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Mathematical Problems in Engineering
Volume 2013, Article ID 149289, 8 pages
http://dx.doi.org/10.1155/2013/149289
Research Article

Texture Enhancement Based on the Savitzky-Golay Fractional Differential Operator

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

Received 13 August 2012; Revised 5 January 2013; Accepted 5 January 2013

Academic Editor: José Tenreiro Machado

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.

Citations to this Article [21 citations]

The following is the list of published articles that have cited the current article.

  • Hamid A. Jalab, and Herman K. Omer, “Human computer interface using hand gesture recognition based on neural network,” 2015 5th National Symposium on Information Technology: Towards New Smart World (NSITNSW), pp. 1–6, . View at Publisher · View at Google Scholar
  • Hamid A. Jalab, and Herman. K. Omer, “Human computer interface using hand gesture recognition based on neural network,” 2015 5th National Symposium on Information Technology: Towards New Smart World (NSITNSW), pp. 1–6, . View at Publisher · View at Google Scholar
  • Hamid A. Jalab, and Rabha W. Ibrahim, “Texture Enhancement for Medical Images Based on Fractional Differential Masks,” Discrete Dynamics in Nature and Society, vol. 2013, pp. 1–10, 2013. View at Publisher · View at Google Scholar
  • Hamid A. Jalab, and Rabha W. Ibrahim, “On Generalized Fractional Differentiator Signals,” Discrete Dynamics in Nature and Society, 2013. View at Publisher · View at Google Scholar
  • Hamid A. Jalab, and Rabha W. Ibrahim, “Fractional Conway Polynomials for Image Denoising with Regularized Fractional Power Parameters,” Journal of Mathematical Imaging and Vision, vol. 51, no. 3, pp. 442–450, 2014. View at Publisher · View at Google Scholar
  • Hamid A. Jalab, and Rabha W. Ibrahim, “Fractional alexander polynomials for image denoising,” Signal Processing, 2014. View at Publisher · View at Google Scholar
  • Shaoxiang Hu, and Ping Liang, “Theory Analysis of Left-Handed Grünwald-Letnikov Formula with to Detect and Locate Singularities,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Hamid A. Jalab, “Regularized Fractional Power Parameters for Image Denoising Based on Convex Solution of Fractional Heat Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–8, 2014. View at Publisher · View at Google Scholar
  • Zhiwu Liao, “A New Definition of Fractional Derivatives Based on Truncated Left-Handed Grünwald-Letnikov Formula with and Median Correction,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • Rabha W. Ibrahim, Zahra Moghaddasi, Hamid A. Jalab, and Rafidah Md Noor, “Fractional Differential Texture Descriptors Based on the Machado Entropy for Image Splicing Detection,” Entropy, vol. 17, no. 7, pp. 4775–4785, 2015. View at Publisher · View at Google Scholar
  • Saeed Islam, Almas Abbasi, Chaw Seng Woo, and Rabha Waell Ibrahim, “Invariant Domain Watermarking Using Heaviside Function of Order Alpha and Fractional Gaussian Field,” Plos One, vol. 10, no. 4, 2015. View at Publisher · View at Google Scholar
  • Peijin Tong, Yiping Du, Kaiyi Zheng, Ting Wu, and Jiajun Wang, “Improvement of NIR model by fractional order Savitzky-Golay derivation (FOSGD) coupled with wavelength selection,” Chemometrics And Intelligent Laboratory Systems, vol. 143, pp. 40–48, 2015. View at Publisher · View at Google Scholar
  • Kai-Yi Zheng, Xuan Zhang, Pei-Jing Tong, Yuan Yao, and Yi-Ping Du, “Pretreating near infrared spectra with fractional order Savitzky-Golay differentiation (FOSGD),” Chinese Chemical Letters, vol. 26, no. 3, pp. 293–296, 2015. View at Publisher · View at Google Scholar
  • Rabha W. Ibrahim, and Hamid A. Jalab, “Discrete boundary value problem based on the fractional Gateaux derivative,” Boundary Value Problems, 2015. View at Publisher · View at Google Scholar
  • Peter Amoako-Yirenkyi, Justice Kwame Appati, and Isaac Kwame Dontwi, “A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative,” Advances in Difference Equations, vol. 2016, no. 1, 2016. View at Publisher · View at Google Scholar
  • H. A. Jalab, and R. W. Ibrahim, “ Image denoising algorithms based on fractional sinc α with the covariance of fractional Gaussian fields ,” The Imaging Science Journal, vol. 64, no. 2, pp. 100–108, 2016. View at Publisher · View at Google Scholar
  • Badr Alkahtani, and Abdon Atangana, “Chaos on the Vallis Model for El Niño with Fractional Operators,” Entropy, vol. 18, no. 4, pp. 100, 2016. View at Publisher · View at Google Scholar
  • Ming Gu, and Renfang Wang, “Fractional Differentiation-Based Active Contour Model Driven by Local Intensity Fitting Energy,” Mathematical Problems in Engineering, vol. 2016, pp. 1–10, 2016. View at Publisher · View at Google Scholar
  • Hamid A. Jalab, Rabha W. Ibrahim, Alaa Ahmed Abbas Al-Abayechi, and Ali M. Hasan, “Image enhancement based on fractional poisson for segmentation of skin lesions using the watershed transform,” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10645, pp. 249–259, 2017. View at Publisher · View at Google Scholar
  • Ala’a Al-Shamasneh, Hamid Jalab, Shivakumara Palaiahnakote, Unaizah Obaidellah, Rabha Ibrahim, and Moumen El-Melegy, “A New Local Fractional Entropy-Based Model for Kidney MRI Image Enhancement,” Entropy, vol. 20, no. 5, pp. 344, 2018. View at Publisher · View at Google Scholar
  • Rabha W. Ibrahim, Ali M. Hasan, and Hamid A. Jalab, “A New Deformable Model Based on Fractional Wright Energy Function for Tumor Segmentation of Volumetric Brain MRI Scans,” Computer Methods and Programs in Biomedicine, 2018. View at Publisher · View at Google Scholar