Modified Poisson compositing technique on skewed grid

Nordin Saad; A'qilah Ahmad Dahalan; Azali Saudi; Nordin Saad; A'qilah Ahmad Dahalan; Azali Saudi

doi:10.3934/math.2022124

AIMS Mathematics

2022, Volume 7, Issue 2: 2176-2194. doi: 10.3934/math.2022124

Previous Article Next Article

Research article

Modified Poisson compositing technique on skewed grid

1.
Faculty of Computing and Informatics, Universiti Malaysia Sabah, Kota Kinabalu, Malaysia
2.
Department of Mathematics, Universiti Pertahanan Nasional Malaysia, Kuala Lumpur, Malaysia

Received: 01 September 2021 Accepted: 14 October 2021 Published: 09 November 2021
MSC : 35J05, 65N06, 94A08

Image compositing is the process of seamlessly inserting a portion of a source image into a target image to create a new desirable image. This work describes an image composition approach based on numerical differentiation utilizing the Laplacian operator. The suggested procedure uses the red-black strategy to speed up computations by using two separate relaxation factors for red and black nodes, as well as two accelerated parameters on a skewed grid. The Skewed Modified Two-Parameter Overrelaxation (SkMTOR) approach is a modification of the existing MTOR method. The SkMTOR has been used to solve numerous linear equations in the past, but its applicability in image processing has never been investigated. Several examples were used to test the suggested method in solving the Poisson equation for image composition. The results demonstrated that the image composition was successfully constructed using all six methods considered in this study. The six methods evaluated yielded identical images based on the similarity measurement results. In terms of computing speed, the skewed variants perform much quicker than their corresponding regular grid variants, with the SkMTOR showing the best performance.
- image compositing,
- Poisson equation,
- finite difference method,
- modified iterative method,
- MSOR,
- MAOR,
- MTOR,
- skewed grid,
- image blending,
- composition
Citation: Nordin Saad, A'qilah Ahmad Dahalan, Azali Saudi. Modified Poisson compositing technique on skewed grid[J]. AIMS Mathematics, 2022, 7(2): 2176-2194. doi: 10.3934/math.2022124

Related Papers:

Abstract

Image compositing is the process of seamlessly inserting a portion of a source image into a target image to create a new desirable image. This work describes an image composition approach based on numerical differentiation utilizing the Laplacian operator. The suggested procedure uses the red-black strategy to speed up computations by using two separate relaxation factors for red and black nodes, as well as two accelerated parameters on a skewed grid. The Skewed Modified Two-Parameter Overrelaxation (SkMTOR) approach is a modification of the existing MTOR method. The SkMTOR has been used to solve numerous linear equations in the past, but its applicability in image processing has never been investigated. Several examples were used to test the suggested method in solving the Poisson equation for image composition. The results demonstrated that the image composition was successfully constructed using all six methods considered in this study. The six methods evaluated yielded identical images based on the similarity measurement results. In terms of computing speed, the skewed variants perform much quicker than their corresponding regular grid variants, with the SkMTOR showing the best performance.

References

[1]	S. Lin, A. Ryabtsev, S. Sengupta, B. Curless, S. Seitz, I. Kemelmacher-Shlizerman, Real-time high-resolution background matting, arXiv: 2012.07810.
[2]	Z. Wang, Z. Yang, Review on image-stitching techniques, Multimedia Systems, 26 (2020), 413–430. doi: 10.1007/s00530-020-00651-y. doi: 10.1007/s00530-020-00651-y
[3]	Y. Yuan, F. Fang, G. Zhang, Superpixel-based seamless image stitching for UAV images, IEEE T. Geosci. Remote, 59 (2021), 1565–1576. doi: 10.1109/TGRS.2020.2999404. doi: 10.1109/TGRS.2020.2999404
[4]	M. Kazhdan, M. Chuang, S. Rusinkiewicz, H. Hoppe, Poisson surface reconstruction with envelope constraints, Comput. Graph. Forum, 39 (2020), 173–182, doi: 10.1111/cgf.14077. doi: 10.1111/cgf.14077
[5]	C. Gao, A. Saraf, J.-B. Huang, J. Kopf, Flow-edge guided video completion, In: ECCV 2020: computer vision – ECCV 2020, Springer, Cham, 2020,713–729. doi: 10.1007/978-3-030-58610-2_42.
[6]	Z. Zhu, J. Lu, M. Wang, S. Zhang, R. R. Martin, H. Liu, et al., A comparative study of algorithms for realtime panoramic video blending, IEEE T. Image Process., 27 (2018), 2952–2965. doi: 10.1109/TIP.2018.2808766. doi: 10.1109/TIP.2018.2808766
[7]	O. Elharrouss, N. Almaadeed, S. Al-Maadeed, Y. Akbari, Image inpainting: A review, Neural Process. Lett., 51 (2020), 2007–2028. doi: 10.1007/s11063-019-10163-0. doi: 10.1007/s11063-019-10163-0
[8]	P. Pérez, M. Gangnet, A. Blake, Poisson image editing, ACM Trans. Graph., 22 (2003), 313–318. doi: 10.1145/882262.882269.
[9]	R. Raskar, A. Ilie, J. Yu, Image fusion for context enhancement and video surrealism, In: Proceedings of the 3rd International Symposium on Non-Photorealistic Animation and Rendering, 2004, 85–152. doi: 10.1145/987657.987671.
[10]	S. Sengupta, V. Jayaram, B. Curless, S. Seitz, I. Kemelmacher-Shlizerman, Background matting: The world is your green screen, In: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020, 2291–2300. doi: 10.1109/CVPR42600.2020.00236.
[11]	Z. Du, A. Robles-Kelly, F. Lu, Robust surface reconstruction from gradient field using the L1 Norm, In: 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications (DICTA 2007), 2007,203–209. doi: 10.1109/DICTA.2007.4426797.
[12]	D. Reddy, A. Agrawal, R. Chellappa, Enforcing integrability by error correction using L1-minimization, In: 2009 IEEE Conference on Computer Vision and Pattern Recognition, 2009, 2350–2357. doi: 10.1109/CVPR.2009.5206603.
[13]	M. W. Tao, M. K. Johnson, S. Paris, Error-tolerant image compositing, Int. J. Comput. Vis., 103 (2013), 178–189. doi: 10.1007/s11263-012-0579-7. doi: 10.1007/s11263-012-0579-7
[14]	R. Sadek, G. Facciolo, P. Arias, V. Caselles, A variational model for gradient-based video editing, Int. J. Comput. Vis., 103 (2013), 127–162. doi: 10.1007/s11263-012-0597-5. doi: 10.1007/s11263-012-0597-5
[15]	J.-M. Morel, A. B. Petro, C. Sbert, Fourier implementation of Poisson image editing, Pattern Recogn. Lett., 33 (2012), 342–348. doi: 10.1016/j.patrec.2011.10.010. doi: 10.1016/j.patrec.2011.10.010
[16]	N. Limare, A. B. Petro, C. Sbert, J.-M. Morel, Retinex Poisson equation: a model for color perception, Image Processing On Line, 1 (2011), 39–50. doi: 10.5201/ipol.2011.lmps_rpe. doi: 10.5201/ipol.2011.lmps_rpe
[17]	H. Zeng, A. Peng, X. Kang, Hiding traces of camera anonymization by Poisson blending, In: ICAIS 2020: artificial intelligence and security, Springer, Cham, 2020, 98–108. doi: 10.1007/978-3-030-57881-7_9.
[18]	K. F. Hussain, R. M. Kamel, Efficient Poisson image editing, Electronic Letters on Computer Vision and Image Analysis, 14 (2015), 45–57. doi: 10.5565/rev/elcvia.765. doi: 10.5565/rev/elcvia.765
[19]	M. Afifi, K. F. Hussain, MPB: A modified Poisson blending technique, Comp. Visual Media, 1 (2015), 331–341. doi: 10.1007/s41095-015-0027-z. doi: 10.1007/s41095-015-0027-z
[20]	J. M. Di Martino, G. Facciolo, E. Meinhardt-Llopis, Poisson image editing, Image Processing On Line, 6 (2016), 300–325. doi: 10.5201/ipol.2016.163.
[21]	E. J. Hong, A. Saudi, J. Sulaiman, Numerical assessment for Poisson image blending problem using MSOR iteration via five-point Laplacian operator, J. Phys.: Conf. Ser., 890 (2017), 012010. doi: 10.1088/1742-6596/890/1/012010. doi: 10.1088/1742-6596/890/1/012010
[22]	F. Cao, T. Wu, C. Qin, Z. Qian, X. Zhang, New paradigm for self-embedding image watermarking with Poisson equation, In: IWDW 2019: digital forensics and watermarking, 2019,184–191. doi: 10.1007/978-3-030-43575-2_15.
[23]	C. Hu, L.-Z. Huo, Z. Zhang, P. Tang, Multi-temporal landsat data automatic cloud removal using poisson blending, IEEE Access, 8 (2020), 46151–46161. doi: 10.1109/ACCESS.2020.2979291. doi: 10.1109/ACCESS.2020.2979291
[24]	Y. Pan, M. Jin, S. Zhang, Y. Deng, TEC map completion using DCGAN and Poisson blending, Space Weather, 18 (2020), e2019SW002390. doi: 10.1029/2019SW002390. doi: 10.1029/2019SW002390
[25]	L. Zhang, T. Wen, J. Shi, Deep image blending, In: 2020 IEEE Winter Conference on Applications of Computer Vision (WACV), 1 (2020), 231–240. doi: 10.1109/WACV45572.2020.9093632.
[26]	A. Agarwala, Efficient gradient-domain compositing using Quadtrees, ACM Trans. Graph., 26 (2007), 94–es. doi: 10.1145/1275808.1276495. doi: 10.1145/1275808.1276495
[27]	M. Kazhdan, H. Hoppe, Streaming multigrid for gradient-domain operations on large images, ACM Trans. Graph., 27 (2008), 1–10. doi: 10.1145/1360612.1360620. doi: 10.1145/1360612.1360620
[28]	H. Zolfaghari, D. Obrist, A high-throughput hybrid task and data parallel Poisson solver for large-scale simulations of incompressible turbulent flows on distributed GPUs, J. Comput. Phys., 437 (2021), 110329. doi: 10.1016/j.jcp.2021.110329. doi: 10.1016/j.jcp.2021.110329
[29]	H. Li, Z. Song, A reduced-order energy-stability-preserving finite difference iterative scheme based on POD for the Allen-Cahn equation, J. Math. Anal. Appl., 491 (2020), 124245. doi: 10.1016/j.jmaa.2020.124245. doi: 10.1016/j.jmaa.2020.124245
[30]	A. Saudi, J. Sulaiman, Red-black strategy for mobile robot path planning, In: Proceedings of International MultiConference of Engineers and Computer Scientists 2010 Vol III, 2010, 2215–2219.
[31]	A. Sunarto, J. Sulaiman, A. Saudi, Solving the time fractional diffusion equations by the Half-Sweep SOR iterative method, In: 2014 International Conference of Advanced Informatics: Concept, Theory and Application (ICAICTA), 2014,272–277. doi: 10.1109/ICAICTA.2014.7005953.
[32]	L. H. Ali, J. Sulaiman, S. R. M. Hashim, Numerical solution of fuzzy fredholm integral equations of second kind using half-sweep gauss-seidel iteration, Journal of Engineering Science and Technology, 15 (2020), 3303–3313.
[33]	D. M. Young, Iterative solution of large linear systems, Academic Press, 1971. doi: 10.1016/C2013-0-11733-3.
[34]	A. Hadjidimos, Accelerated overrelaxation method, Math. Comput., 32 (1978), 149–157. doi: 10.2307/2006264. doi: 10.2307/2006264
[35]	J. Kuang, J. Ji, A survey of AOR and TOR methods, J. Comput. Appl. Math., 24 (1988), 3–12. doi: 10.1016/0377-0427(88)90340-8. doi: 10.1016/0377-0427(88)90340-8
[36]	D. J. Evans, Parallel S.O.R. iterative methods, Parallel Comput., 1 (1984), 3–18. doi: 10.1016/S0167-8191(84)90380-6. doi: 10.1016/S0167-8191(84)90380-6
[37]	D. R. Kincaid, D. M. Young, The modified successive overrelaxation method with fixed parameters, Math. Comput., 26 (1972), 705–717. doi: 10.1090/S0025-5718-1972-0331746-2. doi: 10.1090/S0025-5718-1972-0331746-2
[38]	A. R. Abdullah, The four point explicit decoupled group (EDG) Method: a fast poisson solver, Int. J. Comput. Math., 38 (1991), 61–70. doi: 10.1080/00207169108803958. doi: 10.1080/00207169108803958
[39]	Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Simoncelli, Image quality assessment: from error visibility to structural similarity, IEEE T. Image Process., 13 (2004), 600–612. doi: 10.1109/TIP.2003.819861. doi: 10.1109/TIP.2003.819861
[40]	F. Memon, M. A. Unar, S. Memon, Image quality assessment for performance evaluation of focus measure operators, Mehran University Research Journal of Engineering and Technology, 34 (2015), 379–386.
[41]	S. H. A. Hashim, F. A. Hamid, J. J. Kiram, J. Sulaiman, The relationship investigation between factors affecting demand for broadband and the level of satisfaction among broadband customers in the South East Coast of Sabah, Malaysia, J. Phys.: Conf. Ser., 890 (2017), 012149. doi: 10.1088/1742-6596/890/1/012149. doi: 10.1088/1742-6596/890/1/012149

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)