Open Access

Calibrating Distributed Camera Networks Using Belief Propagation

EURASIP Journal on Advances in Signal Processing20062007:060696

Received: 4 January 2006

Accepted: 22 June 2006

Published: 24 September 2006


We discuss how to obtain the accurate and globally consistent self-calibration of a distributed camera network, in which camera nodes with no centralized processor may be spread over a wide geographical area. We present a distributed calibration algorithm based on belief propagation, in which each camera node communicates only with its neighbors that image a sufficient number of scene points. The natural geometry of the system and the formulation of the estimation problem give rise to statistical dependencies that can be efficiently leveraged in a probabilistic framework. The camera calibration problem poses several challenges to information fusion, including overdetermined parameterizations and nonaligned coordinate systems. We suggest practical approaches to overcome these difficulties, and demonstrate the accurate and consistent performance of the algorithm using a simulated 30-node camera network with varying levels of noise in the correspondences used for calibration, as well as an experiment with 15 real images.


Quantum InformationEstimation ProblemPractical ApproachStatistical DependencyBelief Propagation


Authors’ Affiliations

Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, USA


  1. Davis L, Borovikov E, Cutler R, Harwood D, Horprasert T: Multi-perspective analysis of human action. Proceedings of the 3rd International Workshop on Cooperative Distributed Vision, November 1999, Kyoto, JapanGoogle Scholar
  2. Kanade T, Rander P, Narayanan PJ: Virtualized reality: constructing virtual worlds from real scenes. IEEE Multimedia, Immersive Telepresence 1997,4(1):34-47.View ArticleGoogle Scholar
  3. Durrant-Whyte HF, Stevens M: Data fusion in decentralized sensing networks. Proceedings of the 4th International Conference on Information Fusion, August 2001, Montreal, Canada 302-307.Google Scholar
  4. Smith R, Self M, Cheeseman P: Estimating uncertain spatial relationships in robotics. In Autonomous Robot Vehicles. Springer, New York, NY, USA; 1990:167-193.View ArticleGoogle Scholar
  5. Grime S, Durrant-Whyte HF: Communication in decentralized systems. IFAC Control Engineering Practice 1994,2(5):849-863.View ArticleGoogle Scholar
  6. Murphy KP, Weiss Y, Jordan MI: Loopy belief propagation for approximate inference: an empirical study. Proceedings of Uncertainty in Artificial Intelligence (UAI '99), July-August 1999, Stockholm, Sweden 467-475.Google Scholar
  7. Pearl J: Probablistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco, Calif, USA; 1988.Google Scholar
  8. Freeman WT, Pasztor EC: Learning to estimate scenes from images. In Advances in Neural Information Processing Systems 11. Edited by: Kearns MS, Solla SA, Cohn DA. MIT Press, Cambridge, Mass, USA; 1999.Google Scholar
  9. Frey BJ: Graphical Models for Pattern Classification, Data Compression and Channel Coding. MIT Press, Cambridge, Mass, USA; 1998.Google Scholar
  10. McEliece RJ, MacKay DJC, Cheng J-F: Turbo decoding as an instance of Pearl's "belief propagation" algorithm. IEEE Journal on Selected Areas in Communications 1998,16(2):140-152. 10.1109/49.661103View ArticleGoogle Scholar
  11. Weiss Y, Freeman WT: Correctness of belief propagation in Gaussian graphical models of arbitrary topology. Advances in Neural Information Processing Systems (NIPS '99), November-December 1999, Denver, Colo, USA 12:Google Scholar
  12. Yedidia JS, Freeman W, Weiss Y: Understanding belief propagation and its generalizations. In Exploring Artificial Intelligence in the New Millennium. Edited by: Lakemeyer G, Nebel B. Morgan Kaufmann, San Mateo, Calif, USA; 2003:239-236. chapter 8Google Scholar
  13. Isard M, Blake A: CONDENSATION—conditional density propagation for visual tracking. International Journal of Computer Vision 1998,29(1):5-28. 10.1023/A:1008078328650View ArticleGoogle Scholar
  14. Freeman WT, Pasztor EC, Carmichael OT: Learning low-level vision. International Journal of Computer Vision 2000,40(1):25-47. 10.1023/A:1026501619075View ArticleMATHGoogle Scholar
  15. Coughlan JM, Ferreira SJ: Finding deformable shapes using loopy belief propagation. In Proceedings of the 7th European Conference on Computer Vision (ECCV '02), May-June 2002, London, UK. Springer; 453-468.Google Scholar
  16. Felzenszwalb PF, Huttenlocher DP: Efficient belief propagation for early vision. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June-July 2004, Washington, DC, USA 1: 261-268.Google Scholar
  17. Sudderth EB, Mandel MI, Freeman WT, Willsky AS: Distributed occlusion reasoning for tracking with nonparametric belief propagation. In Advances in Neural Information Processing Systems. Volume 17. Edited by: Saul LK, Weiss Y, Bottou L. MIT Press, Cambridge, Mass, USA; 2005:1369-1376.Google Scholar
  18. Alanyali M, Venkatesh S, Savas O, Aeron S: Distributed Bayesian hypothesis testing in sensor networks. Proceedings of the American Control Conference, June-July 2004, Boston, Mass, USA 6: 5369-5374.Google Scholar
  19. Christopher C, Avi P: Loopy belief propagation as a basis for communication in sensor networks. In Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence (UAI '03), August 2003, San Francisco, Calif, USA. Morgan Kaufmann; 159-166.Google Scholar
  20. Paskin MA, Guestrin CE: Robust probabilistic inference in distributed systems. In Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (UAI '04), July 2004, Banff Park Lodge, Banff, Canada. AUAI Press; 436-445.Google Scholar
  21. Paskin MA, Guestrin CE, McFadden J: A robust architecture for inference in sensor networks. 4th International Symposium on Information Processing in Sensor Networks (IPSN '05), April 2005, Los Angeles, Calif, USAGoogle Scholar
  22. Dellaert F, Kipp A, Krauthausen P: A multifrontal QR factorization approach to distributed inference applied to multirobot localization and mapping. Proceedings of the National Conference on Artificial Intelligence (AAAI '05), July 2005, Pittsburgh, Pa, USA 3: 1261-1266.Google Scholar
  23. Funiak S, Guestrin C, Paskin M, Sukthankar R: Distributed localization of networked cameras. The 5th International Conference on Information Processing in Sensor Networks (IPSN '06), April 2006, Nashville, Tenn, USAGoogle Scholar
  24. Sturm P, Triggs B: A factorization based algorithm for multi-image projective structure and motion. Proceedings of the 4th European Conference on Computer Vision (ECCV '96), April 1996, Cambridge, UK 709-720.Google Scholar
  25. Cheng Z, Devarajan D, Radke RJ: Determining vision graphs for distributed camera networks using feature digests. to appear in EURASIP Journal of Applied Signal Processing, special issue on Visual Sensor NetworksGoogle Scholar
  26. Devarajan D, Radke R, Chung H: Distributed metric calibration of ad-hoc camera networks. ACM Transactions on Sensor Networks 2006.,2(3):Google Scholar
  27. Pollefeys M, Koch R, Van Gool L: Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. Proceedings of the 6th IEEE International Conference on Computer Vision (ICCV '98), January 1998, Bombay, India 90-95.Google Scholar
  28. Andersson M, Betsis D: Point reconstruction from noisy images. Journal of Mathematical Imaging and Vision 1995, 5: 77-90. 10.1007/BF01250254View ArticleGoogle Scholar
  29. Fischler MA, Bolles RC: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM 1981,24(6):381-395. 10.1145/358669.358692MathSciNetView ArticleGoogle Scholar
  30. Triggs B, McLauchlan P, Hartley R, Fitzgibbon A: Bundle adjustment—a modern synthesis. In Vision Algorithms: Theory and Practice, Lecture Notes in Computer Science. Edited by: Triggs W, Zisserman A, Szeliski R. Springer, New York, NY, USA; 2000:298-375.View ArticleGoogle Scholar
  31. Besag J: Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B 1974, 36: 192-236.MathSciNetMATHGoogle Scholar
  32. Hammersley J, Clifford PE: Markov fields on finite graphs and lattices. preprint, 1971Google Scholar
  33. Kschischang FR, Frey BJ, Loeliger H-A: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 2001,47(2):498-519. 10.1109/18.910572MathSciNetView ArticleMATHGoogle Scholar
  34. Hartley R, Zisserman A: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge, UK; 2000.MATHGoogle Scholar
  35. Kanatani K, Morris DD: Gauges and gauge transformations for uncertainty description of geometric structure with indeterminacy. IEEE Transactions on Information Theory 2001,47(5):2017-2028. 10.1109/18.930934MathSciNetView ArticleMATHGoogle Scholar


© D. Devarajan and R. J. Radke. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.