Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide & conquer technique
dc.citation.epage | 559 | |
dc.citation.issue | 3 | |
dc.citation.spage | 549 | |
dc.contributor.affiliation | Університет Мохаммеда Першого | |
dc.contributor.affiliation | Університет Каді Айяд | |
dc.contributor.affiliation | University of Mohammed First | |
dc.contributor.affiliation | Cadi Ayyad University | |
dc.contributor.author | Алаа, К. | |
dc.contributor.author | Атунті, М. | |
dc.contributor.author | Зірхем, М. | |
dc.contributor.author | Alaa, K. | |
dc.contributor.author | Atounti, M. | |
dc.contributor.author | Zirhem, M. | |
dc.coverage.placename | Львів | |
dc.coverage.placename | Lviv | |
dc.date.accessioned | 2023-10-25T07:19:12Z | |
dc.date.available | 2023-10-25T07:19:12Z | |
dc.date.created | 2021-03-01 | |
dc.date.issued | 2021-03-01 | |
dc.description.abstract | У статті представлено новий алгоритм цифрової обробки зображень, які зашумлені змішаним гаусово-імпульсним шумом. Математична модель базується на техніці “розділяй і володарюй” у поєднанні з реакційно-дифузійною системою. Спочатку зображення розкладається на низькочастотні та високочастотні компоненти, згортаючи кожну із заздалегідь визначеним згортковим фільтром. Далі використовується проста схема з різними вагами, щоб інтегрувати та зібрати ці оброблені фрагменти зображення у відфільтроване зображення. Нарешті, застосовується наша реакційно-дифузійна система, щоб збільшити контрастність зображення. Описано ряд експериментальних результатів, щоб проілюструвати роботу запропонованого алгоритму та показати, що він дуже ефективний при усуненні змішаного гаусово-імпульсного шуму, для збільшення контрастності зображення та збереження країв. | |
dc.description.abstract | In this article, we present a new algorithm for digital image processing noised by mixed Gaussian-impulse noise. Our mathematical model is based on the divide and conquer technique coupled with a reaction-diffusion system. We first decompose our image into low and high-frequency components by convolving each with a predefined convolutional filter. Further, we use a simple scheme of different weights to integrate and collect these processed sub-images into a filtered image. Finally, we apply our Reaction-Diffusion system to increase the contrast in the image. A number of experimental results are described to illustrate the performance of our algorithm and show that it is very effective in eliminating mixed Gaussian-impulse noise, increasing the contrast of the image and preserving the edges. | |
dc.format.extent | 549-559 | |
dc.format.pages | 11 | |
dc.identifier.citation | Alaa K. Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide & conquer technique / K. Alaa, M. Atounti, M. Zirhem // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 3. — P. 549–559. | |
dc.identifier.citationen | Alaa K. Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide & conquer technique / K. Alaa, M. Atounti, M. Zirhem // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 3. — P. 549–559. | |
dc.identifier.doi | doi.org/10.23939/mmc2021.03.549 | |
dc.identifier.uri | https://ena.lpnu.ua/handle/ntb/60408 | |
dc.language.iso | en | |
dc.publisher | Видавництво Львівської політехніки | |
dc.publisher | Lviv Politechnic Publishing House | |
dc.relation.ispartof | Mathematical Modeling and Computing, 3 (8), 2021 | |
dc.relation.references | [1] Tomasi C., Manduchi R. Bilateral filtering for gray and color images. Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271). 839–846 (1998). | |
dc.relation.references | [2] Buades A., Coll B., Morel J.-M. A non-local algorithm for image denoising. 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05). 60–65 (2005). | |
dc.relation.references | [3] Helstrom C. W. Image restoration by the method of least squares. Journal of the Optical Society of America. 57 (3), 297–303 (1967). | |
dc.relation.references | [4] Zirhem M., Alaa N. Texture synthesis by reaction diffusion process. Annals of the University of Craiova, Mathematics and Computer Science Series. 42, 56–69 (2015). | |
dc.relation.references | [5] Alaa N., Zirhem M. Entropy solution for a fourth-order nonlinear degenerate problem for image decomposition. J. Adv. Math. Stud. 11, 412–427 (2018). | |
dc.relation.references | [6] Alaa N., Zirhem M. Bio-inspired reaction diffusion system applied to image restoration. International Journal of Bio-inspired Computation. 12 (2), 128–137 (2018). | |
dc.relation.references | [7] Perona P., Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Patterns Analysis and Machine Intelligence. 12 (7), 629–639 (1990). | |
dc.relation.references | [8] Alvarez L., Lions P. L., Morel J. M. Image selective smoothing and edge detection by nonlinear diffusion. II. SIAM Journal of Numerical Analysis. 29 (3), 845–866 (1992). | |
dc.relation.references | [9] Catt´e F., Lions P. L., Morel J. M., Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis. 29 (1), 182–193 (1992). | |
dc.relation.references | [10] Morfu S. On some applications of diffusion processes for image processing. Physics Letters A. 373 (29), 2438–2444 (2009). | |
dc.relation.references | [11] Ait Oussous M., Alaa N., Ait Khouya Y. Anisotropic and nonlinear diffusion applied to image enhancement and edge detection. International Journal of Computer Applications in Technology. 49 (2), 122–133 (2014). | |
dc.relation.references | [12] Mallat S., Hwang W. L. Singularity detection and processing with wavelets. IEEE Transactions on Information Theory. 38 (2), 617–643 (1992). | |
dc.relation.references | [13] Agaian S., McClendon S. A. Novel medical image enhancement algorithms. Proc. SPIE 7532, Image Processing: Algorithms and Systems VIII, 75320W (2010). | |
dc.relation.references | [14] Turing A. M. The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond. B. 237, 37–72 (1952). | |
dc.relation.references | [15] Prigogine I., Nicolis G. Biological order, structure and instabilities. Quart. Rev. Biophys. 4, 107–148 (1971). | |
dc.relation.references | [16] Gierer A., Meinhardt H. A theory of biological pattern formation. Kybernetik. 12, 30–39 (1970). | |
dc.relation.references | [17] Ambrosio B., Aziz-Alaoui M. A. Synchronisation dans un r´eseau d’´equations aux d´eriv´ees partielles de type Fitzhugh-Nagumo g´en´eralis´e, ´equations aux d´eriv´ees partielles et leurs applications. Actes du colloque Edp-Normandie. 119–131 (2012). | |
dc.relation.references | [18] Nomura A., Ichikawa M., Sianipar R. H., Miike H. Reaction-Diffusion Algorithm for Vision Systems. Vision Systems: Segmentation and Pattern Recognition. 61–80 (2007). | |
dc.relation.references | [19] Charbonnier P., Feraud L., Aubert G., Barlaud M. Deterministic edge-preserving regularization in computed imaging. IEEE Transactions on Image processing. 6 (2), 298–311 (1997). | |
dc.relation.references | [20] Lopez-Rubio E. Restoration of images corrupted by gaussian and uniform impulsive noise. Pattern Recognition. 43 (5), 1835–1846 (2010). | |
dc.relation.references | [21] Liu J., Huan Z., Huang H., Zhang H. An adaptive method for recovering image from mixed noisy data. International Journal of Computer Vision. 85, 182–191 (2009). | |
dc.relation.references | [22] Rodriguez P., Rojas R. A., Wohlberg B. Mixed gaussian-impulse noise image restoration via total variation. 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 1077–1080 (2012). | |
dc.relation.references | [23] Liu J., Tai X., Huang H., Huan Z. A Weighted Dictionary Learning Model for Denoising Images Corrupted by Mixed Noise. IEEE Transactions on Image Processing. 22 (3), 1108–1120 (2012). | |
dc.relation.references | [24] Stout Q. F. Supporting divide and conquer algorithm in image processing. J. of Parallel and Distributed Computing. 4 (1), 95–115 (1987). | |
dc.relation.references | [25] Bacquey N. Packing problem: A divide and conquer algorithm on cellular automata. Automata and JAC. 1–10 (2012). | |
dc.relation.references | 26] Zhuang P., Fu X., Huang Y., Ding X. Image enhancement using divide and conquer strategy. Journal of Visual Communication and Image Representation. 45, 137–146 (2017). | |
dc.relation.referencesen | [1] Tomasi C., Manduchi R. Bilateral filtering for gray and color images. Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271). 839–846 (1998). | |
dc.relation.referencesen | [2] Buades A., Coll B., Morel J.-M. A non-local algorithm for image denoising. 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05). 60–65 (2005). | |
dc.relation.referencesen | [3] Helstrom C. W. Image restoration by the method of least squares. Journal of the Optical Society of America. 57 (3), 297–303 (1967). | |
dc.relation.referencesen | [4] Zirhem M., Alaa N. Texture synthesis by reaction diffusion process. Annals of the University of Craiova, Mathematics and Computer Science Series. 42, 56–69 (2015). | |
dc.relation.referencesen | [5] Alaa N., Zirhem M. Entropy solution for a fourth-order nonlinear degenerate problem for image decomposition. J. Adv. Math. Stud. 11, 412–427 (2018). | |
dc.relation.referencesen | [6] Alaa N., Zirhem M. Bio-inspired reaction diffusion system applied to image restoration. International Journal of Bio-inspired Computation. 12 (2), 128–137 (2018). | |
dc.relation.referencesen | [7] Perona P., Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Patterns Analysis and Machine Intelligence. 12 (7), 629–639 (1990). | |
dc.relation.referencesen | [8] Alvarez L., Lions P. L., Morel J. M. Image selective smoothing and edge detection by nonlinear diffusion. II. SIAM Journal of Numerical Analysis. 29 (3), 845–866 (1992). | |
dc.relation.referencesen | [9] Catt´e F., Lions P. L., Morel J. M., Coll T. Image selective smoothing and edge detection by nonlinear diffusion. SIAM Journal on Numerical Analysis. 29 (1), 182–193 (1992). | |
dc.relation.referencesen | [10] Morfu S. On some applications of diffusion processes for image processing. Physics Letters A. 373 (29), 2438–2444 (2009). | |
dc.relation.referencesen | [11] Ait Oussous M., Alaa N., Ait Khouya Y. Anisotropic and nonlinear diffusion applied to image enhancement and edge detection. International Journal of Computer Applications in Technology. 49 (2), 122–133 (2014). | |
dc.relation.referencesen | [12] Mallat S., Hwang W. L. Singularity detection and processing with wavelets. IEEE Transactions on Information Theory. 38 (2), 617–643 (1992). | |
dc.relation.referencesen | [13] Agaian S., McClendon S. A. Novel medical image enhancement algorithms. Proc. SPIE 7532, Image Processing: Algorithms and Systems VIII, 75320W (2010). | |
dc.relation.referencesen | [14] Turing A. M. The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond. B. 237, 37–72 (1952). | |
dc.relation.referencesen | [15] Prigogine I., Nicolis G. Biological order, structure and instabilities. Quart. Rev. Biophys. 4, 107–148 (1971). | |
dc.relation.referencesen | [16] Gierer A., Meinhardt H. A theory of biological pattern formation. Kybernetik. 12, 30–39 (1970). | |
dc.relation.referencesen | [17] Ambrosio B., Aziz-Alaoui M. A. Synchronisation dans un r´eseau d’´equations aux d´eriv´ees partielles de type Fitzhugh-Nagumo g´en´eralis´e, ´equations aux d´eriv´ees partielles et leurs applications. Actes du colloque Edp-Normandie. 119–131 (2012). | |
dc.relation.referencesen | [18] Nomura A., Ichikawa M., Sianipar R. H., Miike H. Reaction-Diffusion Algorithm for Vision Systems. Vision Systems: Segmentation and Pattern Recognition. 61–80 (2007). | |
dc.relation.referencesen | [19] Charbonnier P., Feraud L., Aubert G., Barlaud M. Deterministic edge-preserving regularization in computed imaging. IEEE Transactions on Image processing. 6 (2), 298–311 (1997). | |
dc.relation.referencesen | [20] Lopez-Rubio E. Restoration of images corrupted by gaussian and uniform impulsive noise. Pattern Recognition. 43 (5), 1835–1846 (2010). | |
dc.relation.referencesen | [21] Liu J., Huan Z., Huang H., Zhang H. An adaptive method for recovering image from mixed noisy data. International Journal of Computer Vision. 85, 182–191 (2009). | |
dc.relation.referencesen | [22] Rodriguez P., Rojas R. A., Wohlberg B. Mixed gaussian-impulse noise image restoration via total variation. 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 1077–1080 (2012). | |
dc.relation.referencesen | [23] Liu J., Tai X., Huang H., Huan Z. A Weighted Dictionary Learning Model for Denoising Images Corrupted by Mixed Noise. IEEE Transactions on Image Processing. 22 (3), 1108–1120 (2012). | |
dc.relation.referencesen | [24] Stout Q. F. Supporting divide and conquer algorithm in image processing. J. of Parallel and Distributed Computing. 4 (1), 95–115 (1987). | |
dc.relation.referencesen | [25] Bacquey N. Packing problem: A divide and conquer algorithm on cellular automata. Automata and JAC. 1–10 (2012). | |
dc.relation.referencesen | 26] Zhuang P., Fu X., Huang Y., Ding X. Image enhancement using divide and conquer strategy. Journal of Visual Communication and Image Representation. 45, 137–146 (2017). | |
dc.rights.holder | © Національний університет “Львівська політехніка”, 2021 | |
dc.subject | реакція-дифузія | |
dc.subject | обробка зображення | |
dc.subject | змішаний гаусово-імпульсний шум | |
dc.subject | техніка “розділяй і володарюй” | |
dc.subject | reaction-diffusion | |
dc.subject | image processing | |
dc.subject | mixed Gaussian-impulse noise | |
dc.subject | divide and conquer technique | |
dc.title | Image restoration and contrast enhancement based on a nonlinear reaction-diffusion mathematical model and divide & conquer technique | |
dc.title.alternative | Відновлення зображення та покращення контрастності на основі нелінійної реакційно-дифузійної математичної моделі та техніки “розділяй і володарюй” | |
dc.type | Article |
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