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By implicit camera calibration, we mean the process of calibrating cameras without explicitly computing their physical parameters. We introduce a new implicit model based on a generalized mapping between an image plane and multiple, parallel calibration planes (usually between four to seven planes). This paper presents a method of computing a relationship between a point on a three-dimensional (3D) object and its corresponding two-dimensional (2D) coordinate in a camera image. This relationship is expanded to form a mapping of points in 3D space to points in image (camera) space and visa versa that requires only matrix multiplication operations. This paper presents the rationale behind the selection of the forms of four matrices and the algorithms to calculate the parameters for the matrices. Two of the matrices are used to map 3D points in object space to 2D points on the CCD camera image plane. The other two matrices are used to map 2D points on the image plane to points on user defined planes in 3D object space. The mappings include compensation for lens distortion and measurement errors. The number of parameters used can be increased, in a straight forward fashion, to calculate and use as many parameters as needed to obtain a user desired accuracy. Previous methods of camera calibration use a fixed number of parameters which can limit the obtainable accuracy and most require the solution of nonlinear equations. The procedure presented can be used to calibrate a single camera to make 2D measurements or calibrate stereo cameras to make 3D measurements. Positional accuracy of better than 3 parts in 10,000 have been achieved. The algorithms in this paper were developed and are implemented in MATLABR (registered trademark of The Math Works, Inc.). We have developed a system to analyze the path of optical fiber during high speed payout (unwinding) of optical fiber off a bobbin. This requires recording and analyzing high speed (5 microsecond exposure time), synchronous, stereo images of the optical fiber during payout. A 3D equation for the fiber at an instant in time is calculated from the corresponding pair of stereo images as follows. In each image, about 20 points along the 2D projection of the fiber are located. Each of these 'fiber points' in one image is mapped to its projection line in 3D space. Each projection line is mapped into another line in the second image. The intersection of each mapped projection line and a curve fitted to the fiber points of the second image (fiber projection in second image) is calculated. Each intersection point is mapped back to the 3D space. A 3D fiber coordinate is formed from the intersection, in 3D space, of a mapped intersection point with its corresponding projection line. The 3D equation for the fiber is computed from this ordered list of 3D coordinates. This process requires a method of accurately mapping 2D (image space) to 3D (object space) and visa versa.3173
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