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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 791958, 16 pages
http://dx.doi.org/10.1155/2012/791958
Research Article

Local- and Global-Statistics-Based Active Contour Model for Image Segmentation

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 9 October 2011; Accepted 24 January 2012

Academic Editor: Francesco Pellicano

Copyright © 2012 Boying Wu and Yunyun Yang. 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. M. Kass, A. Witkin, and D. Terzopoulos, “Terzopoulos, Snakes: active contour models,” International Journal of Computer Vision, vol. 1, no. 4, pp. 321–331, 1988. View at Publisher · View at Google Scholar
  2. 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 Zentralblatt MATH
  3. R. Malladi, J. A. Sethian, and B. C. Vemuri, “Shape modeling with front propagation: a level set approach,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 2, pp. 158–175, 1995. View at Publisher · View at Google Scholar
  4. D. Cremers, M. Rousson, and R. Deriche, “A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape,” International Journal of Computer Vision, vol. 72, no. 2, pp. 195–215, 2007. View at Publisher · View at Google Scholar
  5. S. Geman and D. Geman, “Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721–741, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. 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 Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. R. Kimmel, A. Amir, and A. Bruckstein, “Finding shortest paths on surfaces using level set propagation,” International Journal of Computer Vision, vol. 17, no. 6, pp. 635–640, 1995. View at Google Scholar
  8. A. Vasilevskiy and K. Siddiqi, “Flux maximizing geometric flows,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 12, pp. 1565–1578, 2001. View at Google Scholar
  9. C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without reinitialization: a new variational formulation,” Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 430–436, 2005. View at Google Scholar
  10. R. Ronfard, “Region-based strategies for active contour models,” International Journal of Computer Vision, vol. 13, no. 2, pp. 229–251, 1994. View at Publisher · View at Google Scholar
  11. 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 Zentralblatt MATH
  12. C. Samson, L. Blanc-Feraud, G. Aubert, and J. Zerubia, “A variational model for image classification and restoration,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 5, pp. 460–472, 2000. View at Publisher · View at Google Scholar
  13. A. Tsai, A. Yezzi, and A. S. Willsky, “Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification,” IEEE Transactions on Image Processing, vol. 10, no. 8, pp. 1169–1186, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. 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 Zentralblatt MATH
  15. C. Li, C. Kao, J. Gore, and Z. Ding, “Implicit active contours driven by local binary fitting energy,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE Computer Society, pp. 1–7, Washington, DC, USA, 2007.
  16. C. Li, C. Kao, J. C. Gore, and Z. Ding, “Minimization of region-scalable fitting energy for image segmentation,” IEEE Transactions on Image Processing, vol. 17, no. 10, pp. 1940–1949, 2008. View at Publisher · View at Google Scholar
  17. L. Wang, L. He, A. Mishra, and C. Li, “Active contours driven by local gaussian distribution fitting energy,” Signal Process, vol. 89, no. 12, pp. 2435–2447, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. C. Darolti, A. Mertins, C. Bodensteiner, and U. G. Hofmann, “Local region descriptors for active contours evolution,” IEEE Transactions on Image Processing, vol. 17, no. 12, pp. 2275–2288, 2008. View at Publisher · View at Google Scholar
  19. S. Lankton and A. Tannenbaum, “Localizing region-based active contours,” IEEE Transactions on Image Processing, vol. 17, no. 11, pp. 2029–2039, 2008. View at Publisher · View at Google Scholar
  20. L. Wang, C. Li, Q. Sun, D. Xia, and C. Kao, “Active contours driven by local and global intensity fitting energy with application to brain MR image segmentation,” Computerized Medical Imaging and Graphics, vol. 33, no. 7, pp. 520–531, 2009. View at Google Scholar
  21. Y. Yang, C. Li, C. Kao, and S. Osher, “Split Bregman method for minimization of region-scalable fitting energy for image segmentation,” in Proceedings of the 6th International Symposium on Visual Computing, vol. part II, LNCS 6454, pp. 117–128, Springer, 2010.
  22. N. Houhou, J.-P. Thiran, and X. Bresson, “Fast texture segmentation based on semi-local region descriptor and active contour,” Numerical Mathematics. Theory, Methods and Applications, vol. 2, no. 4, pp. 445–468, 2009. View at Google Scholar · View at Zentralblatt MATH
  23. T. Goldstein and S. Osher, “The split Bregman method for L1-regularized problems,” SIAM Journal on Imaging Sciences, vol. 2, no. 2, pp. 323–343, 2009. View at Publisher · View at Google Scholar
  24. S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, “An iterative regularization method for total variation-based image restoration,” Multiscale Modeling Simulation, vol. 4, no. 2, pp. 460–489, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. T. Goldstein, X. Bresson, and S. Osher, “Geometric applications of the split Bregman method: segmentation and surface reconstruction,” Journal of Scientific Computing, vol. 45, no. 1–3, pp. 272–293, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. T. Chan, S. Esedo\=glu, 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 Zentralblatt MATH
  27. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. X. Bresson, S. Esedoglu, P. Vandergheynst, J. 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
  29. Y. Yang and B. Wu, “Convex image segmentation model based on local and global intensity fitting energy and split Bregman method,” Journal of Applied Mathematics, vol. 2012, Article ID 692589, 16 pages, 2012. View at Publisher · View at Google Scholar
  30. Y. Yu, C. Zhang, Y. Wei, and X. Li, “Active contour method combining local fitting energy and global fitting energy dynamically,” in Proceedings of the of International Conference on Medical Biometrics, vol. LNCS 6165, pp. 163–172, Springer, 2010.