Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 960421, 17 pages
http://dx.doi.org/10.1155/2013/960421
Research Article

Bayesian Estimation Applied to Stochastic Localization with Constraints due to Interfaces and Boundaries

1Department of Radiation Oncology, Regensburg University Medical Center, Franz-Josef-Strauss-Allee 11, 93053 Regensburg, Germany
2Department of Computer Science and Mathematics, University of Applied Sciences, Universitaetsstraße 31, 93053 Regensburg, Germany
3Department of Radiation Oncology, Brigham and Women’s Hospital and Harvard Medical School, 75 Francis Street, Boston, MA 02115, USA

Received 21 December 2012; Accepted 13 March 2013

Academic Editor: Marcelo Moreira Cavalcanti

Copyright © 2013 Wolfgang Hoegele et al. 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.

Linked References

  1. R. Hartley and A. Zisserman, Multiple. View Geometry in Computer Vision, Cambridge University Press, 2003. View at Zentralblatt MATH
  2. D. E. Clark and S. Ivekovič, “The Cramer-Rao Lower Bound for 3-D state estimation from rectified stereo cameras,” in Proceedings of the 13th Conference on Information Fusion (Fusion '10), pp. 1–8, July 2010. View at Scopus
  3. W. Hoegele, R. Loeschel, B. Dobler, J. Hesser, O. Koelbl, and P. Zygmanski, “Stochastic formulation of patient positioning using linac-mounted cone beam imaging with prior knowledge,” Medical Physics, vol. 38, no. 2, pp. 668–681, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. W. Hoegele, P. Zygmanski, B. Dobler, M. Kroiss, O. Koelbl, and R. Loeschel, “Localization of deformable tumors from short-arc projections using bavesian estimation,” Medical Physics, vol. 39, no. 12, pp. 7205–7214, 2012. View at Publisher · View at Google Scholar
  5. W. Hoegele, R. Loeschel, B. Dobler, O. Koelbl, C. Beard, and P. Zygmanski, “Stochastic triangulation for prostate positioning during radiotherapy using short ebet arcs,” Radiotherapy & Oncology, 2013. View at Publisher · View at Google Scholar
  6. C. B. Guure, N. A. Ibrahim, and A. O. M. Ahmed, “Bayesian estimation of two-parameter weibull distribution using extension of Jeffreys' prior information with three loss functions,” Mathematical Problems in Engineering, vol. 2012, Article ID 589640, 13 pages, 2012. View at Publisher · View at Google Scholar
  7. N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel approach to nonlinear/non-gaussian Bayesian state estimation,” IEE Proceedings F, vol. 140, no. 2, pp. 107–113, 1993. View at Google Scholar · View at Scopus
  8. M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174–188, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Weckenmann, X. Jiang, K.-D. Sommer et al., “Multisensor data fusion in dimensional metrology,” CIRP Annals - Manufacturing Technology, vol. 58, no. 2, pp. 701–721, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. R. I. Hartley and P. Sturm, “Triangulation,” Computer Vision and Image Understanding, vol. 68, no. 2, pp. 146–157, 1997. View at Google Scholar · View at Scopus
  11. A. S. Bedekar and R. M. Haralick, “A Bayesian method for triangulation and its application to finding corresponding points,” in Proceedings of the IEEE International Conference on Image Processing, vol. 2, pp. 362–365, October 1995. View at Scopus
  12. E. L. Lehmann and G. Casella, Theory of Point Estimation, Springer, New York, NY, USA, 1998.
  13. C. P. Robert, The Bayesian Choice, Springer, New York, NY, USA, 2007.
  14. Y. C. Eldar, “Minimum variance in biased estimation: bounds and asymptotically optimal estimators,” IEEE Transactions on Signal Processing, vol. 52, no. 7, pp. 1915–1930, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Cramér, Mathematical Methods of Statistics, Asia Publishing House, 1946.
  16. Y. C. Eldar, “Rethinking biased estimation: improving maximum likelihood and the cramér-rao bound,” Foundations and Trends in Signal Processing, vol. 1, pp. 305–449, 2008. View at Google Scholar
  17. S. Rohl, S. Bodenstedt, S. Suwelack et al., “Dense gpu-enhanced surface reconstruction from stereo endoscopic images for intraoperative registration,” Medical Physics, vol. 39, no. 3, pp. 1632–1645, 2012. View at Google Scholar
  18. G. Zheng, “Statistical shape model-based reconstruction of a scaled, patient-specific surface model of the pelvis from a single standard AP x-ray radiograph,” Medical Physics, vol. 37, no. 4, pp. 1424–1439, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. R. Schulze, U. Heil, O. Weinheimer et al., “Accurate registration of random radiographic projections based on three spherical references for the purpose of few-view 3D reconstruction,” Medical Physics, vol. 35, no. 2, pp. 546–555, 2008. View at Publisher · View at Google Scholar · View at Scopus