About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 618536, 10 pages
http://dx.doi.org/10.1155/2013/618536
Research Article

Texture Enhancement for Medical Images Based on Fractional Differential Masks

1Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysia
2Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 13 January 2013; Revised 6 March 2013; Accepted 6 March 2013

Academic Editor: Thabet Abdeljawad

Copyright © 2013 Hamid A. Jalab and Rabha W. Ibrahim. 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. R. Hilfer, Applications of Fractional Calculus in Physics, vol. 463, World Scientific, Singapore, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. M. Kanbur, I. Narin, E. Özdemir, E. Dinç, and D. Baleanu, “Fractional wavelet transform for the quantitative spectral analysis of two-component system,” in New Trends in Nanotechnology and Fractional Calculus Applications, pp. 321–331, Springer, New York, NY, USA, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  3. D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Series on Complexity, Nonlinearity and Chaos, World Scientific, Hackensack, NJ, USA, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  4. E. Dinç and D. Baleanu, “Ultra-performance liquid chromatography for the multicomponent analysis of a ternary mixture containing thiamine, pyridoxine, and lidocaine in ampules,” Journal of AOAC International, vol. 95, pp. 903–912, 2010.
  5. E. Dinç and D. Baleanu, “A new fractional wavelet approach for the simultaneous determination of ampicillin sodium and sulbactam sodium in a binary mixture,” Spectrochimica Acta A, vol. 63, no. 3, pp. 631–638, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. H. A. Jalab and R. W. Ibrahim, “Denoising algorithm based on generalized fractional integral operator with two parameters,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 529849, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. C. Sparavigna, “Using fractional differentiation in astronomy,” Computer Vision and Pattern Recognition, http://arxiv.org/abs/0910.2381v3.
  8. R. Marazzato and A. C. Sparavigna, “Astronomical image processing based on fractional calculus: the AstroFracTool,” Instrumentation and Methods for Astrophysics, http://arxiv.org/abs/0910.4637v2.
  9. Y.-F. Pu, X. Yuan, K. Liao, Z.-L. Chen, and J.-L. Zhou, “Five numerical algorithms of fractional calculus applied in modern signal analyzing and processing,” Journal of Sichuan University (Engineering Science Edition), vol. 37, no. 5, article 118, 2005. View at Scopus
  10. Y. Pu, W. Wang, J. Zhou, Y. Wang, and H. Jia, “Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation,” Science in China F, vol. 51, no. 9, pp. 1319–1339, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. T. Glatard, J. Montagnat, and I. E. Magnin, “Texture based medical image indexing and retrieval: application to cardiac imaging,” in Proceedings of the 6th ACM SIGMM International Workshop on Multimedia Information Retrieval (MIR '04), pp. 135–142, New York, NY, USA, October 2004. View at Scopus
  12. K. Lu, N. He, and L. Li, “Nonlocal means-based denoising for medical images,” Computational and Mathematical Methods in Medicine, vol. 2012, Article ID 438617, 7 pages, 2012. View at Publisher · View at Google Scholar
  13. M. N. Kohan and H. Behnam, “Denoising medical images using calculus of variations,” Journal of Medical Signals and Sensors, vol. 1, pp. 184–190, 2011.
  14. F. Luisier, T. Blu, and M. Unser, “A new SURE approach to image denoising: interscale orthonormal wavelet thresholding,” IEEE Transactions on Image Processing, vol. 16, no. 3, pp. 593–606, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  15. H. A. Jalab and R. W. Ibrahim, “Texture feature extraction based on fractional mask convolution with cesáro means for content-based image retrieval,” in Proceedings of the 12th Pacific Rim International Conference on Trends in Artificial Intelligence (PRICAI '12), pp. 170–179, 2012.
  16. G. Castellano, L. Bonilha, L. M. Li, and F. Cendes, “Texture analysis of medical images,” Clinical Radiology, vol. 59, no. 12, pp. 1061–1069, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. J. R. Smith and S. F. Chang, “Automated binary texture feature sets for image retrieval,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '96), pp. 2239–2242, May 1996. View at Scopus
  18. H. A. Jalab and R. W. Ibrahim, “Texture enhancement based on the savitzky-golay fractional, differential operator,” Mathematical Problems in Engineering, vol. 2013, Article ID 149289, 8 pages, 2013. View at Publisher · View at Google Scholar
  19. A. McAndrew, An Introduction to Digital Image Processing with Matlab Notes for SCM2511 Image Processing, School of Computer Science and Mathematics; Victoria University of Technology, 2004.
  20. C. Qing-li, H. Guo, and Z. Xiu-qiong, “A fractional differential approach to low contrast image enhancement,” International Journal of Knowledge and Language Processing, vol. 3, pp. 20–29, 2012.
  21. Z. Yang, F. Lang, X. Yu, and Y. Zhang, “The construction of fractional differential gradient operator,” Journal of Computational Information Systems, vol. 7, pp. 4328–4342, 2011.
  22. V. Garg and K. Singh, “An improved Grunwald-Letnikov fractional differential mask for image texture enhancement,” International Journal, vol. 3, no. 3, pp. 130–135, 2012.
  23. Y.-F. Pu, J.-L. Zhou, and X. Yuan, “Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement,” IEEE Transactions on Image Processing, vol. 19, no. 2, pp. 491–511, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  24. R. W. Ibrahim, “On generalized Srivastava-Owa fractional operators in the unit disk,” Advances in Difference Equations, vol. 2011, article 55, 10 pages, 2011. View at MathSciNet
  25. Y. Zhang, Y. Pu, and J. Zhou, “Construction of fractional differential masks based on Riemann-Liouville definition,” Journal of Computational Information Systems, vol. 6, no. 10, pp. 3191–3199, 2010. View at Scopus
  26. “MathWorks, Inc, 1984–2009”.
  27. R. M. Haralick, K. Shanmugam, and I. Dinstein, “Textural features for image classification,” IEEE Transactions on Systems, Man and Cybernetics, vol. 3, no. 6, pp. 610–621, 1973. View at Scopus
  28. E. Sousa, “How to approximate the fractional derivative of order 1<α2,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 22, no. 4, Article ID 1250075, 13 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet