Multifocus color image fusion is an active research area in image processing, and many fusion algorithms have been developed. However, the existing techniques can hardly deal with the problem of image blur. This study present a novel fusion approach that integrates the quaternion with traditional curvelet transform to overcome the above disadvantage. The proposed method uses a multiresolution analysis procedure based on the quaternion curvelet transform. Experimental results show that the proposed method is promising, and it does significantly improve the fusion quality compared to the existing fusion methods.

© 2012 OSA

1. X. Li, M. He, and M. Roux, “Multifocus image fusion based on redundant wavelet transform,” IET Image Process. 4(4), 283–293 (2010). [CrossRef]
2. S. Li, J. T. Kwok, and Y. Wang, “Multifocus image fusion using artificial neutral networks,” Pattern Recogn. Lett. 23(8), 985–997 (2002). [CrossRef]
3. Z. Wang, Y. Ma, and J. Gu, “Multi-focus image fusion using PCNN,” Pattern Recogn. 43(6), 2003–2016 (2010). [CrossRef]
4. Q. Zhang and B. Guo, “Multifocus image fusion using the nonsubsampled contourlet transform,” Signal Process. 89(7), 1334–1346 (2009). [CrossRef]
5. W. Huang and Z. L. Jing, “Multifocus image fusion using pulse coupled neutral network,” Pattern Recogn. lett. 28(9), 1123–1132 (2007). [CrossRef]
6. N. Wang, Y. Ma, and J. Gu, “Multi-focus image fusion algorithm based on shearlets,” Chin. Opt. Lett. 9(4), 041001 (2011).
7. N. Ma, L. Luo, Z. Zhou, and M. Liang, “A Multifocus image fusion in nonsubsampled contourlet domain with variational fusion stategy,” Proc. SPIE 8004, 800411 (2011). [CrossRef]
8. W. Yajie and X. Xinhe, “A multifocus image fusion new method based on multidecision,” Proc. SPIE 6357, 63570G (2006). [CrossRef]
9. R. Nava, B. E. Ramírez, and G. Cristóbal, “A novel multi-focus image fusion algorithm based on feature extraction and wavelets,” Proc. SPIE 7000, 700028 (2008). [CrossRef]
10. I. De and B. Chanda, “A simple and efficient algorithm for multifocus image fusion using morphological wavelets,” Signal Process. 86(5), 924–936 (2006). [CrossRef]
11. S. Li and B. Yang, “Multifocus image fusion using region segmentation and spatial frequency,” Image Vis. Comput. 26(7), 971–979 (2008). [CrossRef]
12. H. Li, Y. Chai, H. Yin, and G. Liu, “Multifocus image fusion and denoising scheme based on homogeneity similarity,” Opt. Commun. 285(2), 91–100 (2012). [CrossRef]
13. Y. Chai, H. Li, and Z. Li, “Multifocus image fusion scheme using focused region detection and multiresolution,” Opt. Commun. 284(19), 4376–4389 (2011). [CrossRef]
14. S. Gabarda and G. Cristóbal, “Multifocus image fusion through pseudo-Wigner distribution,” Opt. Eng. 44(4), 047001 (2005). [CrossRef]
15. P. L. Lin and P. Y. Huang, “Fusion methods based on dynamic-segmented morphological wavelet or cut and paste for multifocus images,” Signal Process. 88(6), 1511–1527 (2008). [CrossRef]
16. Y. Chai, H. F. Li, and M. Y. Guo, “Multifocus image fusion scheme based on features of multiscale products and PCNN in lifting stationary wavelet domain,” Opt. Commun. 284(5), 1146–1158 (2011). [CrossRef]
17. R. Redonodo, F. S?roubek, S. Fischer, and G. Gristóbal, “Multifocus image fusion using the log-Gabor transform and a Multisize Windows technique,” Inform. Fusion 10(2), 163–171 (2009). [CrossRef]
18. F. Luo, B. Lu, and C. Miao, “Multifocus image fusion with trace-based structure tensor,” Proc. SPIE 8200, 82001G (2011). [CrossRef]
19. A. Baradarani, Q. M. J. Wu, M. Ahmadi, and P. Mendapara, “Tunable halfband-pair wavelet filter banks and application to multifocus image fusion,” Pattern Recogn. 45(2), 657–671 (2012). [CrossRef]
20. Y. Chai, H. Li, and X. Zhang, “Multifocus image fusion based on features contrast of multiscale products in nonsubsampled contourlet transform domain,” Optik 123(7), 569–581 (2012). [CrossRef]
21. H. Zhao, Q. Li, and H. Feng, “Multi-focus color image fusion in the HSI space using the sum-modified-laplacian and the coarse edge map,” Image Vis. Comput. 26(9), 1285–1295 (2008). [CrossRef]
22. W. Huang and Z. Jing, “Evaluation of focus measures in multi-focus image fusion,” Pattern Recogn. Lett. 28(9), 493–500 (2007). [CrossRef]
23. R. Maruthi, “Spatial Domain Method for Fusing Multi-Focus Images using Measure of Fuzziness,” Int. J. Comput. Appl. 20(7), 48–57 (2011).
24. H. Shi and M. Fang, “Multi-focus Color Image Fusion Based on SWT and IHS,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE2007), 461–465. [CrossRef]
25. Y. Chen, L. Wang, Z. Sun, Y. Jiang, and G. Zhai, “Fusion of color microscopic images based on bidimensional empirical mode decomposition,” Opt. Express 18(21), 21757–21769 (2010). [CrossRef] [PubMed]
26. H. Li, B. S. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graphical Models & Image Process. 57(3), 235–245 (1995). [CrossRef] [PubMed]
27. Z. Zhang and R. S. Blum, “A categorization of multiscale-decomposition-based image fusion schemes with a performance study for a digital camera application,” Proc. IEEE. 87(8), 1315–1326 (1999). [CrossRef]
28. K. Amolius, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques–An introduction, review and comparison,” Photogramm. Eng. Remote Sens. 62(1), 249–263 (2007). [CrossRef]
29. S. J. Sangwine, “Fourier transforms of colour images using quaternion, or hypercomplex numbers,” Electron. Lett. 32(1), 1979–1980 (1996). [CrossRef]
30. S. C. Pei and C. M. Cheng, “Color image processing by using binary quaternion-moment-preserving thresholding technique,” IEEE Trans. Signal Process. 8(5), 614–628 (1999).
31. T. A. Ell and S. J. Sangwine, “Hypercomplex Fourier transforms of color images,” IEEE Trans. Image Process. 16(1), 22–35 (2007). [CrossRef] [PubMed]
32. D. S. Alexiadis and G. D. Sergiadis, “Estimation of motions in color image sequences using hypercomplex Fourier transforms,” IEEE Trans. Sig. Process. 18(1), 168–186 (2009).
33. S. J. Sangwine, T. A. Ell, and N. L. Bihan, “Fundamental representations and algebraic properties of biquater-nions or complexified quaternions,” Adv. Appl. Clifford Algebras 21(3), 607–636 (2011). [CrossRef]
34. L. Q. Guo and M. Zhu, “Quaternion Fourier-Mellin moments for color images,” Pattern Recogn. 44(2), 187–195 (2011). [CrossRef]
35. B. J. Chen, H. Z. Shu, H. Zhang, G. Chen, C. Toumoulin, J. L. Dillenseger, and L. M. Luo, “Quaternion Zernike moments and their invariants for color image analysis and object recognition,” Signal Process. 92(2), 308–318 (2012). [CrossRef]
36. S. Sangwine and N. L. Bihan, “Quaternion toolbox for Matlab,” http://qtfm.sourceforge.net
37. E. J. Candès and D. L. Donoho, “Continuous curvelet transform I. Resolution of the wavefront set,” Appl. Comput. Harmon. Anal. 19(2), 162–197 (2005). [CrossRef]
38. E. J. Candès and D. L. Donoho, “Continuous curvelet transform II. Discretization and frames,” Appl. Comput. Harmon. Anal. 19(2), 198–222 (2005). [CrossRef]
39. E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “The curvelet transform website,” http://www.curvelet.org
40. E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transorms,” Multiscale Model. Simul. 5(3), 861–899 (2006). [CrossRef]
41. Y. Yuan, J. Zhang, B. Chang, and Y. Han, “Objective quality evaluation of visible and infrared color fusion image,” Opt. Eng. 50(3), 033202 (2011). [CrossRef]
42. M. Douze, “Blur image data,” http://lear.inrialpes.fr/people/vandeweijer/data.html
43. Helicon Soft, “Helicon Focus Sample images,” http://www.heliconsoft.com/focus_samples.html

Adv. Appl. Clifford Algebras

• S. J. Sangwine, T. A. Ell, and N. L. Bihan, “Fundamental representations and algebraic properties of biquater-nions or complexified quaternions,” Adv. Appl. Clifford Algebras 21(3), 607–636 (2011). [CrossRef]

Appl. Comput. Harmon. Anal.

• E. J. Candès and D. L. Donoho, “Continuous curvelet transform I. Resolution of the wavefront set,” Appl. Comput. Harmon. Anal. 19(2), 162–197 (2005). [CrossRef]
• E. J. Candès and D. L. Donoho, “Continuous curvelet transform II. Discretization and frames,” Appl. Comput. Harmon. Anal. 19(2), 198–222 (2005). [CrossRef]

Chin. Opt. Lett.

• N. Wang, Y. Ma, and J. Gu, “Multi-focus image fusion algorithm based on shearlets,” Chin. Opt. Lett. 9(4), 041001 (2011).

Electron. Lett.

• S. J. Sangwine, “Fourier transforms of colour images using quaternion, or hypercomplex numbers,” Electron. Lett. 32(1), 1979–1980 (1996). [CrossRef]

Graphical Models & Image Process.

• H. Li, B. S. Manjunath, and S. K. Mitra, “Multisensor image fusion using the wavelet transform,” Graphical Models & Image Process. 57(3), 235–245 (1995). [CrossRef] [PubMed]

IEEE Trans. Image Process.

• T. A. Ell and S. J. Sangwine, “Hypercomplex Fourier transforms of color images,” IEEE Trans. Image Process. 16(1), 22–35 (2007). [CrossRef] [PubMed]

IEEE Trans. Sig. Process.

• D. S. Alexiadis and G. D. Sergiadis, “Estimation of motions in color image sequences using hypercomplex Fourier transforms,” IEEE Trans. Sig. Process. 18(1), 168–186 (2009).

IEEE Trans. Signal Process.

• S. C. Pei and C. M. Cheng, “Color image processing by using binary quaternion-moment-preserving thresholding technique,” IEEE Trans. Signal Process. 8(5), 614–628 (1999).

IET Image Process.

• X. Li, M. He, and M. Roux, “Multifocus image fusion based on redundant wavelet transform,” IET Image Process. 4(4), 283–293 (2010). [CrossRef]

Image Vis. Comput.

• S. Li and B. Yang, “Multifocus image fusion using region segmentation and spatial frequency,” Image Vis. Comput. 26(7), 971–979 (2008). [CrossRef]
• H. Zhao, Q. Li, and H. Feng, “Multi-focus color image fusion in the HSI space using the sum-modified-laplacian and the coarse edge map,” Image Vis. Comput. 26(9), 1285–1295 (2008). [CrossRef]

Inform. Fusion

• R. Redonodo, F. S?roubek, S. Fischer, and G. Gristóbal, “Multifocus image fusion using the log-Gabor transform and a Multisize Windows technique,” Inform. Fusion 10(2), 163–171 (2009). [CrossRef]

Int. J. Comput. Appl.

• R. Maruthi, “Spatial Domain Method for Fusing Multi-Focus Images using Measure of Fuzziness,” Int. J. Comput. Appl. 20(7), 48–57 (2011).

Multiscale Model. Simul.

• E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “Fast discrete curvelet transorms,” Multiscale Model. Simul. 5(3), 861–899 (2006). [CrossRef]

Opt. Commun.

• Y. Chai, H. F. Li, and M. Y. Guo, “Multifocus image fusion scheme based on features of multiscale products and PCNN in lifting stationary wavelet domain,” Opt. Commun. 284(5), 1146–1158 (2011). [CrossRef]
• H. Li, Y. Chai, H. Yin, and G. Liu, “Multifocus image fusion and denoising scheme based on homogeneity similarity,” Opt. Commun. 285(2), 91–100 (2012). [CrossRef]
• Y. Chai, H. Li, and Z. Li, “Multifocus image fusion scheme using focused region detection and multiresolution,” Opt. Commun. 284(19), 4376–4389 (2011). [CrossRef]

Opt. Eng.

• S. Gabarda and G. Cristóbal, “Multifocus image fusion through pseudo-Wigner distribution,” Opt. Eng. 44(4), 047001 (2005). [CrossRef]
• Y. Yuan, J. Zhang, B. Chang, and Y. Han, “Objective quality evaluation of visible and infrared color fusion image,” Opt. Eng. 50(3), 033202 (2011). [CrossRef]

Opt. Express

• Y. Chen, L. Wang, Z. Sun, Y. Jiang, and G. Zhai, “Fusion of color microscopic images based on bidimensional empirical mode decomposition,” Opt. Express 18(21), 21757–21769 (2010). [CrossRef] [PubMed]

Optik

• Y. Chai, H. Li, and X. Zhang, “Multifocus image fusion based on features contrast of multiscale products in nonsubsampled contourlet transform domain,” Optik 123(7), 569–581 (2012). [CrossRef]

Pattern Recogn.

• A. Baradarani, Q. M. J. Wu, M. Ahmadi, and P. Mendapara, “Tunable halfband-pair wavelet filter banks and application to multifocus image fusion,” Pattern Recogn. 45(2), 657–671 (2012). [CrossRef]
• L. Q. Guo and M. Zhu, “Quaternion Fourier-Mellin moments for color images,” Pattern Recogn. 44(2), 187–195 (2011). [CrossRef]
• Z. Wang, Y. Ma, and J. Gu, “Multi-focus image fusion using PCNN,” Pattern Recogn. 43(6), 2003–2016 (2010). [CrossRef]

Pattern Recogn. Lett.

• S. Li, J. T. Kwok, and Y. Wang, “Multifocus image fusion using artificial neutral networks,” Pattern Recogn. Lett. 23(8), 985–997 (2002). [CrossRef]
• W. Huang and Z. L. Jing, “Multifocus image fusion using pulse coupled neutral network,” Pattern Recogn. lett. 28(9), 1123–1132 (2007). [CrossRef]
• W. Huang and Z. Jing, “Evaluation of focus measures in multi-focus image fusion,” Pattern Recogn. Lett. 28(9), 493–500 (2007). [CrossRef]

Photogramm. Eng. Remote Sens.

• K. Amolius, Y. Zhang, and P. Dare, “Wavelet based image fusion techniques–An introduction, review and comparison,” Photogramm. Eng. Remote Sens. 62(1), 249–263 (2007). [CrossRef]

Proc. IEEE

• Z. Zhang and R. S. Blum, “A categorization of multiscale-decomposition-based image fusion schemes with a performance study for a digital camera application,” Proc. IEEE. 87(8), 1315–1326 (1999). [CrossRef]

Proc. SPIE

• F. Luo, B. Lu, and C. Miao, “Multifocus image fusion with trace-based structure tensor,” Proc. SPIE 8200, 82001G (2011). [CrossRef]
• N. Ma, L. Luo, Z. Zhou, and M. Liang, “A Multifocus image fusion in nonsubsampled contourlet domain with variational fusion stategy,” Proc. SPIE 8004, 800411 (2011). [CrossRef]
• W. Yajie and X. Xinhe, “A multifocus image fusion new method based on multidecision,” Proc. SPIE 6357, 63570G (2006). [CrossRef]
• R. Nava, B. E. Ramírez, and G. Cristóbal, “A novel multi-focus image fusion algorithm based on feature extraction and wavelets,” Proc. SPIE 7000, 700028 (2008). [CrossRef]

Signal Process.

• I. De and B. Chanda, “A simple and efficient algorithm for multifocus image fusion using morphological wavelets,” Signal Process. 86(5), 924–936 (2006). [CrossRef]
• Q. Zhang and B. Guo, “Multifocus image fusion using the nonsubsampled contourlet transform,” Signal Process. 89(7), 1334–1346 (2009). [CrossRef]
• P. L. Lin and P. Y. Huang, “Fusion methods based on dynamic-segmented morphological wavelet or cut and paste for multifocus images,” Signal Process. 88(6), 1511–1527 (2008). [CrossRef]
• B. J. Chen, H. Z. Shu, H. Zhang, G. Chen, C. Toumoulin, J. L. Dillenseger, and L. M. Luo, “Quaternion Zernike moments and their invariants for color image analysis and object recognition,” Signal Process. 92(2), 308–318 (2012). [CrossRef]

Other

• S. Sangwine and N. L. Bihan, “Quaternion toolbox for Matlab,” http://qtfm.sourceforge.net
• H. Shi and M. Fang, “Multi-focus Color Image Fusion Based on SWT and IHS,” in Proceedings of IEEE Conference on Fuzzy Systems and Knowledge Discovery (IEEE2007), 461–465. [CrossRef]
• M. Douze, “Blur image data,” http://lear.inrialpes.fr/people/vandeweijer/data.html
• Helicon Soft, “Helicon Focus Sample images,” http://www.heliconsoft.com/focus_samples.html
• E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying, “The curvelet transform website,” http://www.curvelet.org

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