PERFORMANCE ANALYSIS OF FOUR-POINT EGAOR ITERATIVE METHOD APPLIED TO POISSON IMAGE BLENDING PROBLEM
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Published:
Feb 28, 2019
Keywords:
Poisson equation Poisson image blending finite difference method 4-EGAOR iteration five-point Laplacian operator
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Abstract
Poisson image blending is one of the useful editing tools in image processing to generate a desirable image which is impossible to acquire. The key to this solution is to obtain the unique solution of Poisson equation. Thus, the motivation of this paper is to examine the effectiveness of 4-EGAOR iterative method to solve the linear system generated from the Poisson image blending problem. To evaluate its effectiveness, the formulation and implementation of 4-EGAOR, SOR and AOR iterative methods are demonstrated. The numerical results revealed that 4-EGAOR iterative method improved the computational time taken and reduced the number of iterations used. In fact, the new images generated by the proposed block iterative method give a satisfactory visual effect.
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Eng, J. H., Saudi, A., & Sulaiman, J. (2019). PERFORMANCE ANALYSIS OF FOUR-POINT EGAOR ITERATIVE METHOD APPLIED TO POISSON IMAGE BLENDING PROBLEM. Malaysian Journal of Science, 38(Sp 1), 55–66. https://doi.org/10.22452/mjs.sp2019no1.5
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Saudi, A. & Sulaiman, J. (2017). Application of harmonic functions through modified SOR (MSOR) method for robot path planning in indoor structured environment. International Journal of Imaging and Robotics 17(3): 77-90.
Wang, Z. & Bovik, A.C. (2002). A universal image quality index. IEEE Signal Processing Letters 9(3): 81-84.
Young, D.M. (1954). Iterative methods for solving partial difference equations of elliptic type. Transactions of the American Mathematical Society 76: 92-111.
Yousif, W.S. & Martins, M.M. (2008). Explicit de-coupled group AOR method for solving elliptic partial differential equations. Neural, Parallel and Scientific Computations 16: 531-542.
Akhir, M.K.M., Othman, M., Sulaiman, J., Majid, Z.A. & Suleiman, M. (2011). Half-sweep modified successive overrelaxation for solving two-dimensional helmholtz equations. Australian Journal of Basic and Applied Sciences 5(12): 3033-3039.
Ali, N.H.M. & Chong, L.S. (2007). Group accelerated overrelaxation methods on rotated grid. Applied Mathematics and Computation 191: 533-542.
Dahalan, A.A., Saudi, A. & Sulaiman, J. (2017). Numerical evaluation of mobile robot navigation in static indoor environment via EGAOR Iteration. Journal of Physics: Conference Series 890: 012064.
Eng, J.H., Saudi, A. & Sulaiman, J. (2017a). Numerical assessment for poisson image blending problem using MSOR iteration via five-point laplacian operator. Journal of Physics: Conference Series 890: 012010.
Eng, J.H., Saudi, A. & Sulaiman, J. (2017b). Numerical analysis of the explicit group iterative method for solving poisson image blending problem. International Journal of Imaging and Robotics 17(4): 15-24.
Eng, J.H., Saudi, A. & Sulaiman, J. (2018a). Performance analysis of the explicit decoupled group iteration via five-point rotated laplacian operator in solving poisson image blending problem. Indian Journal of Science and Technology 11(12).
Eng, J.H., Saudi, A. & Sulaiman, J. (2018b). Implementation of rotated five-point laplacian operator for poisson image blending problem. Advanced Science Letters 24(3): 1727-1731.
Evans, D.J. (1985). Group explicit iterative methods for solving large linear systems. International Journal of Computer Mathematics 17: 81-108.
Gonzalez, R.C. & Woods, R.E. (2001). Digital Image Processing 2nd Edition, New Jersey: Prentice Hall.
Hadjidimos, A. (1978). Accelerated overrelaxation method. Mathematics of Computation 32: 149-157.
Hussain, K.F. & Kamel, R.M. (2015). Efficient poisson image editing. Electronic Letters on Computer Vision and Image Analysis 14(2): 45-57.
Martino, J.M.D., Facciolo, G. & Meinhardt-Llopis, E. (2016). Poisson image editing. Image Processing On Line 6: 300-325.
Martins, M.M., Yousif, W.S. & Evans, D.J. (2002). Explicit group AOR method for solving elliptic partial differential equations. Parallel and Scientific Computations 10(2): 411-422.
Morel, J.M., Petro, A.B. & Sbert, C. (2012). Fourier implementation of poisson image editing. Pattern Recognition Letters 33: 342-348.
PeÌrez, P., Gangnet, M. & Blake, A. (2003). Poisson image editing. ACM Transactions and Graphics 313-318.
Bobek Ltd. (2007) Public Domain Pictures.net. From: https://www.publicdomainpictures.net/en/view-image.php?image=211753&picture=office
-computer (accessed December 29, 2017).
Bobek Ltd. (2007) Public Domain Pictures.net. From: https://www.publicdomainpictures.net/en/view-image.php?image=52663&picture=school (accessed December 29, 2017).
Bobek Ltd. (2007) Public Domain Pictures.net. From: https://www.publicdomainpictures.net/en/view-image.php?image=4433&picture=sand-heart-and-ocean (accessed December 29, 2017).
Bobek Ltd. (2007) Public Domain Pictures.net. From: https://www.publicdomainpictures.net/en/view-image.php?image=36643&picture=games-on-the-beach (accessed December 29, 2017).
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Bobek Ltd. (2007) Public Domain Pictures.net. From: https://www.publicdomainpictures.net/en/view-image.php?image=76803&picture=travelin
g-by-car (accessed December 29, 2017).
Qin, C., Wang, S. & Zhang, X. (2008). Image editing without color inconsistency using modified poisson equation. In International Conference on Intelligent Information Hiding and Multimedia Signal Processing, 15-17 August, pp. 397-401, IEEE, China: Harbin.
Saudi, A. & Sulaiman, J. (2012). Robot path planning using four point-explicit group via nine-point laplacian (4EG9L) iterative method. Procedia Engineering 41: 182-188.
Saudi, A. & Sulaiman, J. (2016). Path planning simulation using harmonic potential fields through four point-EDGSOR method via 9-point laplacian. Jurnal Teknologi 78(8-2): 12-24.
Saudi, A. & Sulaiman, J. (2017). Application of harmonic functions through modified SOR (MSOR) method for robot path planning in indoor structured environment. International Journal of Imaging and Robotics 17(3): 77-90.
Wang, Z. & Bovik, A.C. (2002). A universal image quality index. IEEE Signal Processing Letters 9(3): 81-84.
Young, D.M. (1954). Iterative methods for solving partial difference equations of elliptic type. Transactions of the American Mathematical Society 76: 92-111.
Yousif, W.S. & Martins, M.M. (2008). Explicit de-coupled group AOR method for solving elliptic partial differential equations. Neural, Parallel and Scientific Computations 16: 531-542.