Skip to main content
Log in

Image fusion technique using multivariate statistical model for wavelet coefficients

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

Wavelet-based image fusion techniques have been highly successful in combining important features such as edges and textures of source images. In this work, a new discrete wavelet transform (DWT)-based fusion algorithm is proposed using a locally-adaptive multivariate statistical model for the wavelet coefficients of the source images as well as that of the fused image. The multivariate model is proposed based on the fact that the DWT coefficients of source images are correlated not only with each other but also with the fused image. By using this model as a joint prior function, an estimate of the fused coefficients is derived via the Bayesian maximum a posteriori estimation technique. Experimental results show that performance of the proposed fusion method is better than that of the other methods in terms of commonly-used metrics such as structural similarity, peak signal-to-noise ratio, and cross-entropy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Piella G.: A general framework for multiresolution image fusion: from pixels to regions. Inf. Fusion 4, 259–280 (2003)

    Article  Google Scholar 

  2. Hamza A.B., He Y., Krim H., Willsky A.: A multiscale approach to pixel-level image fusion. Integr. Comput.-Aided Eng. 12, 135–146 (2005)

    Google Scholar 

  3. Petrović V.S., Xydeas C.S.: Gradient-based multiresolution image fusion. IEEE Trans. Image Process. 13(2), 228–237 (2004)

    Article  Google Scholar 

  4. Fan X., Verma B.: Selection and fusion of facial features for face recognition. Expert Syst. Appl. 36, 7157–7169 (2009)

    Article  Google Scholar 

  5. Sasikala M., Kumaravel M.: A comparative analysis of feature based image fusion method. Inf. Technol. J. 6(8), 1224–1230 (2007)

    Article  Google Scholar 

  6. Tao Q., Veldhuis R.: Threshold-optimized decision-level fusion and its application to biometrics. Pattern Recognit. 42, 823–836 (2009)

    Article  Google Scholar 

  7. Wan T., Canagarajah N., Achim A.: Segmentation-driven image fusion based on alpha-stable modeling of wavelet coefficients. IEEE Trans. Multimed. 11, 624–633 (2009)

    Article  Google Scholar 

  8. Toet A.: Hierarchical image fusion. Mach. Vis. Appl. 3, 1–11 (1990)

    Article  Google Scholar 

  9. Li H., Manjunath B.S., Mitra S.K.: Multisensor image fusion using the wavelet transform. Graph. Models Image Process. 57(3), 235–245 (1995)

    Article  Google Scholar 

  10. Zhang Z., Blum R.S.: A categorization of multiscale-decomposition-based image fusion schemes with a performance study for a digital camera application. Proc. IEEE 87, 1315–1326 (1999)

    Article  Google Scholar 

  11. Arivazhagan S., Ganesan L., Kumar T.G.S.: A modified statistical approach for image fusion using wavelet transform. Signal Image Video Process. 3, 137–144 (2009)

    Article  Google Scholar 

  12. Zheng, Y., Essock, E.A., Hansen, B.C.: Advanced discrete wavelet transform fusion algorithm and its optimization by using the metric of image quality index. Opt. Eng. 44(3): 037 003–1–12 (2005)

    Google Scholar 

  13. Pajares G., Cruz J.M.: A wavelet-based image fusion tutorial. Pattern Recognit. 37, 1855–1872 (2004)

    Article  Google Scholar 

  14. Rahman S.M.M., Ahmad M.O., Swamy M.N.S.: Contrast-based fusion of noisy images using discrete wavelet transform. IET Image Process. 4(5), 374–384 (2010)

    Article  MathSciNet  Google Scholar 

  15. Zhang Q., Guo B.: Multifocus image fusion using the nonsubsampled contourlet transform. Signal Process. 89, 1334–1346 (2009)

    Article  MATH  Google Scholar 

  16. Li S., Yang B.: Multifocus image fusion by combining curvelet and wavelet transform. Pattern Recognit. Lett. 29, 1295–1301 (2009)

    Article  MATH  Google Scholar 

  17. De I., Chanda B.: A simple and efficient algorithm for multifocus image fusion using morphological wavelets. Signal Process. 86, 924–936 (2006)

    Article  MATH  Google Scholar 

  18. Scheunders P.: An orthogonal wavelet representation of multivalued images. IEEE Trans. Image Process. 12(6), 718–725 (2003)

    Article  MathSciNet  Google Scholar 

  19. Wang H., Peng J., Wu W.: Fusion algorithm for multisensor images based on discrete multiwavelet transform. IEE Proc. Vis. Image Signal Process. 149(5), 283–289 (2002)

    Article  Google Scholar 

  20. Achim A., Tsakalides P., Bezerianos A.: SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling. IEEE Trans. Geosci. Remote Sens. 41(8), 1773–1784 (2003)

    Article  Google Scholar 

  21. Howlader T., Chaubey Y.P.: Noise reduction of cDNA microarray images using complex wavelets. IEEE Trans. Image Process. 19(8), 1953–1967 (2010)

    Article  MathSciNet  Google Scholar 

  22. Şendur L., Selesnick I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Signal Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  23. Mallat S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11(7), 674–693 (1989)

    Article  MATH  Google Scholar 

  24. Fadili J.M., Boubchir L.: Analytical form for a Bayesian wavelet estimator of images using the Bessel K-form densities. IEEE Trans. Image Process. 14(2), 231–240 (2005)

    Article  MathSciNet  Google Scholar 

  25. Solbo S., Eltoft T.: Homomorphic wavelet-based statistical despeckling of SAR images. IEEE Trans. Geosci. Remote Sens. 42(4), 711–721 (2004)

    Article  Google Scholar 

  26. Chipman H.A., Kolaczyk E.D., McCulloch R.E.: Adaptive Bayesian wavelet shrinkage. J. Am. Stat. Assoc. 92(440), 1413–1421 (1997)

    Article  MATH  Google Scholar 

  27. Abramovich F., Sapatinas T., Silverman B.W.: Wavelet thresholding via a Bayesian approach. J. Royal Stat. Soc. B 60(4), 725–749 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  28. Johnstone I.M., Silverman B.W.: Empirical Bayes selection of wavelet thresholds. Ann. Stat. 33(4), 1700–1752 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  29. Liu J., Moulin P.: Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients. IEEE Trans. Image Process. 10(11), 1647–1658 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  30. Mihçak M.K., Kozintsev I., Ramchandran K., Moulin P.: Low-complexity image denoising based on statistical modeling of wavelet coefficients. IEEE Signal Process. Lett. 6(12), 300–303 (1999)

    Article  Google Scholar 

  31. Kazubek M.: Wavelet domain image denoising by thresholding and Wiener filtering. IEEE Signal Process. Lett. 10(11), 324–326 (2003)

    Article  Google Scholar 

  32. Cai T., Silverman B.: Incorporating information on neighboring coefficients into wavelet estimation. Sankhya Indian J. Stat. 63, 127–148 (2001)

    MathSciNet  MATH  Google Scholar 

  33. Howlader T., Chaubey Y.P.: Wavelet-based noise reduction by joint statistical modeling of cDNA microarray images. J. Stat. Theory Pract. 3(2), 349–370 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  34. Wu, J., Liu, J., Tian, J., Huang, H.: Multi-scale image data fusion based on local deviation of wavelet transform. In: Proceedings of the IEEE International Conference on Intelligent Mechatronics and Automation, Chengdu, China, 2004, pp. 677–680

  35. Pu T., Ni G.Q.: Contrast-based image fusion using the discrete wavelet transform. Opt. Eng. 39(8), 2075–2082 (2000)

    Article  Google Scholar 

  36. Yunhao C., Lei D., Jing L., Xiaobing L., Peijun S.: A new wavelet-based image fusion method for remotely sensed data. Int. J. Remote Sens. 27(7), 1465–1476 (2006)

    Article  Google Scholar 

  37. Blum R.S., Yang J.: A statistical signal processing approach to image fusion using hidden Markov models. In: Blum, R.S., Liu, Z. (eds) Multi-sensor Image Fusion and Its Applications, Ch.8, pp. 265–287. CRC Press, Boca-Raton (2006)

    Google Scholar 

  38. Zhang S.D.B.Y., Scheunders P.: Noise-resistant wavelet-based fusion of multispectral and hyperspectral images. IEEE Trans. Geosci. Remote Sens. 47(11), 3834–3843 (2009)

    Article  Google Scholar 

  39. Wang Z., Bovik A.C., Sheikh H.R., Simoncelli E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 3(4), 600–612 (2004)

    Article  Google Scholar 

  40. Zheng Y., Qin Z., Shao L., Hou X.: A novel objective image quality metric for image fusion based on Renyi entropy. Inf. Technol. J. 7(6), 930–935 (2008)

    Article  Google Scholar 

  41. Zhang Y.: Methods for image fusion quality assessment—a review, comparison and analysis. Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci. XXXVII(B7), 1101–1109 (2008)

    Google Scholar 

  42. Mallat S.: A Wavelet Tour of Signal Processing. 2nd edn. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  43. Urdan T.: Statistics in plain English. Lawrence Erlbaum, Mahwah (2000)

    Google Scholar 

  44. Image fusion web-site. [Online]. Available: http://www.imagefusion.org/

  45. Voloshynovskiy S., Pereira S., Iquise V., Pun T.: Attack modelling: towards a second generation watermarking benchmark. Signal Process. 81, 1177–1214 (2001)

    Article  MATH  Google Scholar 

  46. Mardia K.: Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519–530 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  47. Mardia K.: Applications of some measures of multivariate skewness and kurtosis for testing normality and robustness studies. Sankhya B 36, 115–128 (1974)

    MathSciNet  MATH  Google Scholar 

  48. Johnson R.A., Wichern D.W.: Applied Multivariate Statistical Analysis. 1st edn. Prentice-Hall, NJ (1982)

    MATH  Google Scholar 

  49. Giri N.C.: Introduction to Probability and Statistics, 2nd ed. M. Dekker, New York (1993)

    MATH  Google Scholar 

  50. MRI Database: National Center for Image Guided Therapy. [Online]. Available: http://www.ncigt.org/

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tamanna Howlader.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roy, S., Howlader, T. & Rahman, S.M.M. Image fusion technique using multivariate statistical model for wavelet coefficients. SIViP 7, 355–365 (2013). https://doi.org/10.1007/s11760-011-0241-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-011-0241-9

Keywords

Navigation