Abstract
Multi-focus image fusion is an increasingly important component in image fusion, and it plays a key role in imaging. In this paper, we put forward a novel multi-focus image fusion method which employs fractional-order derivative and intuitionistic fuzzy sets. The original image is decomposed into a base layer and a detail layer. Furthermore, a new fractional-order spatial frequency is built to reflect the clarity of the image. The fractional-order spatial frequency is used as a rule for detail layers fusion, and intuitionistic fuzzy sets are introduced to fuse base layers. Experimental results demonstrate that the proposed fusion method outperforms the state-of-the-art methods for multi-focus image fusion.
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References
Atanassov KT, 1986. Intuitionistic fuzzy sets. Fuzzy Sets Syst, 20(1):87–96. https://doi.org/10.1016/S0165-0114(86)80034-3
Azarang A, Ghassemian H, 2018. Application of fractional-order differentiation in multispectral image fusion. Remote Sens Lett, 9(1):91–100. https://doi.org/10.1080/2150704X.2017.1395963
Bai J, Feng XC, 2007. Fractional-order anisotropic diffusion for image denoising. IEEE Trans Image Process, 16(10):2492–2502. https://doi.org/10.1109/TIP.2007.904971
Balasubramaniam P, Ananthi VP, 2014. Image fusion using intuitionistic fuzzy sets. Inform Fus, 20:21–30. https://doi.org/10.1016/j.inffus.2013.10.011
Baleanu D, Wu GC, 2019. Some further results of the Laplace transform for variable-order fractional difference equations. Fract Calc Appl Anal, 22(6):180–192. https://doi.org/10.1515/fca-2019-0084
Chen DL, Chen YQ, Xue DY, 2015. Fractional-order total variation image denoising based on proximity algorithm. Appl Math Comput, 257:537–545. https://doi.org/10.1016/j.amc.2015.01.012
Chen Y, Qin Z, 2015. Gradient-based compressive image fusion. Front Inform Technol Electron Eng, 16(3):227–237. https://doi.org/10.1631/FITEE.1400217
Eskicioglu AM, Fisher PS, 1995. Image quality measures and their performance. IEEE Trans Commun, 43(12):2959–2965. https://doi.org/10.1109/26.477498
Huang W, Jing ZL, 2007. Multi-focus image fusion using pulse coupled neural network. Patt Recogn Lett, 28(9):1123–1132. https://doi.org/10.1016/j.patrec.2007.01.013
Li ST, Yang B, 2008. Multifocus image fusion using region segmentation and spatial frequency. Image Vis Comput, 26(7):971–979. https://doi.org/10.1016/j.imavis.2007.10.012
Li ST, Kwok JT, Wang YN, 2001. Combination of images with diverse focuses using the spatial frequency. Inform Fus, 2(3):169–176. https://doi.org/10.1016/s1566-2535(01)00038-0
Li ST, Kang XD, Hu JW, 2013. Image fusion with guided filtering. IEEE Trans Image Process, 22(7):2864–2875. https://doi.org/10.1109/TIP.2013.2244222
Podlubny I, 1999. Fractional Differential Equations: Mathematics in Science and Engineering. Academic Press, San Diego, USA.
Pu T, Ni GQ, 2000. Contrast-based image fusion using the discrete wavelet transform. Opt Eng, 39(8):2075–2082. https://doi.org/10.1117/1.1303728
Pu YF, Wang WX, 2007. Fractional differential masks of digital image and their numerical implementation algorithms. Acta Autom Sin, 33(11):1128–1135 (in Chinese).
Pu YF, Zhou JL, Yuan X, et al., 2010. Fractional differential mask: a fractional differential-based approach for multiscale texture enhancement. IEEE Trans Image Process, 19(2):491–511. https://doi.org/10.1109/TIP.2009.2035980
Tao R, Deng B, Wang Y, 2006. Research progress of the fractional Fourier transform in signal processing. Sci China Ser F, 49(1):1–25. https://doi.org/10.1007/s11432-005-0240-y
Wu GC, Deng ZG, Baleanu D, et al., 2019. New variableorder fractional chaotic systems for fast image encryption. Chaos, 29(8):083103. https://doi.org/10.1063/1.5096645
Xu ZS, 2007. Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst, 15(6):1179–1187. https://doi.org/10.1109/TFUZZ.2006.890678
Yang B, Li ST, 2007. Multi-focus image fusion based on spatial frequency and morphological operators. Chin Opt Lett, 5(8):452–453.
Yang Y, Que Y, Huang SY, et al., 2016. Multimodal sensor medical image fusion based on type-2 fuzzy logic in NSCT domain. IEEE Sens J, 16(10):3735–3745. https://doi.org/10.1109/JSEN.2016.2533864
Zadeh LA, 1965. Fuzzy sets. Inform Contr, 8(3):338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhang L, Liu P, Liu YL, et al., 2010. High quality multi-focus polychromatic composite image fusion algorithm based on filtering in frequency domain and synthesis in space domain. J Zhejiang Univ-Sci C (Comput & Electron), 11(5):365–374. https://doi.org/10.1631/jzus.C0910344
Zhang XF, Chen YQ, 2018. Admissibility and robust stabilization of continuous linear singular fractional order systems with the fractional order α: the 0<α<1 case. ISA Trans, 82:42–50.
Zhu K, Liu G, Zhao L, et al., 2017. Label fusion for segmentation via patch based on local weighted voting. Front Inform Technol Electron Eng, 18(5):680–688. https://doi.org/10.1631/FITEE.1500457
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Xue-feng ZHANG and Hui YAN designed the research. Hui YAN processed the data. Hui YAN and Hao HE drafted the manuscript. Xue-feng ZHANG and Hui YAN revised and finalized the paper.
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Xue-feng ZHANG, Hui YAN, and Hao HE declare that they have no conflict of interest.
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Zhang, Xf., Yan, H. & He, H. Multi-focus image fusion based on fractional-order derivative and intuitionistic fuzzy sets. Front Inform Technol Electron Eng 21, 834–843 (2020). https://doi.org/10.1631/FITEE.1900737
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DOI: https://doi.org/10.1631/FITEE.1900737