For both 3-D reconstruction and prediction of image coordinates, cameras can be calibrated implicitly without involving their physical parameters. The authors present a two-plane method for such a complete calibration, which models all kinds of lens distortions. First, the modeling is done in a general case without imposing the pinhole constraint. Epipolar curves considering lens distortions are introduced and are found in a closed form. Then, a set of constraints of perspectivity is derived to constrain the modeling process. With these constraints, the camera physical parameters can be related directly to the modeling parameters. Extensive experimental comparisons of the methods with the classic photogrammetric method and Tsai's method relating to the aspects of 3-D measurement, the effect of the number of calibration points, and the prediction of image coordinates, are made using real images from 15 different depth values.
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