A new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement

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dc.citation.epage202
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage187
dc.contributor.affiliationУніверситет Каді Айяда
dc.contributor.affiliationПерший університет Хасана в Сеттаті
dc.contributor.affiliationCadi Ayyad University
dc.contributor.affiliationHassan First University of Settat
dc.contributor.authorАла, Х.
dc.contributor.authorАла, Н. Е.
dc.contributor.authorАкель, Ф.
dc.contributor.authorЛефрайх, Х.
dc.contributor.authorAlaa, H.
dc.contributor.authorAlaa, N. E.
dc.contributor.authorAqel, F.
dc.contributor.authorLefraich, H.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:14:20Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractМета цієї роботи — запропонувати новий чисельний підхід до відновлення зображення та покращення його контрасту на основі реакційно-дифузійної моделі (модель Грея–Скотта). Для видалення шумів використовується методика граткових рівнянь Больцмана. Зазвичай вона використовується в експериментах з гідродинаміки. Оскільки рух пікселів можна порівняти з рухом рідини, представлена методика демонструє хорошу продуктивність при обробці зашумлених зображень. Ефективність та продуктивність запропонованого алгоритму перевірено на кількох чисельних експериментах.
dc.description.abstractThe aim of this work is to propose a new numerical approach to image restoration and contrast enhancement based on a reaction-diffusion model (Gray–Scott model). For noise removal, a Lattice Boltzmann technique is used. This method is usually used in fluid dynamics experiments. Since pixels motion can be compared to fluids motion, the presented technique also indicates a good performance in processing noisy images. The efficiency and performance of the proposed algorithm are verified by several numerical experiments.
dc.format.extent187-202
dc.format.pages16
dc.identifier.citationA new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement / H. Alaa, N. E. Alaa, F. Aqel, H. Lefraich // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 187–202.
dc.identifier.citationenA new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement / H. Alaa, N. E. Alaa, F. Aqel, H. Lefraich // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 2. — P. 187–202.
dc.identifier.doidoi.org/10.23939/mmc2022.02.187
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63431
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 2 (9), 2022
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dc.relation.references[18] Chaabane R., Askri F., Nasrallah S. B. Analysis of two-dimensional transient conduction?radiation problems in an anisotropically scattering participating enclosure using the lattice Boltzmann method and the control volume finite element method. Computer Physics Communications. 182 (7), 1402–1413 (2011).
dc.relation.references[19] Jawerth B., Lin P., Sinzinger E. Lattice Boltzmann Models for Anisotropic Diffusion of Images. Journal of Mathematical Imaging and Vision. 11, 231–237 (1999).
dc.relation.references[20] Sun X., Wang Z., Chen G. Parallel active contour with Lattice Boltzmann scheme on modern GPU. 2021 19th IEEE International Conference on Image Processing. 1709–1712 (2012).
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dc.relation.references[22] Chang Q., Yang T. A Lattice Boltzmann Method for Image Denoising. IEEE Transactions on Image Processing. 18 (12), 2797–2802 (2009).
dc.relation.references[23] Chen J., Chai Z., Shi B., Zhang W. Lattice Boltzmann method for filtering and contour detection of the natural images. Computers & Mathematics with Applications. 68 (3), 257–268 (2014).
dc.relation.references[24] Ambrosio L., Tortorelli V. M. Approximation of functional depending on jumps by elliptic functional via t-convergence. Communications on Pure and Applied Mathematics. 43 (8), 999–1036 (1990).
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dc.relation.references[28] Black M. J., Sapiro G., Marimont D. H., Heeger D. Robust anisotropic diffusion. IEEE Transactions on Image Processing. 7 (3), 421–432 (1998).
dc.relation.referencesen[1] Murray J.-D. Mathematical biology. Berlin, Springer (1989).
dc.relation.referencesen[2] Teuscher C., Adamatzky A. Proc. of the 2005 Workshop on Unconventional Computing From cellular Automata to Wetwar. Luniver Press Beckington (2005).
dc.relation.referencesen[3] Perona P., Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence. 12 (7), 629–639 (1990).
dc.relation.referencesen[4] Alvarez L., Lions P.-L., Morel J. M. Image Selective Smoothing and Edge Detection by Nonlinear Diffusion. II. SIAM Journal on Numerical Analysis. 29 (3), 845–866 (1992).
dc.relation.referencesen[5] 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[6] Morfu S. On some applications of diffusion processes for image processing. Physics Letters A. 373 (29), 2438–2444 (2009).
dc.relation.referencesen[7] Alaa K., Atounti M., Zirhem M. Image restoration and contrast enhancement based on a nonlinear reactiondiffusion mathematical model and divide & conquer technique. Mathematical Modeling and Computing. 8 (3), 549–559 (2021).
dc.relation.referencesen[8] Morfu S., Marqui´e P., Nofi´el´e B., Ginhac D. Chapter 3 – Nonlinear systems for image processing. Advances in Imaging and Electron Physics. 152, 79–151 (2008).
dc.relation.referencesen[9] Morfu S., Nofiele B., Marqui´e P. On the use of multistability for image processing. Physics Letters A. 367 (3), 192–198 (2007).
dc.relation.referencesen[10] Oussous M. A., Alaa N., Khouya Y. A. 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[11] Hardy J., Pomeau Y., de Pazzis O. Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions. Journal of Mathematical Physics. 14 (12), 1746–1759 (1973).
dc.relation.referencesen[12] Chen S., Doolen G. D. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics. 30 (1), 329–364 (1998).
dc.relation.referencesen[13] Wolf–Gladrow D. A. Lattice Gas Cellular Automata and Lattice Boltzmann Models. Springer–Verlag, Berlin–Heidelberg (2000).
dc.relation.referencesen[14] Shan X. Simulation of Rayleigh–B´enard convection using a lattice Boltzmann method. Physival Review E. 55 (3), 2780–2788 (1997).
dc.relation.referencesen[15] Ho J.-R., Kuo C.-P., Jiaung W.-S., Twu C.-J. Lattice Boltzmann scheme for hyperbolic heat conduction equation. Numerical Heat Transfer, Part B: Fundamentals. 41 (6), 591–607 (2002).
dc.relation.referencesen[16] Shi B., Deng B., Du R., Chen X. A new scheme for source term in LBGK model for convection-diffusion equation. Computers & Mathematics with Applications. 55 (7), 1568–1575 (2008).
dc.relation.referencesen[17] Chai Z., Zhao T. S. Lattice Boltzmann model for the convection-diffusion equation. Physical Review E. 87 (6), 063309 (2013).
dc.relation.referencesen[18] Chaabane R., Askri F., Nasrallah S. B. Analysis of two-dimensional transient conduction?radiation problems in an anisotropically scattering participating enclosure using the lattice Boltzmann method and the control volume finite element method. Computer Physics Communications. 182 (7), 1402–1413 (2011).
dc.relation.referencesen[19] Jawerth B., Lin P., Sinzinger E. Lattice Boltzmann Models for Anisotropic Diffusion of Images. Journal of Mathematical Imaging and Vision. 11, 231–237 (1999).
dc.relation.referencesen[20] Sun X., Wang Z., Chen G. Parallel active contour with Lattice Boltzmann scheme on modern GPU. 2021 19th IEEE International Conference on Image Processing. 1709–1712 (2012).
dc.relation.referencesen[21] Balla-Arab´e S., Gao X. Image multi-thresholding by combining the lattice Boltzmann model and a localized level set algorithm. Neurocomputing. 93, 106–114 (2012).
dc.relation.referencesen[22] Chang Q., Yang T. A Lattice Boltzmann Method for Image Denoising. IEEE Transactions on Image Processing. 18 (12), 2797–2802 (2009).
dc.relation.referencesen[23] Chen J., Chai Z., Shi B., Zhang W. Lattice Boltzmann method for filtering and contour detection of the natural images. Computers & Mathematics with Applications. 68 (3), 257–268 (2014).
dc.relation.referencesen[24] Ambrosio L., Tortorelli V. M. Approximation of functional depending on jumps by elliptic functional via t-convergence. Communications on Pure and Applied Mathematics. 43 (8), 999–1036 (1990).
dc.relation.referencesen[25] Nomura A., Ichikawa M., Sianipar R. H., Miike H. Edge detection with reaction-diffusion equations having a local average threshold. Pattern Recognition and Image Analysis. 18 (2), 289–299 (2008).
dc.relation.referencesen[26] Witkin A., Kass M. Reaction-diffusion textures. ACM SIGGRAPH Computer Graphics. 25 (4), 299–308 (1991).
dc.relation.referencesen[27] Sanderson A. R., Johnson C. R., Kirby R. M., Yang L. Advanced reaction-diffusion models for texture synthesis. Journal of Graphics Tools. 11 (3), 47–71 (2006).
dc.relation.referencesen[28] Black M. J., Sapiro G., Marimont D. H., Heeger D. Robust anisotropic diffusion. IEEE Transactions on Image Processing. 7 (3), 421–432 (1998).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectвідновлення зображення
dc.subjectметод граткових рівнянь Больцмана
dc.subjectмодель Грея—Скотта
dc.subjectреакція–дифузія
dc.subjectпокращення контрасту
dc.subjectсхема D2Q9
dc.subjectсхема D2Q5
dc.subjectimage restoration
dc.subjectLattice Boltzmann method
dc.subjectGray–Scott model
dc.subjectreaction–diffusion
dc.subjectcontrast enhancement
dc.subjectD2Q9 scheme
dc.subjectD2Q5 scheme
dc.titleA new Lattice Boltzmann method for a Gray–Scott based model applied to image restoration and contrast enhancement
dc.title.alternativeНовий метод граткових рівнянь Больцмана для базової моделі Грея–Скотта, застосований для відновлення зображень та покращення їхнього контрасту
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 2