Geometric interpretations of the relation between the image of the absolute conic and sphere images

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 28, Issue 12, 2006, Pages 2031-2036

  Ying, Xianghua ^a   Zha, Hongbin ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Camera calibration; Double contact theorem; Geometric interpretation; Image of the absolute conic; Sphere image

Indexed keywords

CAMERAS; IMAGE PROCESSING; LINEAR ALGEBRA; PATTERN RECOGNITION; PROJECTION SYSTEMS;

CAMERA CALIBRATION; DOUBLE-CONTACT THEOREM; GEOMETRIC INTERPRETATION; IMAGE OF THE ABSOLUTE CONIC; SPHERE IMAGE;

COMPUTATIONAL GEOMETRY;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; COMPUTER ASSISTED DIAGNOSIS; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; THREE DIMENSIONAL IMAGING;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; INFORMATION STORAGE AND RETRIEVAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 33947097614     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2006.245     Document Type: Article

References (20)

1. M. Agrawal and L.S. Davis, "Camera Calibration Using Spheres: A Semi-Definite Programming Approach," Proc. Ninth Int'l Conf. Computer Vision, pp. 782-791, 2003.
2. P. Beardsley, D. Murray, and A. Zisserman, "Camera Calibration Using Multiple Images," Proc. Second European Conf. Computer Vision, pp. 312-320, 1992.
3. K. Daniilidis and J. Ernst, "Active Intrinsic Calibration Using Vanishing Points," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 708-713, 1996.
4. N. Daucher, M. Dhome, and J. Lapresté, "Camera Calibration from Spheres Images," Proc. Third European Conf. Computer Vision, pp. 449-454, 1994.
5. C.J.A. Evelyn, G.B. Money-Coutts, and J.A. Tyrrell, The Seven Circles Theorem and Other New Theorems. Slacey Int'l, 1974.
6. A. Fitzgibbon, M. Pilu, and R. Fisher, "Direct Least Square Fitting of Ellipses," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 476-480, May 1999.
7. R. Hartley, "An Algorithm for Self-Calibration from Several Views," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 908-912, 1994.
8. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision. Cambridge Univ. Press, 2000.
9. K. Kanatani and W. Liu, "3D Interpretation of Conies and Orthogonality," Computer Vision and Image Understanding, vol. 58, no. 3, pp. 286-301, 1993.
10. J. Kim, P. Gurdjos, and I. Kweon, "Geometric and Algebraic Constraints of Projected Concentric Circles and Their Applications to Camera Calibration," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 4, pp. 637-642, Apr. 2005.
11. S. Maybank and O. Faugeras, "A Theory of Self-Calibration of a Moving Camera," Int'l J. Computer Vision, vol. 8, no. 2, pp. 123-151, 1992.
12. M. Penna, "Camera Calibration: A Quick and Easy Way to Determine the Scale Factor," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 12, pp. 1240-1245, Dec. 1991.
13. M. Pollefeys, R. Koch, and L. Van Gool, "Self-Calibration and Metric Reconstruction in Spite of Varying and Unknown Internal Camera Parameters," Proc. Sixth Int'l Conf. Computer Vision, pp. 90-95, 1998.
14. J. Semple and G. Kneebone, Algebraic Projective Geometry-Oxford Science, 1952.
15. P. Sturm and S. Maybank, "On Plane-Based Camera Calibration: A General Algorithm, Singularities and Applications," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 432-437, 1999.
16. H. Teramoto and G. Xu, "Camera Calibration by a Single Image of Balls: From Conics to the Absolute Conic," Proc. Asian Conf. Computer Vision, pp. 499-506, 2002.
17. B. Triggs, "Autocalibration and the Absolute Quadric," Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 609-614, 1997.
18. R.Y. Tsai, "A Versatile Camera Calibration Technique for High-Accuracy 3D Machine Vision Metrology Using Off-the-Shelf TV Cameras and Lenses," IEEE J. Robotics and Automation, vol. 3, no. 4, pp. 323-344, 1987.
19. X. Ying and Z. Hu, "Catadioptric Camera Calibration Using Geometric Invariants," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 10, pp. 1260-1271, Oct. 2004.
20. Z. Zhang, "Flexible Camera Calibration by Viewing Planes from Unknown Orientations," Proc. Seventh Int'l Conf. Computer Vision, pp. 666-673, 1999.