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<p>By implicit camera calibration, we mean the process of calibrating a camera without explicitly computing its physical parameters. Implicit calibration can be used for both three-dimensional (3-D) measurement and generation of image coordinates. In this paper, we present a new implicit model based on the generalized projective mappings between the image plane and two calibration planes. The back-projection and projection processes are modelled separately to ease the computation of distorted image coordinates from known world points. A set of constraints of perspectivity is derived to relate the transformation parameters of the two calibration planes. Under the assumption of the radial distortion model, we present a computationally efficient method for explicitly correcting the distortion of image coordinates in frame buffer without involving the computation of camera position and orientation. By combining with any linear calibration techniques, this method makes explicit the camera physical parameters. Extensive experimental comparison of our methods with the classic photogrammetric method and Tsai's (1986) method in the aspects of 3-D measurement (both absolute and relative errors), the prediction of image coordinates, and the effect of the number of calibration points, is made using real images from 15 different depth values.</p>
cameras; calibration; camera calibration; 3-D measurement; image coordinate generation; projective mappings; distorted image coordinates; radial distortion model; computationally efficient method; camera position; camera orientation

G. Wei and S. Ma, "Implicit and Explicit Camera Calibration: Theory and Experiments," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 16, no. , pp. 469-480, 1994.
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