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Advances in Mathematical Physics
Volume 2016, Article ID 8745706, 7 pages
http://dx.doi.org/10.1155/2016/8745706
Research Article

A New Nonlinear Diffusion Equation Model for Noisy Image Segmentation

1College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
2Shenzhen Key Laboratory of Media Security, Shenzhen University, Shenzhen 518060, China
3School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China
4College of Computer Science and Technology, Beijing University of Technology, Beijing 100124, China

Received 3 September 2015; Revised 21 December 2015; Accepted 3 January 2016

Academic Editor: Ricardo Weder

Copyright © 2016 Bo Chen 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. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D: Nonlinear Phenomena, vol. 60, no. 1–4, pp. 259–268, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. P. Blomgren and T. F. Chan, “Color TV: total variation methods for restoration of vector-valued images,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 304–309, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Esedoglu and S. J. Osher, “Decomposition of images by the anisotropic Rudin-Osher-Fatemi model,” Communications on Pure and Applied Mathematics, vol. 57, no. 12, pp. 1609–1626, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. T. F. Chan, S. Osher, and J. Shen, “The digital TV filter and nonlinear denoising,” IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 231–241, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. B. Chen, J.-L. Cai, W. Chen, and Y. Li, “A multiplicative noise removal approach based on partial differential equation model,” Mathematical Problems in Engineering, vol. 2012, Article ID 242043, 14 pages, 2012. View at Publisher · View at Google Scholar
  6. C. Xu and J. L. Prince, “Snakes, shapes, and gradient vector flow,” IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 359–369, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. L. D. Cohen and I. Cohen, “Finite-element methods for active contour models and balloons for 2-D and 3-D images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 11, pp. 1131–1147, 1993. View at Publisher · View at Google Scholar · View at Scopus
  8. V. Caselles, F. Catté, T. Coll, and F. Dibos, “A geometric model for active contours in image processing,” Numerische Mathematik, vol. 66, no. 1, pp. 1–31, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. 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 Scopus
  10. 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 · View at Scopus
  11. K. Zhang, L. Zhang, H. Song, and W. Zhou, “Active contours with selective local or global segmentation: a new formulation and level set method,” Image and Vision Computing, vol. 28, no. 4, pp. 668–676, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. B. Chen, Q.-H. Zou, W.-S. Chen, and Y. Li, “A fast region-based segmentation model with Gaussian kernel of fractional order,” Advances in Mathematical Physics, vol. 2013, Article ID 501628, 7 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  13. F. Catt{\'e}, P.-L. Lions, J.-M. Morel, and T. Coll, “Image selective smoothing and edge detection by nonlinear diffusion,” SIAM Journal on Numerical Analysis, vol. 29, no. 1, pp. 182–193, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. C . Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: a new variational formulation,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '05), vol. 1, pp. 430–436, IEEE, San Diego, Calif, USA, June 2005. View at Publisher · View at Google Scholar
  15. Y. Shi and W. Karl, “Real-time tracking using level sets,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR '05), vol. 2, pp. 34–41, June 2005.
  16. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629–639, 1990. View at Publisher · View at Google Scholar · View at Scopus