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Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 186507, 14 pages
http://dx.doi.org/10.1155/2011/186507
Research Article

A Numerical Method for Preserving Curve Edges in Nonlinear Anisotropic Smoothing

1School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
2School of Computer Science, Sichuan Normal University, Chengdu 610066, China
3Institute of Medical Information and Technology, School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China

Received 28 January 2011; Accepted 18 February 2011

Academic Editor: Ming Li

Copyright © 2011 Shaoxiang Hu 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. H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, USA, 2001.
  2. J. V. Lorenzo-Ginori, K. N. Plataniotis, and A. N. Venetsanopoulos, “Nonlinear filtering for phase image denoising,” IEE Proceedings, vol. 149, no. 5, pp. 290–296, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. Y. J. Zhang and L. L. Geb, “Edge preserving regularization for the pde-based piecewise smooth mumford-shah algorithm,” Imaging Science Journal, vol. 57, no. 3, pp. 119–127, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. S. Y. Chen and Y. F. Li, “Determination of stripe edge blurring for depth sensing,” IEEE Sensors Journal, vol. 11, no. 2, pp. 389–390, 2011. View at Publisher · View at Google Scholar
  5. Z. Jun and W. Zhihui, “A class of fractional-order multi-scale variational models and alternating projection algorithm for image denoising,” Applied Mathematical Modelling, vol. 35, no. 5, pp. 2516–2528, 2011. View at Publisher · View at Google Scholar
  6. E. G. Bakhoum and C. Toma, “Dynamical aspects of macroscopic and quantum transitions due to coherence function and time series events,” Mathematical Problems in Engineering, vol. 2010, Article ID 428903, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. G. Mattioli, M. Scalia, and C. Cattani, “Analysis of large-amplitude pulses in short time intervals: application to neuron interactions,” Mathematical Problems in Engineering, vol. 2010, Article ID 895785, 15 pages, 2010. View at Zentralblatt MATH
  8. Y. Shih, C. Rei, and H. Wang, “A novel PDE based image restoration: convection-diffusion equation for image denoising,” Journal of Computational and Applied Mathematics, vol. 231, no. 2, pp. 771–779, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  9. C. Chaux, L. Duval, A. Benazza-Benyahia, and J. C. Pesquet, “A nonlinear Stein-based estimator for multichannel image denoising,” IEEE Transactions on Signal Processing, vol. 56, no. 8, pp. 3855–3870, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Y. Chen, H. Tong, Z. Wang, S. Liu, M. Li, and B. Zhang, “Improved generalized belief propagation for vision processing,” Mathematical Problems in Engineering, vol. 2011, Article ID 416963, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. Z. Liao, S. Hu, and W. Chen, “Determining neighborhoods of image pixels automatically for adaptive image denoising using nonlinear time series analysis,” Mathematical Problems in Engineering, vol. 2010, Article ID 914564, 14 pages, 2010. View at Zentralblatt MATH
  12. 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
  13. L. Alvarez, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion. II,” SIAM Journal on Numerical Analysis, vol. 29, no. 3, pp. 845–866, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. L. Alvarez and L. Mazorra, “Signal and image restoration using shock filters and anisotropic diffusion,” SIAM Journal on Numerical Analysis, vol. 31, no. 2, pp. 590–605, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  15. J. Weickert, “Coherence-enhancing diffusion filtering,” International Journal of Computer Vision, vol. 31, no. 2, pp. 111–127, 1999. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Yu, Y. Yang, and A. Campo, “Approximate solution of the nonlinear heat conduction equation in a semi-infinite domain,” Mathematical Problems in Engineering, vol. 2010, Article ID 421657, 24 pages, 2010. View at Zentralblatt MATH
  17. M. Li, M. Scalia, and C. Toma, “Nonlinear time series: computations and applications,” Mathematical Problems in Engineering, vol. 2010, Article ID 101523, 5 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. N. Sochen, G. Gilboa, and Y. Y. Zeevi, “Color image enhancement by a forward and backwardadaptive Beltrami flow,” in Proceedings of the 2nd International Workshop Algebraic Frames for the Perception-Action Cycle (AFPAC '00), G. Sommer and Y. Y. Zeevi, Eds., Lecture Notes in Computer Science 1888, pp. 319–328, Springer, 2000.
  19. F. Zhang, Y. M. Yoo, L. M. Koh, and Y. Kim, “Nonlinear diffusion in laplacian pyramid domain for ultrasonic speckle reduction,” IEEE Transactions on Medical Imaging, vol. 26, no. 2, pp. 200–211, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. M. Ceccarelli, V. De Simone, and A. Murli, “Well-posed anisotropic diffusion for image denoising,” IEE Proceedings, vol. 149, no. 4, pp. 244–252, 2002. View at Publisher · View at Google Scholar · View at Scopus
  21. V. B. S. Prasath and A. Singh, “Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising,” Journal of Applied Mathematics, vol. 2010, Article ID 763847, 14 pages, 2010. View at Zentralblatt MATH
  22. J. Ling and A. C. Bovik, “Smoothing low-SNR molecular images via anisotropic median-diffusion,” IEEE Transactions on Medical Imaging, vol. 21, no. 4, pp. 377–384, 2002. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Buades, B. Coll, and J.-M. Morel, “Nonlocal image and movie denoising,” International Journal of Computer Vision, vol. 76, no. 2, pp. 123–139, 2008, special section: selection of papers for CVPR 2005, Guest Editors: C. Schmid, S. Soatto and C. Tomasi. View at Publisher · View at Google Scholar
  24. A. Buades, B. Coll, and J. M. Morel, “Image denoising methods. A new nonlocal principle,” SIAM Review, vol. 52, no. 1, pp. 113–147, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  25. M. Li, “Modeling autocorrelation functions of long-range dependent teletraffic series based on optimal approximation in Hilbert space-A further study,” Applied Mathematical Modelling, vol. 31, no. 3, pp. 625–631, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  26. C. Cattani, “Harmonic wavelet approximation of random, fractal and high frequency signals,” Telecommunication Systems, vol. 43, no. 3-4, pp. 207–217, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. C. Cattani, “Fractals and hidden symmetries in DNA,” Mathematical Problems in Engineering, vol. 2010, Article ID 507056, 31 pages, 2010. View at Zentralblatt MATH
  28. M. Li, “Generation of teletraffic of generalized Cauchy type,” Physica Scripta, vol. 81, no. 2, Article ID 025007, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  29. M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584–2594, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Li and W. Zhao, “Representation of a Stochastic Traffic Bound,” IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 9, pp. 1368–1372, 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. M. Li, W. Zhao, and S. Chen, “MBm-based scalings of traffic propagated in internet,” Mathematical Problems in Engineering, vol. 2011, Article ID 389803, 21 pages, 2011. View at Publisher · View at Google Scholar
  32. M. Li, “Fractal time series—a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. View at Zentralblatt MATH
  33. B. B. Mandelbrot, Gaussian Self-Affinity and Fractals, Selected Works of Benoit B. Mandelbrot, Springer, New York, NY, USA, 2002.