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P–M equation based multiscale decomposition and its application to image fusion

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Abstract

P–M equation proposed by Perona and Malik can not only perform scale-space, but also preserve edges while smoothing an image. In this paper, we employ this property to construct a new multiscale decomposition method, by which an image can be decomposed into a sequence of detail images and a base image, and the initial image can be perfectly reconstructed by adding up these decomposed images. This decomposition method is applied to multisensor image fusion. The source images are first decomposed into the detail images and the base image. Then, these images are combined according to the given fusion rules. Finally, the fused image is reconstructed by adding up the fused detail images and base image. Compared with conventional methods based on multiscale decomposition, experimental results over multifocus images, visible and infrared images, and medical images demonstrate the superiority of our method in terms of visual inspection and objective measures.

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References

  1. Toet A (1990) Hierarchical image fusion. Mach Vision Appl 3:1–11 doi:10.1007/BF01211447

    Article  Google Scholar 

  2. Goshtasby AA, Nikolov S (2007) Image fusion: advances in the state of the art. Inf Fusion 8(2):114–118. doi:10.1016/j.inffus.2006.04.001

    Article  Google Scholar 

  3. Pohl C, Van Genderen JL (1998) Multisensor image fusion in remote sensing: concepts, methods and applications. Int J Remote Sens 19(5):823–854. doi:10.1080/014311698215748

    Article  Google Scholar 

  4. Burt P, Adelson E (1983) The laplacian pyramid as a compact image code. IEEE Trans Commun 31(4):532–540. doi:10.1109/TCOM.1983.1095851

    Article  Google Scholar 

  5. Toet A (1989) A morphological pyramidal image decomposition. Pattern Recogn Lett 9(4):255–261 doi:10.1016/0167-8655(89)90004-4

    Article  MATH  Google Scholar 

  6. Petrovic V, Xydeas C (2004) Gradient-based multiresolution image fusion. IEEE Trans Image Process 13(2):228–237. doi:10.1109/TIP.2004.823821

    Article  Google Scholar 

  7. Hui L, Manjunath BS, Mitra SK (1995) Multi-sensor image fusion using the wavelet transform. Graph Models Image Process 57(3):235–245. doi:10.1109/ICIP.1994.413273

    Article  Google Scholar 

  8. Pajares G, de la Cruz JM (2004) A wavelet-based image fusion tutorial. Pattern Recogn 37(9):1855–1872. doi:10.1016/j.patcog.2004.03.010

    Article  Google Scholar 

  9. Rockinger O (1997) Image sequence fusion using a shift-invariant wavelet transform. In: Proceedings of international conference on image processing, Santa Barbara, CA, USA, 1997, vol 3, pp 288–291. doi:10.1109/ICIP.1997.632093

  10. Beaulieu M, Foucher S, Gagnon L (2003) Multi-spectral image resolution refinement using stationary wavelet transform. In: Proceedings of IEEE international conference on geoscience and remote sensing, 2003, vol 6, pp 4032–4034. doi:10.1109/IGARSS.2003.1295352

  11. Lewis JJ, O’Callaghan RJ, Nikolov SG, Bull DR, Canagarajah N (2007) Pixel- and region-based image fusion with complex wavelets. Inf Fusion 8(2):119–130. doi:10.1016/j.inffus.2005.09.006

    Google Scholar 

  12. Tessens L, Ledda A, Pizurica A, Philips W (2007) Extending the depth of field in microscopy through curvelet-based frequency-adaptive image fusion. In: Processing of IEEE international conference on acoustics, speech and signal processing, vol 1, pp 861–864. doi:10.1109/ICASSP.2007.366044

  13. Ren S, Cheng J, Li M (2010) Multiresolution fusion of pan and MS images based on the curvelet transform. In: Proceedings of IEEE international conference on geoscience and remote sensing, 2010, pp 472–475. doi:10.1109/IGARSS.2010.5652557

  14. da Cunha A, Zhou J, Do M (2006) The nonsubsampled contourlet transform: theory, design, and applications. IEEE Trans Image Process 15(10):3089–3101. doi:10.1109/TIP.2006.877507

    Article  Google Scholar 

  15. Tang L, Zhao F, Zhao ZG (2007) The nonsubsampled contourlet transform for image fusion. In: Proceedings of international conference on wavelet analysis and pattern recognition, 2007, vol 1, pp 305–310. doi:10.1109/ICWAPR.2007.4420684

  16. Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12(7):629–639. doi:10.1109/34.56205

    Article  Google Scholar 

  17. Witkin A (1984) Scale-space filtering: a new approach to multi-scale description. In: IEEE international conference on acoustics, speech, and signal processing, vol 9, pp 150–153. doi:10.1109/ICASSP.1984.1172729

  18. Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell PAMI-8(6):679 –698. doi:10.1109/TPAMI.1986.4767851

    Google Scholar 

  19. Clark J (1988) Singularity theory and phantom edges in scale space. IEEE Trans Pattern Anal Mach Intell 10(5):720 –727. doi:10.1109/34.6782

    Article  MATH  Google Scholar 

  20. Catté F, Lions PL, Morel JM, Coll T (1992) Image selective smoothing and edge detection by nonlinear diffusion. SIAM J Numerical Anal 29:182–193. doi:10.1137/0729012

    Google Scholar 

  21. Weickert J, Romeny B, Viergever M (1998) Efficient and reliable schemes for nonlinear diffusion filtering. IEEE Trans Image Process 7(3):398–410. doi:10.1109/83.661190

    Article  Google Scholar 

  22. Niessen WJ, Romeny BMTH, Florack LM, Viergever MA (1997) A general framework for geometry-driven evolution equations. Int J Comput Vision 21:187–205

    Article  Google Scholar 

  23. Chen Q, Montesinos P, Sun QS, Xia DS (2010) Ramp preserving Perona-Malik model. Signal Process 90(6):1963–1975. doi:10.1016/j.sigpro.2009.12.015

    Article  MATH  Google Scholar 

  24. Qu G, Zhang D, Yan P (2002) Information measure for performance of image fusion. Electron Lett 38(7):313–315. doi:10.1049/el:20020212

    Article  Google Scholar 

  25. Piella G, Heijmans H (2003) A new quality metric for image fusion. In: Proceedings of international conference on image processing, 2003, vol 3, pp III-173–III-176. doi:10.1109/ICIP.2003.1247209

  26. Hshiung TG, Tzeng GH, Huang JJ (1981) Multiple attribute decision making: methods and applications. Springer, New York

  27. Hwang CL, Lai YJ, Liu TY (1993) A new approach for multiple objective decision making. Comput Oper Res 20(8):889–899. doi:10.1016/0305-0548(93)90109-V

    Article  MATH  Google Scholar 

  28. Hu J, Li S (2012) The multiscale directional bilateral filter and its application to multisensor image fusion. Inf Fusion 13(3):196–206. doi:10.1016/j.inffus.2011.01.002

    Article  Google Scholar 

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Acknowledgements

We would like to sincerely thank the anonymous reviewers for their constructive suggestions. This paper is supported by the National Natural Science Foundation of China (No.61071162)

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Correspondence to Yong Jiang.

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Jiang, Y., Wang, M. P–M equation based multiscale decomposition and its application to image fusion. Pattern Anal Applic 17, 167–178 (2014). https://doi.org/10.1007/s10044-013-0343-9

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