Generalized harmonic maps and applications in image processing

Articles in Press

Document Type : Original Article

Authors

1 Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran.

2 Faculty of Engineering, University of Bojnord, Bojnord , Iran

Abstract

The article discusses the application of tension field and harmonic maps in image processing. It introduces the concept of (α,f)- harmonic maps, which encompasses both α- harmonic maps and f-harmonic maps, and delves into their characteristics. Furthermore, it presents a Liouville type theorem for this kind of harmonic maps

Keywords

References

 1. W. Birkfellner, Applied medical image processing: a basic course, CRC Press, 2024.
2. W. Burger and M. J. Burge, Digital image processing: An algorithmic introduction,Springer Nature, 2022.
3. M.J. Canty, Image analysis classification and change detection in remote sensing: with algorithms for Python, Crc Press, 2019.
4. A. M. Cherif, M. Djaa and K. Zegga, Stable f-harmonic maps on sphere, Commun. Korean Math Soc, 30(4) (2015), 471-479.
5. N. Course, , f-harmonic maps, Ph.D thesis, University of Warwick, Coventry, England, 2004.
6. A. Lichnerowicz, Applications harmoniques et varietes kahleriennes, Symposia Mathematica III, Academic Press London, (1970), 341-402.
7. Y. Ou, f-Harmonic morphisms between Riemannian manifolds, Chinese Annals of Mathematics, 35B(2) (2014), 225-236.
8. J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J.
Math. 86(1964), 109-160.
9. S. M. Kazemi Torbaghan, K. Salehi and S. Babaie, Existence and Stability of Harmonic Maps, J. Math. 2022(1) (2022), 1906905.
10. T. Lamm, A. Malchiodi andd M. Micallef, A gap theorem for α-harmonic maps between two-spheres, Analysis and PDE, 14(3) (2021), 881-889.
11. T. Lamm, Energy identity for approximations of harmonic maps from surfaces, Trans. Amer. Math. Soc. 362(2010), 4077-4097.
12. J. Li, C. Zhu and M. Zhu, The qualitative behavior for α-harmonic maps from a surface with boundary into a sphere, Trans. Amer. Math. Soc. 376(01) (2023), 391-417.
13. J. Li and X. Zhu, Energy identity and recklessness for a sequence of Sacks-Uhlenbeck maps to a sphere, Ann. Ins. Henri. Poincari. Analyse non linnaire, 36(1) (2019), 103-118.
14. W. Park, A new conformal heat flow of harmonic maps, J. Geom. Analysis, 33(12) (2023), 376.
15. G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain threemanifolds. arXiv preprint math/0307245, 2003.
16. E. Remli and A. M. Cherif, On the generalized of p-harmonic and f-harmonic maps, Kyungpook. Math. J. 61(1) (2021), 169-179.
17. J. Sacks and K. Uhlenbeck, The existence of minimal immersions of 2-spheres, Ann.Math. (1981), 1-24.
18. A. Shahnavaz, SM. Kazemi Torbaghan and N. Kouhestani, Sacks-Uhlenbeck α- harmonic maps from Finsler manifolds, J. Finsler Geom. Appl. 5(2) (2024), 70-86.
19. A. Shahnavaz , N. Kouhestani and SM. Kazemi Torbaghan, The morse index of SacksUhlenbeck α-harmonic maps for Riemannian manifolds, J. Math. 1(2024), 2692876. 
Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 11 January 2025

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