A Novel Blurring and Sharpening Techniques Using Different Images Based on Heat Equations
DOI:
https://doi.org/10.29304/jqcm.2021.13.1.771Keywords:
MATLAB program, color image, mathematical methods, compressed image, physical imageAbstract
This paper is dedicated to show the practical part of the heat equation and its influence on images from real-life. Examples of one dimension and two dimensions are given in this paper to show how applying the forward and backward time steps on an image that is inserted as a pixel matrix in the well-known heat equation with certain parameters can make the blurring, noising, and sharpening effects. In addition, we are going to make a model for a heat diffusion in two directions x and y and assemble letters from components in matrices to apply our experiment on some medical and colorful images. Finally, we conclude that undesired details in an image can be removed by using the proposed equation.
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References
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[84] M. Enneffati, B. Louati, K. Guidara, M. Rasheed, R. Barillé, Crystal structure characterization and AC electrical conduction behavior of sodium cadmium orthophosphate, Journal of Materials Science: Materials in Electronics, vol. 29 (1) (2018), pp. 171-179.
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[2] K. P. Behzad, B. Kamgar-Parsi and K. K. Parsim, "Notes on image processing with partial differential equations", In 2015 IEEE International Conference on Image Processing (ICIP), pp. 1737-1741. IEEE, (2015).
[3] F. Dai, Z. Nanning and X. Jianru, "Image smoothing and sharpening based on nonlinear diffusion equation", Signal processing, vol. 88 (11) (2008), pp. 2850-2855.
[4] C. Jeff, A. Mansouri and A. Yezzi, "Image sharpening via Sobolev gradient flows", SIAM Journal on Imaging Sciences, vol. 3(4), (2010), pp. 981-1014.
[5] T. Xue-Cheng, K. A. Lie, T. F. Chan and S. Osher, "Image Processing Based on Partial Differential Equations", Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, Springer Science & Business Media, (2006).
[6] A. Gilles and P. Kornprobst, "Mathematical problems in image processing: partial differential equations and the calculus of variations", vol. 147, Springer Science & Business Media, (2006).
[7] M. M. Delphi and S. N. Shihab, "State Parameterization Basic Spline Functions for Trajectory Optimization", Journal of Nature, Life and Applied Sciences, vol. 3 (4) (2019), pp. 110-119.
[8] S. Shihab and M. Delphi, "Direct Iterative Algorithm for Solving Optimal Control Problems Using B-Spline Polynomials", Emirates Journal for Engineering Research, vol. 24 (4) (2019), pp. 1-9.
[9] M. Delphi and S. Shihab, "Modified Iterative Algorithm for Solving Optimal Control Problems", Open Science Journal of Statistics and Application, vol. 6 (2) (2019), pp. 20-27.
[10] S. N. Shihab, A. A. Abdulrahman and M. N. Mohammed Ali, "Collocation Orthonormal Bernstein Polynomials Method for Solving Integral Equations", Engineering and Technology Journal, vol. 33 (8) (2015), pp. 1493-1502.
[11] S. N. Shihab and T. N. Naif, "On the orthonormal Bernstein polynomial of order eight", Open Science Journal of Mathematics and Application, vol. 2 (2) (2014), pp. 15-19.
[12] S. N. Shihab and A. A. Abdalrehman, "Solving Optimal Control Linear Systems by Using New Third kind Chebyshev Wavelets Operational Matrix of Derivative", Baghdad Science Journal, vol. 11 (2) (2014), pp. 229-234.
[13] S. N. Shihab and A. A. Abdelrehman, "Some New Relationships Between the Derivatives of First and Second Chebyshev Wavelets", International Journal of Engineering, Business and Enterprise Application, (2012), pp. 64-68.
[14] S. N. Shihab and A. A. Abdalrehman, "Numerical solution of calculus of variations by using the second Chebyshev wavelets", Engineering and Technology Journal, vol. 30 (18) (2012), pp. 3219-3229.
[15] S. N. Shehab, H. A. Ali, H. M. Yaseen, "Least squares method for solving integral equations with multiple time lags", Engineering & Technology Journal, vol. 28 (10) (2010), pp. 1893-1899.
[16] S. N. Al-Rawi, "On the Solution of Certain Fractional Integral Equations", Journal of Kirkuk University–Scientific Studies, vol. 1 (2) (2006).
[17] S. N. Al-Rawi, R. K. Salih and A. A. Mohammed, "Numerical Solution of Nth Order Linear Delay Differential Equation Using Runge-Kutta Method", Um - Salama Science Journal, vol. 3 (1) (2006), pp. 140-146.
[18] M. RASHEED, A. A. Abdulrahman, and S. Shihab, "The Effect of Set Partitioning in Hierarchical Trees with Wavelet Decomposition Levels Algorithm for Image Compression", Electronics Science Technology and Application, vol. 7 (3) (2020), pp. 40-46.
[19] A. A. Abdulrahman, M. RASHEED and S. SHIHAB, "Various Techniques for De-noise Image, Various Techniques for De-noise Image, vol. 7 (4) (2020), pp. 79-84.
[20] A. A. Abdulrahman, M. RASHEED and S. SHIHAB, "Discrete Hermite Wavelet Filters with Prove Mathematical Aspects", Journal of Southwest Jiaotong University, vol. 55 (2) (2020), pp. 1-12.
[21] A. A. Abdulrahman, M. RASHEED and S. SHIHAB, "Discrete Chebyshev Wavelet Transformation with Image Processing", Journal of Southwest Jiaotong University, vol. 55 (2) (2020), pp. 1-17.
[22] M. RASHEED, A. A. Abdulrahman, S. SHIHAB, "The analytic of image processing smoothing spaces using wavelet", Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[23] M. S. Rasheed, H. S. Mahde, "Electronic Combination Lock Design Using Remote Control", Journal of the College of Basic Education, vol. 18 (75) (2012), pp. 265-280.
[24] M. S. Rasheed and Balqis M. Diah, "Study of the effects of acidic solutions on the physical properties of polymeric materials superimposed", Al-Mustansiriyah Journal of Science, vol. 13 (49) (2002), pp. 6.
[25] M. RASHEED and M. A. Sarhan, "Solve and Implement the main Equations of Photovoltaic Cell Parameters Using Visual Studio Program", Insight-Mathematics, vol. 1 (1) (2019), pp. 17-25.
[26] M. Rasheed and M. A. Sarhan, "Characteristics of Solar Cell Outdoor Measurements Using Fuzzy Logic Method", Insight-Mathematics, vol. 1 (1) (2019), pp. 1-8.
[27] M. RASHEED and M. A. Sarhan, "Measuring the Solar Cell Parameters Using Fuzzy Set Technique", Insight-Electronic, vol. 1 (1) (2019), pp. 1-9.
[28] M. RASHEED, "Linear Programming for Solving Solar Cell Parameters", Insight-Electronic, vol. 1 (1) (2019), pp. 10-16.
[29] M. RASHEED, "Investigation of Solar Cell Factors using Fuzzy Set Technique", Insight-Electronic, vol. 1 (1) (2019), pp. 17-23.
[30] M. RASHEED and S. SHIHAB, "Analytical Modeling of Solar Cells", Insight Electronics, vol. 1 (2) (2019), pp. 1-9.
[31] S. SHIHAB and M. RASHEED, "Modeling and Simulation of Solar Cell Mathematical Model Parameters Determination Based on Different Methods", Insight Mathematics, vol. 1 (1) (2019), pp. 1-16.
[32] M. RASHEED and S. SHIHAB, "Parameters Estimation for Mathematical Model of Solar Cell", Electronics Science Technology and Application, vol. 6, (1) (2019), pp. 20-28.
[33] M. Rasheed and S. Shihab, "Numerical Techniques for Solving Parameters of Solar Cell", Applied Physics, vol. 3 (1) (2020), pp. 16-27.
[34] M. RASHEED and S. SHIHAB, "Modifications to Accelerate the Iterative Algorithm for the Single Diode Model of PV Model", Iraqi Journal of Physics (IJP), vol. 18 (47) (2020), pp. 33-43.
[35] M. S. Rasheed and S. Shihab, "Modelling and Parameter Extraction of PV Cell Using Single-Diode Model". Advanced Energy Conversion Materials, 1 (2) (2020), pp. 96-104. Available from: http://ojs.wiserpub.com/index.php/AECM/article/view/550.
[36] M. S. Rasheed and S. Shihab, "Analysis of Mathematical Modeling of PV Cell with Numerical Algorithm". Advanced Energy Conversion Materials, vol. 1 (2) (2020), pp. 70-79. Available from: http://ojs.wiserpub.com/index.php/AECM/article/view/328.
[37] M. A. Sarhan, "Effect of Silicon Solar Cell Physical Factors on Maximum Conversion Efficiency Theoretically and Experimentally", Insight-Electronic, vol. 1 (1) (2019), pp. 24-30.
[38] M. M. Abbas and M. Rasheed, "Solid State Reaction Synthesis and Characterization of Cu doped TiO2 Nanomaterials", Journal of Physics: Conference Series, IOP Publishing, (2021), in press.
[39] Muna Muzahim Abbas, Mohammed Rasheed, "Solid State Reaction Synthesis and Characterization of Aluminum Doped Titanium Dioxide Nanomaterials", Journal of Southwest Jiaotong University, vol. 55 (2), pp. 1-10.
[40] M. RASHEED, S. SHIHAB and O. W. Sabah, "An investigation of the Structural, Electrical and Optical Properties of Graphene-Oxide Thin Films Using Different Solvents", Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[41] M. Enneffatia, M. Rasheed, B. Louatia, K. Guidaraa, S. Shihab and R. Barillé, "Investigation of structural, morphology, optical properties and electrical transport conduction of Li0.25Na0.75CdVO4 compound", Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[42] M. Rasheed, O. Alabdali and S. Shihab, "A New Technique for Solar Cell Parameters Estimation of The Single-Diode Model", Journal of Physics: Conference Series. IOP Publishing, (2021), in press.
[43] M. Rasheed and R. Barillé, "Room temperature deposition of ZnO and Al: ZnO ultrathin films on glass and PET substrates by DC sputtering technique", Optical and Quantum Electronics, vol. 49 (5) (2017), pp. 1-14.
[44] M. Rasheed and Régis Barillé, Optical constants of DC sputtering derived ITO, TiO2 and TiO2: Nb thin films characterized by spectrophotometry and spectroscopic ellipsometry for optoelectronic devices, Journal of Non-Crystalline Solids, vol. 476 (2017), pp. 1-14.
[45] M. Rasheed and R. Barillé, Comparison the optical properties for Bi2O3 and NiO ultrathin films deposited on different substrates by DC sputtering technique for transparent electronics, Journal of Alloys and Compounds, vol. 728 (2017), pp. 1186-1198.
[46] M. M. Abbas and M. RASHEED, "Investigation of structural, Mechanical, Thermal and Optical Properties of Cu Doped TiO2", Iraqi Journal of Physics (IJP), (2020), in press.
[47] M. S. Rasheed, "Approximate Solutions of Barker Equation in Parabolic Orbits", Engineering & Technology Journal, vol. 28 (3) (2010), pp. 492-499.
[48] M. S. Rasheed, "An Improved Algorithm For The Solution of Kepler‘s Equation For An Elliptical Orbit", Engineering & Technology Journal, vol. 28 (7) (2010), pp. 1316-1320.
[49] M. S. Rasheed, "Acceleration of Predictor Corrector Halley Method in Astrophysics Application", International Journal of Emerging Technologies in Computational and Applied Sciences, vol. 1 (2) (2012), pp. 91-94.
[50] M. S. Rasheed, "Fast Procedure for Solving Two-Body Problem in Celestial Mechanic", International Journal of Engineering, Business and Enterprise Applications, vol. 1 (2) (2012), pp. 60-63.
[51] M. S. Rasheed, "Solve the Position to Time Equation for an Object Travelling on a Parabolic Orbit in Celestial Mechanics", DIYALA JOURNAL FOR PURE SCIENCES, vol. 9 (4) (2013), pp. 31-38.
[52] M. S. Rasheed, "Comparison of Starting Values for Implicit Iterative Solutions to Hyperbolic Orbits Equation", International Journal of Software and Web Sciences (IJSWS), vol. 1 (2) (2013), pp. 65-71.
[53] M. S. Rasheed, "On Solving Hyperbolic Trajectory Using New Predictor-Corrector Quadrature Algorithms", Baghdad Science Journal, vol. 11 (1) (2014), pp. 186-192.
[54] M. S. Rasheed, "Modification of Three Order Methods for Solving Satellite Orbital Equation in Elliptical Motion", Journal of university of Anbar for Pure science, vol. 14 (1) (2020), pp. 33-37.
[55] Mohammed RASHEED, Suha SHIHAB, Taha RASHEED and Tarek Diab Ounis, "Parameters Determination of PV Cell Using Computation Methods", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 1-9.
[56] Rasha Jalal Mitlif, Mohammed RASHEED, Suha SHIHAB, Taha RASHEED and Saad Hussein Abed Hamed, "Linear Programming Method Application in a Solar Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 10-21.
[57] Maiada Nazar Mohammedali, Mohammed RASHEED, Suha SHIHAB, Taha RASHEED and Saad Hussein Abed Hamed, "Optimal Parameters Estimation of Silicon Solar Cell Using Fuzzy Logic: Analytical Method", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 22-33.
[58] Mohammed RASHEED, Osama Alabdali, Suha SHIHAB and Taha RASHID, "Evaluation and Determination of the Parameters of a Photovoltaic Cell by an Iterative Method", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 34-42.
[59] M. RASHEED, S. SHIHAB, T. RASHID and T. D. Ounis, "Determination of PV Model Parameters Using Bisection and Secant Methods", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13, (1), (2021), 43-54.
[60] Raghad I Sabri, Mohammed RASHEED, Osama Alabdali, Suha SHIHAB and Taha RASHID, "On Some Properties in Fuzzy Metric Space", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 55-61.
[61] Maiada Nazar Mohammedali, Mohammed RASHEED, Suha SHIHAB, Taha RASHID and Saad Hussein Abed Hamed, "Fuzzy Set Technique Application: The Solar Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 62-69.
[62] Mohammed RASHEED, Suha SHIHAB, Taha RASHID and Olfa Maalej, "Determining the Voltage and Power of a Single Diode PV Cell in Matlab by Iteration", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 70-78.
[63] Mohammed RASHEED, Suha SHIHAB, Taha RASHID and Olfa Maalej, "Numerical Simulation of Photovoltaic Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 79-86.
[64] Mohammed RASHEED, Suha SHIHAB, Taha RASHID and Marwa Enneffati, "Two Numerical Algorithms for Solving Nonlinear Equation of Solar Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 87-94.
[65] Mohammed RASHEED, Suha SHIHAB, Taha RASHID and Marwa Enneffati, "Some Step Iterative Method for Finding Roots of a Nonlinear Equation", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 95-102.
[66] M. A. Sarhan, S. SHIHAB and M. RASHEED, "Some Results on a Two Variables Pell Polynomials", Al-Qadisiyah Journal of Pure Science, vol. 26, (1), (2020), pp. 55-70.
[67] M. RASHEED, S. SHIHAB and T. RASHID, "Two Step and Newton- Raphson Algorithms in the Extraction for the Parameters of Solar Cell", Al-Qadisiyah Journal of Pure Science, vol. 26 (1), (2021), pp.143-154.
[68] M. A. Sarhan, S. SHIHAB and M. RASHEED, "A novel Spectral Modified Pell Algorithm for Solving Singular Differential Equations", Al- Mustansiriyah Journal of Science, vol. 32, (1), (2021), pp. 18-24.
[69] M. RASHEED, S. SHIHAB and T. RASHID, "Extraction of a Photovoltaic Cell's Single-Diode Model Parameters from Equivalent Circuit", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 147-154.
[70] M. RASHEED, S. SHIHAB and T. RASHID, "Estimation of Single-Diode Model Parameters of PV Cell", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 139-146.
[71] M. RASHEED, S. SHIHAB and T. RASHID, "The Single Diode Model for PV Characteristics Using Electrical Circuit", Journal of Al-Qadisiyah for Computer Science and Mathematics, vol. 13 (1), (2021), pp. 131-138.
[72] R. J. Mitlif, M. Rasheed and S. Shihab, "An Optimal Algorithm for a Fuzzy Transportation Problem", Journal of Southwest Jiaotong University, vol. 55 (3), (2020).
[73] R. I. Sabri, M. N. Mohammedali, M. Rasheed and S. Shihab, "Compactness of Soft Fuzzy Metric Space", Journal of Southwest Jiaotong University, vol. 55 (3), (2020).
[74] B. E. Kashem, E. H. Ouda, S. H. Aziz, M. Rasheed and S. Shihab, "Some Results for Orthonormal Boubaker Polynomials with Application", Journal of Southwest Jiaotong University, vol. 55 (3), (2020).
[75] M. N. Mohammedali, R. I. Sabri, M. Rasheed and S. Shihab, "Some Results on G-Normed Linear Spaces", Journal of Southwest Jiaotong University, vol. 55 (3), (2020).
[76] T. Saidani, M. Zaabat, M. S. Aida, R. Barille, M. Rasheed, Y. Almohamed, Influence of precursor source on sol–gel deposited ZnO thin films properties, Journal of Materials Science: Materials in Electronics, vol. 28 (13) (2017), pp. 9252-9257.
[77] K. Guergouria A. Boumezoued, R. Barille, D. Rechemc, M. Rasheed M. Zaabata, ZnO nanopowders doped with bismuth oxide, from synthesis to electrical application, Journal of Alloys and Compounds, vol. 791 (2019), pp. 550-558.
[78] D. Bouras, A. Mecif, R. Barillé, A. Harabi, M. Rasheed, A. Mahdjoub, M. Zaabat, Cu: ZnO deposited on porous ceramic substrates by a simple thermal method for photocatalytic application, Ceramics International, vol. 44 (17) (2018), pp. 21546-21555.
[79] W. Saidi, N. Hfaidh, M. Rasheed, M. Girtan, A. Megriche, M. EL Maaoui, Effect of B2O3 addition on optical and structural properties of TiO2 as a new blocking layer for multiple dye sensitive solar cell application (DSSC), RSC Advances, vol. 6 (73) (2016), pp. 68819-68826.
[80] A. AUKŠTUOLIS, M. Girtan, G. A. Mousdis, R. Mallet, M. Socol, M. Rasheed, A. Stanculescu, Measurement of charge carrier mobility in perovskite nanowire films by photo-CELIV method, Proceedings of the Romanian Academy Series a-Mathematics Physics Technical Sciences Information Science, vol. 18 (1) (2017), pp. 34-41.
[81] F. Dkhilalli, S. Megdiche, K. Guidara, M. Rasheed, R. Barillé, M. Megdiche, AC conductivity evolution in bulk and grain boundary response of sodium tungstate Na2WO4, Ionics, vol. 24 (1) (2018), pp. 169-180.
[82] F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, K. Guidara, M. Megdiche, Structural, dielectric, and optical properties of the zinc tungstate ZnWO4 compound, Journal of Materials Science: Materials in Electronics, vol. 29 (8) (2018), pp. 6297-6307.
[83] F. Dkhilalli, S. M. Borchani, M. Rasheed, R. Barille, S. Shihab, K. Guidara, M. Megdiche, Characterizations and morphology of sodium tungstate particles, Royal Society open science, vol. 5 (8) (2018), pp. 1-12.
[84] M. Enneffati, B. Louati, K. Guidara, M. Rasheed, R. Barillé, Crystal structure characterization and AC electrical conduction behavior of sodium cadmium orthophosphate, Journal of Materials Science: Materials in Electronics, vol. 29 (1) (2018), pp. 171-179.
[85] E. Kadri, M. Krichen, R. Mohammed, A. Zouari, K. Khirouni, Electrical transport mechanisms in amorphous silicon/crystalline silicon germanium heterojunction solar cell: impact of passivation layer in conversion efficiency, Optical and Quantum Electronics, vol. 48 (12) (2016), pp. 1-15.
[86] E. Kadri, O. Messaoudi, M. Krichen, K. Dhahri, M. Rasheed, E. Dhahri, A. Zouari, K. Khirouni, R. Barillé, Optical and electrical properties of SiGe/Si solar cell heterostructures: Ellipsometric study, Journal of Alloys and Compounds, vol. 721 (2017), pp. 779-783.
[87] E. Kadri, K. Dhahri, A. Zaafouri, M. Krichen, M. Rasheed, K. Khirouni, R. Barillé, Ac conductivity and dielectric behavior of a−Si:H/c− Si1−yGey/p−Si thin films synthesized by molecular beam epitaxial method, Journal of Alloys and Compounds, vol. 705 (2017), pp. 708-713.
[88] N. B. Azaza, S. Elleuch, M. Rasheed, D. Gindre, S. Abid, R. Barille, Y. Abid, H. Ammar, 3-(p-nitrophenyl) Coumarin derivatives: Synthesis, linear and nonlinear optical properties, Optical Materials, vol. 96, (2019), pp. 109328.
[89] M. Enneffati, M. Rasheed, B. Louati, K. Guidara, R. Barillé, Morphology, UV–visible and ellipsometric studies of sodium lithium orthovanadate, Optical and Quantum Electronics, vol. 51 (9) (2019), vol. 299.
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Published
2021-03-11
How to Cite
Ali, A. H., RASHEED, M., SHIHAB, S., RASHID, T., & Abed Hamed, S. H. (2021). A Novel Blurring and Sharpening Techniques Using Different Images Based on Heat Equations. Journal of Al-Qadisiyah for Computer Science and Mathematics, 13(1), Comp Page 45 – 57. https://doi.org/10.29304/jqcm.2021.13.1.771
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Computer Articles
