About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 131207, 8 pages
http://dx.doi.org/10.1155/2013/131207
Research Article

Construction of Target Controllable Image Segmentation Model Based on Homotopy Perturbation Technology

College of Information and Electrical Engineering, China Agricultural University, Postbox 53, East Campus, 17 Qinghua Donglu Road, Haidian District, Beijing 100083, China

Received 31 December 2012; Revised 4 January 2013; Accepted 6 January 2013

Academic Editor: Lan Xu

Copyright © 2013 Shu-Li Mei. 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. O. Wirjadi, “Survey of 3rd image segmentation methods,” Berichte Des Fraunhofer ITWM 123, 2007.
  2. 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
  3. T. F. Chan, S. Esedoglu, and M. Nikolova, “Algorithms for finding global minimizers of image segmentation and denoising models,” UCLA Report, 2004.
  4. 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 · View at MathSciNet
  5. J.-H. He, “A coupling method of a homotopy technique and a perturbation technique for non-linear problems,” International Journal of Non-Linear Mechanics, vol. 35, no. 1, pp. 37–43, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  6. J.-H. He, “Homotopy perturbation technique,” Computer Methods in Applied Mechanics and Engineering, vol. 178, no. 3-4, pp. 257–262, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. J.-H. He, “Asymptotology by homotopy perturbation method,” Applied Mathematics and Computation, vol. 156, no. 3, pp. 591–596, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J.-H. He, “Homotopy perturbation method: a new nonlinear analytical technique,” Applied Mathematics and Computation, vol. 135, no. 1, pp. 73–79, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. H. He, “Limit cycle and bifurcation of nonlinear problems,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 827–833, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. J. H. He, “Application of homotopy perturbation method to nonlinear wave equations,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 695–700, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. J.-H. He, “Periodic solutions and bifurcations of delay-differential equations,” Physics Letters A, vol. 347, no. 4–6, pp. 228–230, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-H. He, “The homotopy perturbation method nonlinear oscillators with discontinuities,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 287–292, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. H. He, “Homotopy perturbation method for bifurcation of nonlinear problems,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 6, no. 2, pp. 207–208, 2005. View at Scopus
  14. J.-H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. View at Publisher · View at Google Scholar
  15. J.-H. He, “New interpretation of homotopy perturbation method,” International Journal of Modern Physics B, vol. 20, no. 18, pp. 2561–2568, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  16. L. Cveticanin, “Homotopy-perturbation method for pure nonlinear differential equation,” Chaos, Solitons and Fractals, vol. 30, no. 5, pp. 1221–1230, 2006. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Abbasbandy, “Application of He's homotopy perturbation method for Laplace transform,” Chaos, Solitons and Fractals, vol. 30, no. 5, pp. 1206–1212, 2006. View at Publisher · View at Google Scholar · View at Scopus
  18. M. Rafei and D. D. Ganji, “Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 3, pp. 321–328, 2006. View at Scopus
  19. A. M. Siddiqui, R. Mahmood, and Q. K. Ghori, “Thin film flow of a third grade fluid on a moving belt by he's homotopy perturbation method,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 7–14, 2006. View at Scopus
  20. A. M. Siddiqui, M. Ahmed, and Q. K. Ghori, “Couette and poiseuille flows for non-newtonian fluids,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 15–26, 2006. View at Scopus
  21. J.-H. He, “Variational iteration method: a kind of non-linear analytical technique: some examples,” International Journal of Non-Linear Mechanics, vol. 34, no. 4, pp. 699–708, 1999. View at Scopus
  22. J.-H. He, “Variational iteration method for autonomous ordinary differential systems,” Applied Mathematics and Computation, vol. 114, no. 2-3, pp. 115–123, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. J.-H. He and X.-H. Wu, “Construction of solitary solution and compacton-like solution by variational iteration method,” Chaos, Solitons & Fractals, vol. 29, no. 1, pp. 108–113, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. J.-H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57–68, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. J.-H. He, “Approximate solution of nonlinear differential equations with convolution product nonlinearities,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 69–73, 1998. View at Scopus
  26. J.-H. He, “Asymptotic methods: the next frontier towards nonlinear science,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 1907–1908, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. M. A. Abdou and A. A. Soliman, “Variational iteration method for solving Burger's and coupled Burger's equations,” Journal of Computational and Applied Mathematics, vol. 181, no. 2, pp. 245–251, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  28. A. A. Soliman, “A numerical simulation and explicit solutions of KdV-Burgers' and Lax's seventh-order KdV equations,” Chaos, Solitons and Fractals, vol. 29, no. 2, pp. 294–302, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. E. M. Abulwafa, M. A. Abdou, and A. A. Mahmoud, “The solution of nonlinear coagulation problem with mass loss,” Chaos, Solitons & Fractals, vol. 29, no. 2, pp. 313–330, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. S. Momani and S. Abuasad, “Application of He's variational iteration method to Helmholtz equation,” Chaos, Solitons & Fractals, vol. 27, no. 5, pp. 1119–1123, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. N. Bildik and A. Konuralp, “The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 65–70, 2006. View at Scopus
  32. Z. M. Odibat and S. Momani, “Application of variational iteration method to nonlinear differential equations of fractional order,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 7, no. 1, pp. 27–34, 2006. View at Scopus
  33. J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141–1199, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  34. Z. Wan-Xie, “On precise integration method,” Journal of Computer and Applied Mathematics, vol. 163, no. 1, pp. 59–78, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  35. D.-C. Wan and G.-W. Wei, “The study of quasi wavelets based numerical method applied to Burgers' equations,” Applied Mathematics and Mechanics, vol. 21, no. 10, pp. 991–1001, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  36. G. W. Wei, “Quasi wavelets and quasi interpolating wavelets,” Chemical Physics Letters, vol. 296, no. 3-4, pp. 253–258, 1998. View at Scopus
  37. S.-L. Mei, C. J. Du, and S. W. Zhang, “Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems,” Chaos, Solitons and Fractals, vol. 35, no. 3, pp. 536–542, 2008. View at Publisher · View at Google Scholar · View at Scopus