Abstract
Multi-focus image fusion, which aims to combine multi-focus images of a scene to construct an all-in-focus image, has become a major topic in image processing. Different methods have been proposed in spatial or transform domain. But many methods usually suffer from fusion quality degradations, such as contrast reduction, artificial edges, and discontinuous phenomena at boundaries of focused regions, which may cause issues when going for further processing. In order to overcome these problems, we introduce a nonsubsampled compactly supported shearlet transform (NSCSST), which possesses multi-scale, multi-direction, translation invariance and spatial localization characteristics that are very important for image fusion in transform domain. The transform can be implemented sequentially by the shear transform and the separable anisotropic nonsubsampled wavelet transform (SANSWT). Furthermore, we propose a new image fusion method based on NSCSST. It consists of two aspects: multi-direction fusion and transform domain fusion, which respectively correspond to the shear transform and the SANSWT of NSCSST. For each sheared image pair, the SANSWT coefficients are firstly fused by the transform domain fusion rules. And then, the final fused image is obtained by the multi-direction fusion rules, ranging from the simple averaging method to the proposed complex genetic algorithm based method. Experimental results show that our method outperforms some other methods, such as the method based on bilateral gradient, the method based on nonsubsampled contourlet transform, the method based on simultaneous empirical wavelet transform, and the method based on guided filtering.
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References
Aiazzi B, Alparone L, Barducci A, Baronti S, Pippi I (1999) Multispectral fusion of multisensor image data by the generalized Laplacian pyramid. In: Proceeding of 1999 IEEE international geoscience and remote sensing symposium, vol 2. IEEE, pp 1183–1185
Aslantas V, Kurban R (2009) A comparison of criterion functions for fusion of multi-focus noisy images. Opt Commun 282(16):3231–3242
Aslantas V, Toprak AN (2014) A pixel based multi-focus image fusion method. Opt Commun 332(1):350–358
Baradarani A, Wu QMJ, Ahmadi M, Mendapara P (2012) Tunable halfband-pair wavelet filter banks and application to multifocus image fusion. Pattern Recogn 45(2):657–671
Candès E, Demanet L, Donoho D, Ying L (2006) Fast discrete curvelet transforms. Multiscale Model Simul 5(3):861–899
Cao Y, Li S, Hu J (2011) Multi-focus image fusion by nonsubsampled shearlet transform. In: Proceedings of the 6th international conference on image and graphics. IEEE, pp 17–21
Chen L, Li J, Chen C (2013) Regional multifocus image fusion using sparse representation. Opt Express 21(4):5182–5197
Cunha ALD, Zhou J, Do MN (2006) The nonsubsampled contourlet transform: theory, design, and applications. IEEE Trans Image Process 15(10):3089–3101
Desai UY, Mizuki MM, Masaki I, Horn BKP (1996) Edge and mean based image compression. Technical Report AIM-1584, Massachusetts Institute of Technology, Cambridge, MA USA
Ding G, Guo Y, Zhou J, Gao Y (2016) Large-scale cross-modality search via collective matrix factorization hashing. IEEE Trans Image Process 25(11):5427–5440
Do MN, Vetterli M (2002) Contourlets: a directional multiresolution image representation. In: Proceedings of 2002 international conference on image processing, vol 1. IEEE, pp 357–360
Do MN, Vetterli M (2005) The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans Image Process 14(12):2091–2106
Easley G, Labate D, Lim WQ (2008) Sparse directional image representations using the discrete shearlet transform. Appl Comput Harmon Anal 25(1):25–46
Eltoukhy HA, Kavusi S (2003) A computationally efficient algorithm for multi-focus image reconstruction. In: Proceedings of SPIE electronic imaging, pp 332–341
Eskicioglu AM, Fisher PS (1995) Image quality measures and their performance. IEEE Trans Commun 43(12):2959–2965
Gao G, Xu L, Feng D (2013) Multi-focus image fusion based on non-subsampled shearlet transform. IET Image Process 7(6):633–639
Gao Y, Wang M, Tao D, Ji R, Dai Q. (2012) 3-D object retrieval and recognition with hypergraph analysis. IEEE Trans Image Process 21(9):4290–4303
Geng P, Huang M, Liu S, Feng J, Bao P (2016) Multifocus image fusion method of ripplet transform based on cycle spinning. Multimed Tools Appl 75(17):10,583–10,593
Goshtasby AA, Nikolov S (2007) Image fusion: advances in the state of the art. Information Fusion 8(2):114–118
Guo D, Yan J, Qu X (2015) High quality multi-focus image fusion using self-similarity and depth information. Opt Commun 338:138–144
Guo K, Kutyniok G, Labate D (2006) Sparse multidimensional representations using anisotropic dilation and shear operators. In: Wavelets and splines. Nashboro Press, Athens, GA, pp 189–201
Guo K, Labate D (2007) Optimally sparse multidimensional representation using shearlets. SIAM J Math Anal 39(1):298–318
Holland JH (1992) Adaptation in natural and artificial systems. MIT Press, Cambridge, MA USA
Holshneider M, Kronland-Martinet R, Morlet J, Tchamitchian P (1989) A real-time algorithm for signal analysis with the help of the wavelet transform. In: Combes JM, Grossmann A, Tchamitchian P (eds) Proceedings of the International conference time-frequency methods and phase space wavelets. Springer-Verlag, Berlin, pp 286–297
Huang W, Jing Z (2007) Evaluation of focus measures in multi-focus image fusion. Pattern Recogn Lett 28(4):493–500
Ji X, Zhang G (2015) Image fusion method of SAR and infrared image based on curvelet transform with adaptive weighting. Multimed Tools Appl 1–17. doi:10.1007/s11042-015-2879-8
Kutyniok G, Labate D (2009) Resolution of the wavefront set using continuous shearlets. Trans Am Math Soc 361(5):2719–2754
Kutyniok G, Lim WQ, Zhuang X (2012) Digital shearlet transforms. In: Kutyniok G, Labate D (eds) Shearlets: Multiscale analysis for multivariate data, chap 7.Birkhäuser Basel, pp 239–282
Labate D, Lim WQ, Kutyniok G, Weiss G (2005) Sparse multidimensional representation using shearlets. In: Papadakis M, Laine AF, Unser MA (eds) Proceedings of the SPIE wavelets XI, vol 5914, pp 254–262
Lewis JJ, O’callaghan RJ, Nikolov SG, Bull DR, Canagarajah N (2007) Pixel- and region-based image fusion with complex wavelets. Information Fusion 8(2):119–130
Li C, Yang X, Chu B, Lu W, Pang L (2010) A new image fusion quality assessment method based on contourlet and SSIM. In: Proceedings of the 3rd IEEE international conference on computer science and information technology, vol 5. IEEE, pp 246–249
Li S, Kang X (2012) Fast multi-exposure image fusion with median filter and recursive filter. IEEE Trans Consum Electron 58(2):626–632
Li S, Kang X, Hu J (2013) Image fusion with guided filtering. IEEE Trans Image Process 22(7):2864–2875
Li S, Kwok JT, Wang Y (2001) Combination of images with diverse focuses using the spatial frequency. Information Fusion 2(3):169–176
Li S, Kwok JT, Wang Y (2002) Multifocus image fusion using artificial neural networks. Pattern Recogn Lett 23(8):985–997
Li S, Yang B (2008) Multifocus image fusion using region segmentation and spatial frequency. Image Vis Comput 26(7):971–979
Li S, Yang B, Hu J (2011) Performance comparison of different multi-resolution transforms for image fusion. Information Fusion 12(2):74–84
Lim WQ (2010) The discrete shearlet transform: a new directional transform and compactly supported shearlet frames. IEEE Trans Image Process 19(5):1166–1180
Lin Z, Ding G, Han J, Wang J (2016) Cross-view retrieval via probability-based semantics-preserving hashing. IEEE Trans Cybern 1–14. doi:10.1109/TCYB.2016.2608906
Lin Z, Ding G, Hu M, Lin Y, Ge SS (2014) Image tag completion via dual-view linear sparse reconstructions. Comput Vis Image Underst 124:42–60
Liu X, Zhou Y, Wang J (2014) Image fusion based on shearlet transform and regional features. AEU-Int J Electron C 68(6):471–477
Liu Y, Liu S, Wang Z (2015) A general framework for image fusion based on multi-scale transform and sparse representation. Information Fusion 24:147–164
Miao Q, Shi C, Li W (2013) Image fusion based on shearlets. In: Miao Q (ed) New advances in image fusion, chap 7. Intech, pp 113–133
Miao Q, Shi C, Xu P, Yang M, Shi Y (2011) Multi-focus image fusion algorithm based on shearlets. Chin Opt Lett 9(4):1–5
Miao Q, Shi C, Xu P, Yang M, Shi Y (2011) A novel algorithm of image fusion using shearlets. Opt Commun 284(6):1540–1547
Miao Q, Wang B (2005) A novel adaptive multi-focus image fusion algorithm based on PCNN and sharpness. In: Proceedings of SPIE, vol 5778. pp 704–712
Moonon AU, Hu J (2015) Multi-focus image fusion based on NSCT and NSST. Sensing and Imaging 16(1):1–16
Naidu V, Raol J (2008) Pixel-level image fusion using wavelets and principal component analysis. Def Sci J 58(3):338–352
Nayar SK, Nakagawa Y (1994) Shape from focus. IEEE Trans Pattern Anal Mach Intell 16(8):824–831
Nejatia M, Samavi S, Shiranib S (2015) Multi-focus image fusion using dictionary-based sparse representation. Information Fusion 25:72–84
Pajares G, de la Cruz JM (2004) A wavelet-based image fusion tutorial. Pattern Recogn 37(9):1855–1872
Patel R, Rajput M, Parekh P (2015) Comparative study on multi-focus image fusion techniques in dynamic scene. Int J Comput Appl 109(6):5–9
Pennec EL, Mallat S (2005) Sparse geometric image representations with bandelets. IEEE Trans Image Process 14(4):423–438
Peyré G, Mallat S (2005) Discrete bandelets with geometric orthogonal filters. In: Proceedings of 2005 IEEE International Conference on Image Processing, IEEE, pp i–65–8
Piella G, Heijmans H (2003) A new quality metric for image fusion. In: Proceedings of 2003 International Conference on Image Processing. IEEE, Barcelona, Spain, pp 173–176
Qu X, Yan J, Xiao H, Zhu Z (2008) Image fusion algorithm based on spatial frequency-motivated pulse coupled neural networks in nonsubsampled contourlet transform domain. Acta Automatica Sinica 34(12):1508–1514
Qu X, Yan J, Xie G, Zhu Z, Chen B (2007) A novel image fusion algorithm based on bandelet transform. Chin Opt Lett 5(10):569–572
Qu XB, Yan JW, Yang GD (2005) Sum-modified-Laplacian-based multifocus image fusion method in cycle spinning sharp frequency localized contourlet transform domain. Opt Precis Eng 13(2)
Sharma M (2016) A review: image fusion techniques and applications. Int J Comput Sci Inf Technol 7(3):1082–1085
Tian J, Chen L (2012) Adaptive multi-focus image fusion using a wavelet-based statistical sharpness measure. Signal Process 92(9):2137–2146
Tian J, Chen L, Ma L, Yu W (2011) Multi-focus image fusion using a bilateral gradient-based sharpness criterion. Opt Commun 284(1):80–87
Wang H, Nie C, Li Y, Zhang K, Chen L (2011) A novel fusion algorithm for multi-focus image. In: Zhang J (ed) Applied informatics and communication, communications in computer and information science, vol 227. Springer, Berlin Heidelberg, pp 641–647
Wang J, Wang W, Li B, Xu G, Zhang R, Zhang J (2016) Exposure fusion via sparse representation and shiftable complex directional pyramid transform. Multimed Tools Appl pp 1–21. doi:10.1007/s11042-016-3868-2
Wang Z, Bovik AC (2002) A universal image quality index. IEEE Signal Process Lett 9(3):81–84
Wang Z, Ma Y, Gu J (2010) Multi-focus image fusion using PCNN. Pattern Recogn 43(6):2003–2016
Xiang T, Yan L, Gao R (2015) A fusion algorithm for infrared and visible images based on adaptive dual-channel unit-linking PCNN in NSCT domain. Infrared Phys Technol 69:53–61
Xu J, Yang L, Wu D (2011) Ripplet: a new transform for image processing. J Vis Commun Image Represent 21(7):627–639
Yang L, Guo BL, Ni W (2008) Multimodality medical image fusion based on multiscale geometric analysis of contourlet transform. Neurocomputing 72(1-3):203–211
Yang Y, Huang S, Gao J, Qian Z (2014) Multi-focus image fusion using an effective discrete wavelet transform based algorithm. Meas Sci Rev 14(2):102–108
Yang Y, Tong S, Huang S, Lin P (2015) Multifocus image fusion based on NSCT and focused area detection. IEEE Sensors J 15(5):2824–2838
You X, Chen Q, Fang B, Tang YY (2006) Thinning character using modulus minima of wavelet transform. Int J Pattern Recognit Artif Intell 20(3):361–375
Zhang D, You X, Wang P, Yanushkevich SN, Tang YY (2009) Facial biometrics using nontensor product wavelet and 2D discriminant techniques. Int J Pattern Recognit Artif Intell 23(3):521–543
Zhang Q, Guo BL (2009) Multifocus image fusion using the nonsubsampled contourlet transform. Signal Process 89(7):1334–1346
Zhang X, Li X, Feng Y (2017) Image fusion based on simultaneous empirical wavelet transform. Multimed Tools Appl 76(6):8175–8193
Zhao S, Yao H, Gao Y, Ding G, Chua TS (2016) Predicting personalized image emotion perceptions in social networks. IEEE Trans Affective Comput. doi:10.1109/TAFFC.2016.2628787
Zhao S, Yao H, Gao Y, Ji R, Ding G (2017) Continuous probability distribution prediction of image emotions via multi-task shared sparse regression. IEEE Trans Multimedia 19(3):632–645
Zhao S, Yao H, Yang Y, Zhang Y (2014) Affective image retrieval via multi-graph learning. In: Proceedings of the 22nd ACM international conference on multimedia. ACM, pp 1025–1028
Zhao S, Yao H, Zhang Y, Wang Y, Liu S (2015) View-based 3D object retrieval via multi-modal graph learning. Signal Process 112:110–118
Acknowledgments
The authors would like to thank the editor and anonymous reviewers for their detailed review and valuable comments. This work was supported by the NSF of China (No. 11301137), the NSF of Hebei Province, China (No. A2014205100), the Educational Commission of Hebei Province, China (No. ZD2014062).
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Wei, C., Zhou, B. & Guo, W. Multi-focus image fusion based on nonsubsampled compactly supported shearlet transform. Multimed Tools Appl 77, 8327–8358 (2018). https://doi.org/10.1007/s11042-017-4731-9
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DOI: https://doi.org/10.1007/s11042-017-4731-9