Camera self-calibration: Theory and experiments
The problem of finding the internal orientation of a camera (camera calibration) is extremely important for practical applications. In this paper a complete method for calibrating a camera is presented. In contrast with existing methods it does not require a calibration object with a known 3D shape. The new method requires only point matches from image sequences. It is shown, using experiments with noisy data, that it is possible to calibrate a camera just by pointing it at the environment, selecting points of interest and then tracking them in the image as the camera moves. It is not necessary to know the camera motion.
The camera calibration is computed in two steps. In the first step the epipolar transformation is found. Two methods for obtaining the epipoles are discussed, one due to Sturm is based on projective invariants, the other is based on a generalisation of the essential matrix. The second step of the computation uses the so-called Kruppa equations which link the epipolar transformation to the image of the absolute conic. After the camera has made three or more movements the Kruppa equations can be solved for the coefficients of the image of the absolute conic. The solution is found using a continuation method which is briefly described. The intrinsic parameters of the camera are obtained from the equation for the image of the absolute conic.
The results of experiments with synthetic noisy data are reported and possible enhancements to the method are suggested.
- R. Deriche and G. Giraudon. Accurate corner detection: An analytical study. In Proceedings ICCV, 1990.
- Rachid Deriche and Olivier D. Faugeras. Tracking Line Segments. Image and vision computing, 8(4):261–270, November 1990. A shorter version appeared in the Proceedings of the 1st ECCV.
- O.D. Faugeras. Three-dimensional computer vision. MIT Press, 1992. To appear.
- O.D. Faugeras and G. Toscani. The calibration problem for stereo. In Proceedings of CVPR'86, pages 15–20, 1986.
- C. Harris and M. Stephens. A combined corner and edge detector. In Proc. 4th Alvey Vision Conf., pages 189–192, 1988.
- O. Hesse. Die cubische Gleichung, von welcher die Lösung des Problems der Homographie von M. Chasles abhängt. J. reine angew. Math., 62:188–192, 1863.
- T.S. Huang and O.D. Faugeras. Some properties of the e matrix in two view motion estimation. IEEE Proc. Pattern Analysis and Machine Intelligence, 11:1310–1312, 1989.
- H.C. Longuet-Higgins. A Computer Algorithm for Reconstructing a Scene from Two Projections. Nature, 293:133–135, 1981.
- S.J. Maybank and O.D. Faugeras. A Theory of Self-Calibration of a Moving Camera. The International Journal of Computer Vision, 1992. Submitted.
- Rudolf Sturm. Das Problem der Projektivität und seine Anwendung auf die Flächen zweiten Grades. Math. Ann., 1:533–574, 1869.
- G. Toscani, R. Vaillant, R. Deriche, and O.D. Faugeras. Stereo camera calibration using the environment. In Proceedings of the 6th Scandinavian conference on image analysis, pages 953–960, 1989.
- Roger Tsai. An Efficient and Accurate Camera Calibration Technique for 3D Machine Vision. In Proceedings CVPR '86, Miami Beach, Florida, pages 364–374. IEEE, June 1986.
- C.W. Wampler, A.P. Morgan, and A.J. Sommese. Numerical continuation methods for solving polynomial systems arising in kinematics. Technical Report GMR-6372, General Motors Research Labs, August 1988.
- Camera self-calibration: Theory and experiments
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- Computer Vision — ECCV'92
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- Second European Conference on Computer Vision Santa Margherita Ligure, Italy, May 19–22, 1992 Proceedings
- pp 321-334
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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