover, the reconstruction of the space model is determined through a stereo-pair, i.e., two photos of the object from different positions.
In some cases a reflecting surface such as water, mirror, etc. can be detected in a photo. In the present paper it will be shown that if only four known coplanar points with their images appear in a photo, then the above problem of a non-metric camera can be solved, together with the reconstruction of the space object using only one photo. Here we use a mirror plane (in general position) to reflect the control points and the object and all appear in the photo. The new method is simple and direct and needs no linearization of equations.

Keywords: Close range photogrammetry, projective geometry, affine and collinear transformation, orientation parameters.

MSC: 51N05

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