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A fractional osmosis model for image fusion

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Abstract

This paper introduces a novel model for image fusion that is based on a fractional-order osmosis approach. The model incorporates a definition of osmosis energy that takes into account nonlocal pixel relationships using fractional derivatives and contrast change. The proposed model was subjected to theoretical and experimental investigation. The semigroup theory was used to demonstrate the existence and uniqueness of the evolution equation solution. Additionally, the model was validated and tested using numerical experiments and compared to local image fusion methods. The findings demonstrate that the proposed model outperforms the competitive local image fusion models.

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References

  1. Kaur, K.D.H., Kadyan, V.: Image fusion techniques: a survey. Arch. Computat. Methods Eng. 28, 4425–4447 (2021)

    Article  Google Scholar 

  2. Li, S., Kang, X., Fang, L., Hu, J., Yin, H.: Pixel-level image fusion: a survey of the state of the art. Inform. Fusion. 33, 100–112 (2017)

    Article  Google Scholar 

  3. Pérez, P., Gangnet, M., Blake, A.: Poisson image editing. ACM Trans. Graphics. 22, 313–318 (2003)

    Article  Google Scholar 

  4. Ancuti, C., Ancuti, C.O., De Vleeschouwer, C., Bovik, A.C.: Night-time dehazing by fusion. In: 2016 IEEE International conference on image processing (ICIP), pp. 2256–2260 (2016)

  5. Ancuti, C., Ancuti, C.O., Haber, T., Bekaert, P.: Enhancing underwater images and videos by fusion. In: 2012 IEEE Conference on computer vision and pattern recognition, pp. 81–88 (2012)

  6. Li, S., Yang, B.: Multifocus image fusion by combining curvelet and wavelet transform. Pattern Recogn. Lett. 29(9), 1295–1301 (2008)

    Article  ADS  Google Scholar 

  7. Mertens, T., Kautz, J., Van Reeth, F.: Exposure fusion: a simple and practical alternative to high dynamic range photography. Comp. Graphics Forum. 28(1), 161–171 (2009)

    Article  Google Scholar 

  8. Thies, J., Zollhöfer, M., Nießner, M., Valgaerts, L., Stamminger, M., Theobalt, C.: Real-time expression transfer for facial reenactment. ACM Trans. Graph. 34(6) (2015)

  9. Parisotto, S., Calatroni, L., Bugeau, A., Papadakis, N., Schönlieb, C.-B.: Variational osmosis for non-linear image fusion. IEEE Transactions on Image Processing, 5507–5516 (2020)

  10. Darwish, S.M.: Multi-level fuzzy contourlet-based image fusion for medical applications. IET Image Process. 7, 694–7006 (2013)

    Article  Google Scholar 

  11. James, A.P., Dasarathy, B.V.: Medical image fusion: a survey of the state of the art. Information Fusion. 19, 4–19 (2014). Special Issue on Information Fusion in Medical Image Computing and Systems

  12. Ma, J., Ma, Y., Li, C.: Infrared and visible image fusion methods and applications: a survey. Inform. Fusion. 45, 153–178 (2019)

    Article  Google Scholar 

  13. Gabarda, S., Cristóbal, G.: Cloud covering denoising through image fusion. Image Vision Comput. 25(5), 523–530 (2007)

    Article  Google Scholar 

  14. Amolins, K., Zhang, Y., Dare, P.: Wavelet based image fusion techniques -an introduction, review and comparison. ISPRS J. Photogrammetry Remote Sensing. 62(4), 249–263 (2007)

    Article  ADS  Google Scholar 

  15. Kim, Y., Lee, C., Han, D., Kim, Y., Kim, Y.: Improved additive-wavelet image fusion. IEEE Geosci. Remote Sensing Lett. 8(2), 263–267 (2011)

    Article  ADS  Google Scholar 

  16. Dogra, A., Goyal, B., Agrawal, S.: From multi-scale decomposition to non-multi-scale decomposition methods: a comprehensive survey of image fusion techniques and its applications. IEEE Access. 5, 16040–16067 (2017)

    Article  Google Scholar 

  17. Zhao, W., Lu, H., Wang, D.: Multisensor image fusion and enhancement in spectral total variation domain. IEEE Trans. Multimed. 20(4), 866–879 (2018)

    Article  Google Scholar 

  18. Liu, Y., Chen, X., Wang, Z., Wang, Z.J., Ward, R.K., Wang, X.: Deep learning for pixel-level image fusion: recent advances and future prospects. Inform. Fusion. 42, 158–173 (2018)

    Article  Google Scholar 

  19. Hafner, D., Weickert, J.: Variational image fusion with optimal local contrast. Comput. Graphics Forum. 35(1), 100–112 (2016)

    Article  Google Scholar 

  20. Yuan, J., Miles, B., Garvin, G., Tai, X.-C., Fenster, A.: Efficient convex optimization approaches to variational image fusion. Numerical Math. 7, 234–250 (2014)

    MathSciNet  Google Scholar 

  21. Wang, W., Shui, P.-L., Feng, X.: Variational models for fusion and denoising of multifocus images. Signal Process. Lett. IEEE. 15, 65–68 (2008)

    Article  ADS  Google Scholar 

  22. Li, F., Zeng, T.: Variational image fusion with first and second-order gradient information. J. Computat. Math. 34(2), 200–222 (2016)

    Article  MathSciNet  Google Scholar 

  23. Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. In: 2005 IEEE Computer society conference on computer vision and pattern recognition (CVPR’05), vol. 2, pp. 60–652 (2005)

  24. Mairal, J., Bach, F., Ponce, J., Sapiro, G., Zisserman, A.: Non-local sparse models for image restoration. In: 2009 IEEE 12th International Conference on Computer Vision, pp. 2272–2279 (2009)

  25. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Modeling and Simulation, 1005–1028 (2009)

  26. Benalia, S., Hachama, M.: A nonlocal method for image shadow removal. Comput. Math. Appl. 107, 95–103 (2022)

    Article  MathSciNet  Google Scholar 

  27. Bai, J., Feng, X.-C.: Fractional-order anisotropic diffusion for image denoising. IEEE Trans. Image Process. 16(10), 2492–2502 (2007)

    Article  MathSciNet  PubMed  ADS  Google Scholar 

  28. Yin, X., Zhou, S., Siddique, M.: Fractional nonlinear anisotropic diffusion with p-Laplace variation method for image restoration. Multimedia Tools and Applications. 75 (2015)

  29. Yang, Q., Chen, D., Zhao, T., Chen, Y.Q.: Fractional calculus in image processing: a review. Fractional Calculus Appl. Anal. 19, 1222–1249 (2016)

    Article  MathSciNet  Google Scholar 

  30. Motłoch , S., Sarwas, G., Dzieliński, A.: Fractional derivatives application to image fusion problems. Sensors. 22(3) (2022)

  31. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences, (1983)

  32. Liu, Z., Zheng, S.: Semigroups associated with dissipative systems. CRC Press, (1999)

  33. Brezis, H.: Function analysis. Springer, Sobolev Spaces and Partial Differential Equations (2010)

    Google Scholar 

  34. Vrabie, I.: Co-semigroups and applications. Elsevier, (2003)

  35. Di Martino, J.M., Facciolo, G., Meinhardt-Llopis, E.: Poisson image editing. Image Processing On Line, 300–325 (2016)

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Authors and Affiliations

  1. National Higher School of Mathematics, Scientific and Technology Hub of Sidi Abdellah, P.O. Box 75, Algiers, 16093, Algeria

    Mohammed Hachama

  2. Department of Mathematics, University of Blida 1, P.O. Box 270, Blida, 09000, Algeria

    Fatiha Boutaous

  3. Lab. NLPDE and Hist. of Maths, Ecole Normale Supérieure, Kouba, 16050, Algeria

    Fatiha Boutaous

Authors
  1. Mohammed Hachama
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  2. Fatiha Boutaous
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Correspondence to Mohammed Hachama.

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Communicated by: Russell Luke

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Hachama, M., Boutaous, F. A fractional osmosis model for image fusion. Adv Comput Math 50, 7 (2024). https://doi.org/10.1007/s10444-023-10103-6

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