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Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 950405, 15 pages
http://dx.doi.org/10.1155/2010/950405
Research Article

A New Variational Model for Segmenting Objects of Interest from Color Images

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

Received 9 December 2009; Revised 14 April 2010; Accepted 17 May 2010

Academic Editor: Panos Liatsis

Copyright © 2010 Yanli Zhai 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. M. Kass, A. Witkin, and D. 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 · View at Scopus
  2. 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 · View at Scopus
  3. C. Li, J. Liu, and M. D. Fox, “Segmentation of external force field for automatic initialization and splitting of snakes,” Pattern Recognition, vol. 38, no. 11, pp. 1947–1960, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. 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, vol. 1, pp. 430–436, 2005. View at Scopus
  5. 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
  6. A. Tsai, A. Yezzi Jr., 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 · View at Scopus
  7. 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 MathSciNet
  8. 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 · View at Scopus
  9. C. Li, C.-Y. 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 · View at MathSciNet
  10. 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 · View at Scopus
  11. J. Piovano, M. Rousson, and T. Papadopoulo, “Efficient segmentation of piecewise smooth images,” in Proceedings of the Scale Space Methods and Variational Methods (SSVM '07), vol. 4485 of Lecture Notes in Computer Science, pp. 709–720, 2007. View at Scopus
  12. T. Brox, From pixels to regions: partial differential equations in image analysis, Ph.D. thesis, Saarland University, Saarbrücken, Germany, 2005.
  13. B. Rosenhahn, T. Brox, and J. Weickert, “Three-dimensional shape knowledge for joint image segmentation and pose tracking,” International Journal of Computer Vision, vol. 73, no. 3, pp. 243–262, 2007. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Brox and D. Cremers, “On the statistical interpretation of the piecewise smooth Mumford-Shah functional,” in Proceedings of the Scale Space Methods and Variational Methods (SSVM '07), vol. 4485 of Lecture Notes in Computer Science, pp. 203–213, Ischia, Italy, 2007. View at Scopus
  15. 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 · View at MathSciNet
  16. T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham, “Active shape models-their training and application,” Computer Vision and Image Understanding, vol. 61, no. 1, pp. 38–59, 1995. View at Publisher · View at Google Scholar · View at Scopus
  17. M. E. Leventon, W. E. L. Grimson, and O. Faugeras, “Statistical shape influence in geodesic active contours,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 316–323, 2000.
  18. 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 · View at Scopus
  19. F. Li, C. Shen, and L. Pi, “A new diffusion-based variational model for image denoising and segmentation,” Journal of Mathematical Imaging and Vision, vol. 26, no. 1-2, pp. 115–125, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  20. F. Li, C. Shen, and L. Pi, “Color image segmentation for objects of interest with modified geodesic active contour method,” Journal of Mathematical Imaging and Vision, vol. 27, no. 1, pp. 51–57, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  21. P. V. 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
  22. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, New York, NY, USA, 2nd edition, 1984. View at MathSciNet
  23. L. Pi, C. M. Shen, F. Li, and J. S. Fan, “A variational formulation for segmenting desired objects in color images,” Image and Vision Computing, vol. 25, no. 9, pp. 1414–1421, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. B. Mory and R. Ardon, “Fuzzy region competition: a convex two-phase segmentation framework,” in Lecture Notes in Computer Science, vol. 4485, pp. 214–226, 2007. View at Scopus
  25. 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 Zentralblatt MATH · View at MathSciNet
  26. T. F. Chan, G. H. Golub, and P. Mulet, “A nonlinear primal-dual method for total variation-based image restoration,” SIAM Journal on Scientific Computing, vol. 20, no. 6, pp. 1964–1977, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J.-F. Aujol and A. Chambolle, “Dual norms and image decomposition models,” International Journal of Computer Vision, vol. 63, no. 1, pp. 85–104, 2005. View at Publisher · View at Google Scholar · View at Scopus
  28. J.-F. Aujol, G. Gilboa, T. Chan, and S. Osher, “Structure-texture image decomposition-modeling, algorithms, and parameter selection,” International Journal of Computer Vision, vol. 67, no. 1, pp. 111–136, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. 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 MathSciNet