- Research Article
- Open access
- Published:
Calibrating Distributed Camera Networks Using Belief Propagation
EURASIP Journal on Advances in Signal Processing volume 2007, Article number: 060696 (2006)
Abstract
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.
References
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, Japan
Kanade T, Rander P, Narayanan PJ: Virtualized reality: constructing virtual worlds from real scenes. IEEE Multimedia, Immersive Telepresence 1997,4(1):34–47.
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.
Smith R, Self M, Cheeseman P: Estimating uncertain spatial relationships in robotics. In Autonomous Robot Vehicles. Springer, New York, NY, USA; 1990:167–193.
Grime S, Durrant-Whyte HF: Communication in decentralized systems. IFAC Control Engineering Practice 1994,2(5):849–863.
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.
Pearl J: Probablistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Francisco, Calif, USA; 1988.
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.
Frey BJ: Graphical Models for Pattern Classification, Data Compression and Channel Coding. MIT Press, Cambridge, Mass, USA; 1998.
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. 10.1109/49.661103
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:
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 8
Isard M, Blake A: CONDENSATION—conditional density propagation for visual tracking. International Journal of Computer Vision 1998,29(1):5–28. 10.1023/A:1008078328650
Freeman WT, Pasztor EC, Carmichael OT: Learning low-level vision. International Journal of Computer Vision 2000,40(1):25–47. 10.1023/A:1026501619075
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.
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.
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.
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.
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.
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.
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, USA
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.
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, USA
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.
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 Networks
Devarajan D, Radke R, Chung H: Distributed metric calibration of ad-hoc camera networks. ACM Transactions on Sensor Networks 2006.,2(3):
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.
Andersson M, Betsis D: Point reconstruction from noisy images. Journal of Mathematical Imaging and Vision 1995, 5: 77–90. 10.1007/BF01250254
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. 10.1145/358669.358692
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.
Besag J: Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, Series B 1974, 36: 192–236.
Hammersley J, Clifford PE: Markov fields on finite graphs and lattices. preprint, 1971
Kschischang FR, Frey BJ, Loeliger H-A: Factor graphs and the sum-product algorithm. IEEE Transactions on Information Theory 2001,47(2):498–519. 10.1109/18.910572
Hartley R, Zisserman A: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge, UK; 2000.
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. 10.1109/18.930934
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Devarajan, D., Radke, R.J. Calibrating Distributed Camera Networks Using Belief Propagation. EURASIP J. Adv. Signal Process. 2007, 060696 (2006). https://doi.org/10.1155/2007/60696
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1155/2007/60696