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Research Article

A novel convolutional Atangana-Baleanu fractional derivative mask for medical image edge analysis

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Pages 815-837 | Received 04 Oct 2021, Accepted 26 Jul 2022, Published online: 22 Aug 2022

References

  • Alkahtani, B. S. T. (2016). Chua’s circuit model with Atangana-Baleanu derivative with fractional order. Chaos, Solitons & Fractals, 89, 547–551. https://doi.org/10.1016/j.chaos.2016.03.020
  • Amoako-Yirenkyi, P., Appati, J. K., & Dontwi, I. K. (2016a). A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative. Advances in Difference Equations, 2016(1), 1–23. https://doi.org/10.1186/s13662-016-0946-8
  • Amoako-Yirenkyi, P., Appati, J. K., & Dontwi, I. K. (2016b). Performance analysis of image smoothing techniques on a new fractional convolution mask for image edge detection. Open Journal of Applied Sciences, 6(7), 478. https://doi.org/10.4236/ojapps.2016.67048
  • Atangana, A., & Koca, I. (2016). Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Chaos, Solitons & Fractals, 89, 447–454. https://doi.org/10.1016/j.chaos.2016.02.012
  • Bahaa, G. M. (2019). Optimal control problem for variable-order fractional differential systems with time delay involving Atangana-Baleanu derivatives. Chaos, Solitons & Fractals, 122, 129–142. https://doi.org/10.1016/j.chaos.2019.03.001
  • Bist, A., & Sondhi, S. G. (2017). Fractional Order Approach for Edge Detection of Low Contrast Images ( Doctoral dissertation).
  • Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without Singular kernel. Progress in Fractional Differentiation and Applications, 1 (2) , 73–85.
  • Davis, L. S. (1975). A survey of edge detection techniques. Computer Graphics and Image Processing, 4(3), 248–270. https://doi.org/10.1016/0146-664X(75)90012-X
  • Ding, L., & Goshtasby, A. (2001). On the Canny edge detector. Pattern Recognition, 34(3), 721–725. https://doi.org/10.1016/S0031-3203(00)00023-6
  • Eser, S. E. R. T., & Derya, A. V. C. I. (2019). A new edge detection approach via neutrosophy based on maximum norm entropy. Expert Systems with Applications, 115, 499–511. https://doi.org/10.1016/j.eswa.2018.08.019
  • Ghanbari, B., & Atangana, A. (2020a). A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing. Physica A: Statistical Mechanics and Its Applications, 542, 123516. https://doi.org/10.1016/j.physa.2019.123516
  • Ghanbari, B., & Atangana, A. (2020b). Some new edge detecting techniques based on fractional derivatives with nonlocal and nonsingular kernels. Advances in Difference Equations, 2020(1), 1–19. https://doi.org/10.1186/s13662-020-02890-9
  • Ghimpeţeanu, G., Batard, T., Bertalmío, M., & Levine, S. (2015). A decomposition framework for image denoising algorithms. IEEE Transactions on Image Processing, 25(1), 388–399. https://doi.org/10.1109/TIP.2015.2498413
  • Gómez-Aguilar, J. F. (2017). Space-time fractional diffusion equation using a derivative with nonsingular and regular kernel. Physica A: Statistical Mechanics and Its Applications, 465, 562–572. https://doi.org/10.1016/j.physa.2016.08.072
  • Gómez-Aguilar, J. F., Escobar-Jiménez, R. F., López-López, M. G., & Alvarado-Martínez, V. M. (2016). Atangana-Baleanu fractional derivative applied to electromagnetic waves in dielectric media. Journal of Electromagnetic Waves and Applications, 30(15), 19–37 doi:https://doi.org/10.1080/09205071.2016.1225521.
  • Gonzalez, R. C., & Woods, R. E. (2006). Digital Image Processing (3rd ed.). Prentice-Hall, Inc.
  • Henriques, M., Valério, D., Gordo, P., & Melicio, R. (2021 Fractional-order colour image processing Mathematics 9 (5) doi:https://doi.org/10.3390/math9050457). .
  • Ioannidou, A., Halkidis, S. T., & Stephanides, G. (2012). A novel technique for image steganography based on a high payload method and edge detection. Expert Systems with Applications, 39(14), 11517–11524. https://doi.org/10.1016/j.eswa.2012.02.106
  • Ismail, S. M., Said, L. A., Madian, A. H., & Radwan, A. G. (2021). Fractional-Order Edge Detection Masks for Diabetic Retinopathy Diagnosis as a Case Study. Computers, 10(3), 30. https://doi.org/10.3390/computers10030030
  • Jarad, F., Abdeljawad, T., & Hammouch, Z. (2018). On a class of ordinary differential equations in the frame of Atangana-Baleanu fractional derivative. Chaos, Solitons & Fractals, 117, 16–20. https://doi.org/10.1016/j.chaos.2018.10.006
  • Kaur, K., Jindal, N., & Singh, K. (2021). Fractional Fourier Transform based Riesz fractional derivative approach for edge detection and its application in image enhancement. Signal Processing, 180, 107852. https://doi.org/10.1016/j.sigpro.2020.107852
  • Kilbasi, A. A., & Saigo, M. (1996). On Mittag-Leffler type function, fractional calculas operators and solutions of integral equations. Integral Transforms and Special Functions, 4(4), 355–370. https://doi.org/10.1080/10652469608819121
  • Kumar, S., Saxena, R., & Singh, K. (2017). Fractional Fourier transform and fractional-order calculus-based image edge detection. Circuits, Systems, and Signal Processing, 36(4), 1493–1513. https://doi.org/10.1007/s00034-016-0364-x
  • Lavín-Delgado, J. E., Solís-Pérez, J. E., Gómez-Aguilar, J. F., & Escobar-Jiménez, R. F. (2020). A new fractional-order mask for image edge detection based on Caputo–Fabrizio fractional-order derivative without singular kernel. Circuits, Systems, and Signal Processing, 39(3), 1419–1448. https://doi.org/10.1007/s00034-019-01200-3
  • Lv, H., Zhang, F., & Wang, R. (2021). Robust Active Contour Model Using Patch-Based Signed Pressure Force and Optimized Fractional-Order Edge. IEEE Access, 9, 8771–8785. https://doi.org/10.1109/ACCESS.2021.3049513
  • Nandal, A., Gamboa-Rosales, H., Dhaka, A., Celaya-Padilla, J. M., Galvan-Tejada, J. I., Galvan-Tejada, C. E., & Guzman-Valdivia, C. (2018). Image edge detection using fractional calculus with feature and contrast enhancement. Circuits, Systems, and Signal Processing, 37(9), 3946–3972. https://doi.org/10.1007/s00034-018-0751-6
  • Pan, X., Zhu, J., Yu, H., Chen, L., Liu, Y., & Li, L. (2021). Robust corner detection with fractional calculus for magnetic resonance imaging. Biomedical Signal Processing and Control, 63, 102–112. https://doi.org/10.1016/j.bspc.2020.102112
  • Pu, Y. F., Zhou, J. L., & Yuan, X. (2009). Fractional differential mask: A fractional differential-based approach for multiscale texture enhancement. IEEE Transactions on Image Processing, 19(2), 491–511. https://doi.org/10.1109/TIP.2009.2035980
  • Seba, C., Logeswari, K., & Jarad, F. (2019). New results on existence in the framework of Atangana-Baleanu derivative for fractional integro-differential equations. Chaos, Solitons & Fractals, 125, 194–200. https://doi.org/10.1016/j.chaos.2019.05.014
  • Selvy, P. T., Palanisamy, V., & Purusothaman, T. (2011). Performance analysis of clustering algorithms in brain tumor detection of MR images. European Journal of Scientific Research, 62(3), 321–330 http://www.eurojournals.com/ejsr.htm.
  • Sheng, J., Jiang, W., & Pang, D. (2020). Finite-Time Stability of Atangana–Baleanu Fractional-Order Linear Systems. Complexity, 2020, 1–8. https://doi.org/10.1155/2020/1727358
  • Telke, C., & Beitelschmidt, M. (2015). Edge detection based on fractional order differentiation and its application to railway track images. Pamm, 15(1), 671–672. https://doi.org/10.1002/pamm.201510325
  • Wang, H. D., & Gao, S. J. (2017). Bilateral discoid medial meniscus associated with meniscal tears and hypoplasia of the medial femoral condyle: A case report. Medicine, 96(46 1–5 doi:10.1097/MD.0000000000008637).
  • Yan, R., & Shao, L. (2016). Blind image blur estimation via deep learning. IEEE Transactions on Image Processing, 25(4), 1910–1921. https://doi.org/10.1109/TIP.2016.2535273

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