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Applied Computational Intelligence and Soft Computing
Volume 2013 (2013), Article ID 921721, 9 pages
http://dx.doi.org/10.1155/2013/921721
Research Article

A New Multiphase Soft Segmentation with Adaptive Variants

1School of Information Science & Engineering, Changzhou University, Changzhou 213164, China
2Department of Natural Science & Mathematics, West Liberty University, West Liberty, WV 26074, USA
3Department of Mathematics, University of Florida, Gainesville, FL 36011, USA

Received 19 February 2013; Accepted 9 May 2013

Academic Editor: Zhang Yi

Copyright © 2013 Hongyuan Wang 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. X. Bresson, S. Esedoglu, P. Vandergheynst, J.-P. Thiran, and S. Osher, “Fast global minimization of the active contour/snake model,” Journal of Mathematical Imaging and Vision, vol. 28, no. 2, pp. 151–167, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. X. Bresson and T. F. Chan, “Non-local unsupervised variational image segmentation models,” UCLA CAM Report, 2008, http://www.math.ucla.edu/.
  3. V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic active contours,” International Journal of Computer Vision, vol. 22, no. 1, pp. 61–79, 1997. View at Scopus
  4. T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 266–277, 2001. View at Publisher · View at Google Scholar · View at Scopus
  5. T. F. Chan, S. Esedoglu, and M. Nikolova, “Algorithms for finding global minimizers of image segmentation and denoising models,” SIAM Journal on Applied Mathematics, vol. 66, no. 5, pp. 1632–1648, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. D. Mumford and J. Shah, “Optimal approximations by piecewise smooth functions and associated variational problems,” Communications on Pure and Applied Mathematics, vol. 42, no. 5, pp. 577–685, 1989.
  7. N. Paragios and R. Deriche, “Geodesic active regions and level set methods for supervised texture segmentation,” International Journal of Computer Vision, vol. 46, no. 3, pp. 223–247, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. S. C. Zhu, “Region competition: unifying snakes, region growing, and bayes/mdl for multiband image segmentation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, no. 9, pp. 884–900, 1996. View at Scopus
  9. S. Osher and J. A. Sethian, “Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations,” Journal of Computational Physics, vol. 79, no. 1, pp. 12–49, 1988. View at Scopus
  10. G. Chung and L. A. Vese, “Energy minimization based segmentation and denoising using a multilayer level set approach,” Energy Minimization Methods in Computer Vision and Pattern Recognition, vol. 3757, pp. 439–455, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Lie, M. Lysaker, and X. C. Tai, “A variant of the level set method and applications to image segmentation,” Mathematics of Computation, vol. 75, no. 255, pp. 1155–1174, 2006. View at Publisher · View at Google Scholar · View at Scopus
  12. L. A. Vese and T. F. Chan, “A multiphase level set framework for image segmentation using the Mumford and Shah model,” International Journal of Computer Vision, vol. 50, no. 3, pp. 271–293, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. H.-K. Zhao, T. Chan, B. Merriman, and S. Osher, “A variational level set approach to multiphase motion,” Journal of Computational Physics, vol. 127, no. 1, pp. 179–195, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Pock, T. Schoenemann, G. Graber, H. Bischof, and D. Cremers, “A convex formulation of continuous multi-label problems,” in Proceedings of the European Conference on Computer Vision (ECCV '08), Marseille, France, October 2008.
  15. E. S. Brown, T. F. Chan, and X. Bresson, “Convex formulation and exact global solutions for multi-phase piecewise constant Mumford-Shah image segmentation,” UCLA CAM Report cam09-66, 2009.
  16. E. Bae, J. Yuan, and X.-C. Tai, “Global minimization for continuous multiphase partitioning problems using a dual approach,” UCLA CAM Report, 2009, http://www.math.ucla.edu/.
  17. S. Chen and D. Zhang, “Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 34, no. 4, pp. 1907–1916, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. X. Li, L. Li, H. Lu, and Z. Liang, “Partial volume segmentation of brain magnetic resonance images based on maximum a posteriori probability,” Medical Physics, vol. 32, no. 7, pp. 2337–2345, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. B. Mory and R. Ardon, “Fuzzy region competition: a convex two-phase segmentation framework,” in Proceedings of the International Conference on Scale-Space and Variational Methods in Computer Vision, pp. 214–226, 2007.
  20. B. Mory, R. Ardon, and J. P. Thiran, “Variational segmentation using fuzzy region competition and local non-parametric probability density functions,” in Proceedings of the IEEE 11th International Conference on Computer Vision (ICCV '07), pp. 1–8, October 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. D. L. Pham and J. L. Prince, “An adaptive fuzzy C-means algorithm for image segmentation in the presence of intensity inhomogeneities,” Pattern Recognition Letters, vol. 20, no. 1, pp. 57–68, 1999. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Shen, “A stochastic-variational model for soft Mumford-Shah segmentation,” International Journal of Biomedical Imaging, vol. 2006, Article ID 92329, 14 pages, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. J. C. Bezdek, “A convergence theorem for the fuzzy ISODATA clustering algorithm,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 2, no. 1, pp. 1–8, 1980. View at Scopus
  24. J. C. Dunn, “A fuzzy relative of the ISODATA process and its use in detecting compact wellseparated clusters,” Jounal of Cybernetics, vol. 3, no. 3, pp. 32–57, 1973. View at Scopus
  25. F. Chen, Y. Chen, and H. D. Tagare, “An extension of sine-sinc model based on logarithm of likelihood,” in Proceedings of the International Conference on Image Processing, Computer Vision, and Pattern Recognition (IPCV '08), pp. 222–227, July 2008. View at Scopus
  26. A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” Journal Royal Statistical Society B, vol. 39, no. 1, pp. 1–8, 1977.
  27. M. N. Ahmed, S. M. Yamany, N. Mohamed, A. A. Farag, and T. Moriarty, “A modified fuzzy C-means algorithm for bias field estimation and segmentation of MRI data,” IEEE Transactions on Medical Imaging, vol. 21, no. 3, pp. 193–199, 2002. View at Publisher · View at Google Scholar · View at Scopus
  28. C. Li, R. Huang, Z. Ding, C. Gatenby, D. Metaxas, and J. Gore, “A variational level set approach to segmentation and bias correction of images with intensity inhomogeneity,” Medical Image Computing and Computer Assisted Intervention, vol. 11, part 2, pp. 1083–1091, 2008. View at Publisher · View at Google Scholar · View at Scopus
  29. W. M. Wells III, W. E. L. Crimson, R. Kikinis, and F. A. Jolesz, “Adaptive segmentation of mri data,” IEEE Transactions on Medical Imaging, vol. 15, no. 4, pp. 429–442, 1996. View at Scopus
  30. Y. Boykov and G. Funka-Lea, “Graph cuts and efficient N-D image segmentation,” International Journal of Computer Vision, vol. 70, no. 2, pp. 109–131, 2006. View at Publisher · View at Google Scholar · View at Scopus
  31. J.-B. Hiriart-Urruty and C. Lemarechal, “Convex analysis and minimization algorithms,” in Grundlehren der Mathematischen Wissenschaften, pp. 305–306, Springer, New York, NY, USA, 1993.
  32. A. Chambolle, “An algorithm for total variation minimization and applications,” Journal of Mathematical Imaging and Vision, vol. 20, no. 1-2, pp. 89–97, 2004. View at Publisher · View at Google Scholar · View at Scopus
  33. M. Zhu and T. Chan, “An efficient primal-dual hybrid gradient algorithm for total variation image restoration,” CAM Report cam08-34, 2008.
  34. E. S. Brown, T. F. Chan, and X. Bresson, “Convex relaxation method for a class of vector-valued minimization problems with applications to Mumford-Shah segmentation,” UCLA CAM Report cam10-43, 2010.
  35. E. Esser, X. Zhang, and T. Chan, “A general framework for a class of first order primal-dual algorithms for TV minimization,” Cam Report cam09-67, 2009.
  36. T. Pock, D. Cremers, H. Bischof, and A. Chambolle, “An algorithm for minimizing the Mumford-Shah functional,” in Proceedings of the 12th International Conference on Computer Vision (ICCV '09), pp. 1133–1140, Kyoto, Japan, October 2009. View at Publisher · View at Google Scholar · View at Scopus
  37. T. Pock, D. Cremers, H. Bischof, and A. Chambolle, “An algorithm for minimizing the Mumford-Shah functional,” in Proceedings of the 12th International Conference on Computer Vision (ICCV '09), pp. 1133–1140, October 2009. View at Publisher · View at Google Scholar · View at Scopus