Abstract

This work explores the possibility of clustering spectral wavelengths based on the maximum dissimilarity of iris textures. The eventual goal is to determine how many bands of spectral wavelengths will be enough for iris multispectral fusion and to find these bands that will provide higher performance of iris multispectral recognition. A multispectral acquisition system was first designed for imaging the iris at narrow spectral bands in the range of 420 to 940 nm. Next, a set of 60 human iris images that correspond to the right and left eyes of 30 different subjects were acquired for an analysis. Finally, we determined that 3 clusters were enough to represent the 10 feature bands of spectral wavelengths using the agglomerative clustering based on two-dimensional principal component analysis. The experimental results suggest (1) the number, center, and composition of clusters of spectral wavelengths and (2) the higher performance of iris multispectral recognition based on a three wavelengths–bands fusion.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Grading of iris color with an extended photographic reference set,” J. Opt. 1, 36–40 (2008).
    [CrossRef]
  8. W. Zuo, D. Zhang, and K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition,” IEEE Trans. Syst. Man Cybern. B 36, 863–872(2006).
    [CrossRef]
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    [CrossRef]
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  17. S. Theodoridis and K. Koutroumbas, Pattern Recognition, 3rd ed. (Elsevier, 2006).
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  20. H. Chang, Y. Yao, A. Koschan, B. Abidi, and M. Abidi, “Spectral range selection for face recognition under various illuminations,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE, 2008), pp. 2756–2759.
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    [CrossRef]
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    [CrossRef]

2011

Z. Guo, D. Zhang, L. Zhang, W. Zuo, and G. Lu, “Empirical study of light source selection for palmprint recognition,” Pattern Recogn. Lett. 32, 120–126 (2011).
[CrossRef]

2009

M. J. Burge and M. K. Monaco, “Multispectral iris fusion for enhancement, interoperability, and cross wavelength matching,” Proc. SPIE 7334, 73341D (2009).
[CrossRef]

2008

L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Grading of iris color with an extended photographic reference set,” J. Opt. 1, 36–40 (2008).
[CrossRef]

M. Vatsa, R. Singh, and A. Noore, “Improving iris recognition performance using segmentation, quality enhancement, match score fusion and indexing,” Proc. IEEE Trans. Syst. Man Cybern. B 38, 1021–1035 (2008).
[CrossRef]

M. Vilaseca, R. Mercadal, J. Pujol, M. Arjona, M. de Lasarte, R. Huertas, M. Melgosa, and F. H. Imai, “Characterization of the human iris spectral reflectance with a multispectral imaging system,” Appl. Opt. 47, 5622–5630 (2008).
[CrossRef]

2007

Z. Liu, J.-Q. Yan, D. Zhang, and Q.-L. Li, “Automated tongue segmentation in hyperspectral images for medicine,” Appl. Opt. 46, 8328–8334 (2007).
[CrossRef]

J. Daugman, “New methods in iris recognition,” IEEE Trans. Syst. Man Cybern. B 37, 1167–1175 (IEEE, 2007).
[CrossRef]

J. Park and M. Kang, “Multispectral iris authentication system against counterfeit attack using gradient-based image fusion,” Opt. Eng. 46, 117003 (2007).
[CrossRef]

S. Ghosal and A. W. van der Vaart, “Posterior convergence rates of Dirichlet mixtures at smooth densities,” Ann. Stat. 35, 697–723 (2007).
[CrossRef]

2006

S. T. Tokdar, “Posterior consistency of Dirichlet location-scale mixture of normals in density estimation and regression,” Sankhya 68, 90–110 (2006).

W. Zuo, D. Zhang, and K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition,” IEEE Trans. Syst. Man Cybern. B 36, 863–872(2006).
[CrossRef]

B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson, “Band selection for hyperspectral image classification using mutual information,” IEEE Geosci. Remote Sens. Lett. 3, 522–526 (2006).
[CrossRef]

H. Wang and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Proc. 1, 109–121 (2006).
[CrossRef]

H. Wang, and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Process. 1, 109–121 (2006).
[CrossRef]

M. Vilaseca, J. Pujol, M. Arjona, and M. de Lasarte, “Multispectral system for reflectance reconstruction in the near infrared region,” Appl. Opt. 45, 4241–4253 (2006).
[CrossRef]

2001

S. Ghosal and A. W. van der Vaart, “Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities,” Ann. Stat. 29, 1233–1263 (2001).

1999

S. Ghosal, J. K. Ghosh, and R. V. Ramamoorthi, “Posterior consistency of Dirichlet mixtures in density estimation,” Ann. Stat. 27, 143–158 (1999).
[CrossRef]

1996

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

1994

1983

K. Ozawa, “CLASSIC: a hierarchical clustering algorithm based on asymmetric similarities,” Pattern Recogn. 16, 201–211 (1983).
[CrossRef]

Abidi, B.

H. Chang, Y. Yao, A. Koschan, B. Abidi, and M. Abidi, “Spectral range selection for face recognition under various illuminations,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE, 2008), pp. 2756–2759.

Abidi, M.

H. Chang, Y. Yao, A. Koschan, B. Abidi, and M. Abidi, “Spectral range selection for face recognition under various illuminations,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE, 2008), pp. 2756–2759.

Albert, D. M.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

Angelopoulou, E.

H. Wang and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Proc. 1, 109–121 (2006).
[CrossRef]

H. Wang, and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Process. 1, 109–121 (2006).
[CrossRef]

Arjona, M.

Beaver, B. M.

W. Mendenhall, R. J. Beaver, and B. M. Beaver, Probability and Statistics (Brooks/Cole, 2003).

Beaver, R. J.

W. Mendenhall, R. J. Beaver, and B. M. Beaver, Probability and Statistics (Brooks/Cole, 2003).

Boyce, C. K.

C. K. Boyce, “Multispectral iris recognition analysis: techniques and evaluation,” Master’s thesis (West Virginia University, 2006), pp. 101–102.

Burge, M. J.

M. J. Burge and M. K. Monaco, “Multispectral iris fusion for enhancement, interoperability, and cross wavelength matching,” Proc. SPIE 7334, 73341D (2009).
[CrossRef]

Chang, H.

H. Chang, Y. Yao, A. Koschan, B. Abidi, and M. Abidi, “Spectral range selection for face recognition under various illuminations,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE, 2008), pp. 2756–2759.

Comtet, L.

L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. (Reidel, 1974), pp. 176–177.

Coppens, J. E.

L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Grading of iris color with an extended photographic reference set,” J. Opt. 1, 36–40 (2008).
[CrossRef]

Cover, T.

T. Cover and J. Thomas, Elements of Information Theory(Wiley, 1991).

Damper, R. I.

B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson, “Band selection for hyperspectral image classification using mutual information,” IEEE Geosci. Remote Sens. Lett. 3, 522–526 (2006).
[CrossRef]

Daugman, J.

J. Daugman, “New methods in iris recognition,” IEEE Trans. Syst. Man Cybern. B 37, 1167–1175 (IEEE, 2007).
[CrossRef]

de Lasarte, M.

Everitt, B.

B. Everitt, S. Landau, and M. Leese, Cluster Analysis, 4th ed. (Edward Arnold, 2001).

Fisher, M. R.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

Franssen, L.

L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Grading of iris color with an extended photographic reference set,” J. Opt. 1, 36–40 (2008).
[CrossRef]

Ghosal, S.

S. Ghosal and A. W. van der Vaart, “Posterior convergence rates of Dirichlet mixtures at smooth densities,” Ann. Stat. 35, 697–723 (2007).
[CrossRef]

S. Ghosal and A. W. van der Vaart, “Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities,” Ann. Stat. 29, 1233–1263 (2001).

S. Ghosal, J. K. Ghosh, and R. V. Ramamoorthi, “Posterior consistency of Dirichlet mixtures in density estimation,” Ann. Stat. 27, 143–158 (1999).
[CrossRef]

Ghosh, J. K.

S. Ghosal, J. K. Ghosh, and R. V. Ramamoorthi, “Posterior consistency of Dirichlet mixtures in density estimation,” Ann. Stat. 27, 143–158 (1999).
[CrossRef]

Gunn, S. R.

B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson, “Band selection for hyperspectral image classification using mutual information,” IEEE Geosci. Remote Sens. Lett. 3, 522–526 (2006).
[CrossRef]

Guo, B.

B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson, “Band selection for hyperspectral image classification using mutual information,” IEEE Geosci. Remote Sens. Lett. 3, 522–526 (2006).
[CrossRef]

Guo, Z.

Z. Guo, D. Zhang, L. Zhang, W. Zuo, and G. Lu, “Empirical study of light source selection for palmprint recognition,” Pattern Recogn. Lett. 32, 120–126 (2011).
[CrossRef]

Z. Guo, L. Zhang, and D. Zhang, “Feature band selection for multispectral palmprint recognition,” in Proceedings of the 20th International Conference on Pattern Recognition (IEEE, 2010), pp. 1136–1139.

Hornak, L.

A. Ross, R. Pasula, and L. Hornak, “Exploring multispectral iris recognition beyond 900 nm,” in Proceedings of the IEEE Third International Conference on Biometrics: Theory, Applications, and Systems, 2009 (IEEE, 2009), pp. 1–8.

Huertas, R.

Imai, F. H.

Jain, A. K.

A. A. Ross, K. Nadakumar, and A. K. Jain, Handbook of Multibiometrics (Springer, 2006).

Johnson, D. H.

D. H. Johnson and S. Sinanović, “Symmetrizing the Kullback–Leibler distance,” in Proceedings of IEEE Transactions on Information Theory (IEEE, 2001), pp. 1–10.

Kang, M.

J. Park and M. Kang, “Multispectral iris authentication system against counterfeit attack using gradient-based image fusion,” Opt. Eng. 46, 117003 (2007).
[CrossRef]

Koschan, A.

H. Chang, Y. Yao, A. Koschan, B. Abidi, and M. Abidi, “Spectral range selection for face recognition under various illuminations,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE, 2008), pp. 2756–2759.

Koutroumbas, K.

S. Theodoridis and K. Koutroumbas, Pattern Recognition, 3rd ed. (Elsevier, 2006).

Landau, S.

B. Everitt, S. Landau, and M. Leese, Cluster Analysis, 4th ed. (Edward Arnold, 2001).

Leese, M.

B. Everitt, S. Landau, and M. Leese, Cluster Analysis, 4th ed. (Edward Arnold, 2001).

Li, Q.-L.

Liu, Z.

Lu, G.

Z. Guo, D. Zhang, L. Zhang, W. Zuo, and G. Lu, “Empirical study of light source selection for palmprint recognition,” Pattern Recogn. Lett. 32, 120–126 (2011).
[CrossRef]

Masek, L.

L. Masek, “Recognition of human iris patterns for biometric identification,” M.S. thesis (University of Western Australia, 2003).

Melgosa, M.

Mendenhall, W.

W. Mendenhall, R. J. Beaver, and B. M. Beaver, Probability and Statistics (Brooks/Cole, 2003).

Mercadal, R.

Monaco, M. K.

M. J. Burge and M. K. Monaco, “Multispectral iris fusion for enhancement, interoperability, and cross wavelength matching,” Proc. SPIE 7334, 73341D (2009).
[CrossRef]

Nadakumar, K.

A. A. Ross, K. Nadakumar, and A. K. Jain, Handbook of Multibiometrics (Springer, 2006).

Nelson, J. D. B.

B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson, “Band selection for hyperspectral image classification using mutual information,” IEEE Geosci. Remote Sens. Lett. 3, 522–526 (2006).
[CrossRef]

Noore, A.

M. Vatsa, R. Singh, and A. Noore, “Improving iris recognition performance using segmentation, quality enhancement, match score fusion and indexing,” Proc. IEEE Trans. Syst. Man Cybern. B 38, 1021–1035 (2008).
[CrossRef]

Ozawa, K.

K. Ozawa, “CLASSIC: a hierarchical clustering algorithm based on asymmetric similarities,” Pattern Recogn. 16, 201–211 (1983).
[CrossRef]

Park, J.

J. Park and M. Kang, “Multispectral iris authentication system against counterfeit attack using gradient-based image fusion,” Opt. Eng. 46, 117003 (2007).
[CrossRef]

Pasula, R.

A. Ross, R. Pasula, and L. Hornak, “Exploring multispectral iris recognition beyond 900 nm,” in Proceedings of the IEEE Third International Conference on Biometrics: Theory, Applications, and Systems, 2009 (IEEE, 2009), pp. 1–8.

Price, J. C.

Pujol, J.

Ramamoorthi, R. V.

S. Ghosal, J. K. Ghosh, and R. V. Ramamoorthi, “Posterior consistency of Dirichlet mixtures in density estimation,” Ann. Stat. 27, 143–158 (1999).
[CrossRef]

Robinson, N. L.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

Ross, A.

A. Ross, R. Pasula, and L. Hornak, “Exploring multispectral iris recognition beyond 900 nm,” in Proceedings of the IEEE Third International Conference on Biometrics: Theory, Applications, and Systems, 2009 (IEEE, 2009), pp. 1–8.

Ross, A. A.

A. A. Ross, K. Nadakumar, and A. K. Jain, Handbook of Multibiometrics (Springer, 2006).

Sinanovic, S.

D. H. Johnson and S. Sinanović, “Symmetrizing the Kullback–Leibler distance,” in Proceedings of IEEE Transactions on Information Theory (IEEE, 2001), pp. 1–10.

Singh, R.

M. Vatsa, R. Singh, and A. Noore, “Improving iris recognition performance using segmentation, quality enhancement, match score fusion and indexing,” Proc. IEEE Trans. Syst. Man Cybern. B 38, 1021–1035 (2008).
[CrossRef]

Syed, N. A.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

Theodoridis, S.

S. Theodoridis and K. Koutroumbas, Pattern Recognition, 3rd ed. (Elsevier, 2006).

Thomas, J.

T. Cover and J. Thomas, Elements of Information Theory(Wiley, 1991).

Tokdar, S. T.

S. T. Tokdar, “Posterior consistency of Dirichlet location-scale mixture of normals in density estimation and regression,” Sankhya 68, 90–110 (2006).

van den Berg, T. J. T. P.

L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Grading of iris color with an extended photographic reference set,” J. Opt. 1, 36–40 (2008).
[CrossRef]

van der Vaart, A. W.

S. Ghosal and A. W. van der Vaart, “Posterior convergence rates of Dirichlet mixtures at smooth densities,” Ann. Stat. 35, 697–723 (2007).
[CrossRef]

S. Ghosal and A. W. van der Vaart, “Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities,” Ann. Stat. 29, 1233–1263 (2001).

Vatsa, M.

M. Vatsa, R. Singh, and A. Noore, “Improving iris recognition performance using segmentation, quality enhancement, match score fusion and indexing,” Proc. IEEE Trans. Syst. Man Cybern. B 38, 1021–1035 (2008).
[CrossRef]

Vilaseca, M.

Wallow, I. H. L.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

Wang, H.

H. Wang, and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Process. 1, 109–121 (2006).
[CrossRef]

H. Wang and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Proc. 1, 109–121 (2006).
[CrossRef]

Wang, K.

W. Zuo, D. Zhang, and K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition,” IEEE Trans. Syst. Man Cybern. B 36, 863–872(2006).
[CrossRef]

Wilkerson, C. L.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

Yan, J.-Q.

Yao, Y.

H. Chang, Y. Yao, A. Koschan, B. Abidi, and M. Abidi, “Spectral range selection for face recognition under various illuminations,” in Proceedings of the 15th IEEE International Conference on Image Processing (IEEE, 2008), pp. 2756–2759.

Zhang, D.

Z. Guo, D. Zhang, L. Zhang, W. Zuo, and G. Lu, “Empirical study of light source selection for palmprint recognition,” Pattern Recogn. Lett. 32, 120–126 (2011).
[CrossRef]

Z. Liu, J.-Q. Yan, D. Zhang, and Q.-L. Li, “Automated tongue segmentation in hyperspectral images for medicine,” Appl. Opt. 46, 8328–8334 (2007).
[CrossRef]

W. Zuo, D. Zhang, and K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition,” IEEE Trans. Syst. Man Cybern. B 36, 863–872(2006).
[CrossRef]

Z. Guo, L. Zhang, and D. Zhang, “Feature band selection for multispectral palmprint recognition,” in Proceedings of the 20th International Conference on Pattern Recognition (IEEE, 2010), pp. 1136–1139.

Zhang, L.

Z. Guo, D. Zhang, L. Zhang, W. Zuo, and G. Lu, “Empirical study of light source selection for palmprint recognition,” Pattern Recogn. Lett. 32, 120–126 (2011).
[CrossRef]

Z. Guo, L. Zhang, and D. Zhang, “Feature band selection for multispectral palmprint recognition,” in Proceedings of the 20th International Conference on Pattern Recognition (IEEE, 2010), pp. 1136–1139.

Zuo, W.

Z. Guo, D. Zhang, L. Zhang, W. Zuo, and G. Lu, “Empirical study of light source selection for palmprint recognition,” Pattern Recogn. Lett. 32, 120–126 (2011).
[CrossRef]

W. Zuo, D. Zhang, and K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition,” IEEE Trans. Syst. Man Cybern. B 36, 863–872(2006).
[CrossRef]

Ann. Stat.

S. Ghosal, J. K. Ghosh, and R. V. Ramamoorthi, “Posterior consistency of Dirichlet mixtures in density estimation,” Ann. Stat. 27, 143–158 (1999).
[CrossRef]

S. Ghosal and A. W. van der Vaart, “Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities,” Ann. Stat. 29, 1233–1263 (2001).

S. Ghosal and A. W. van der Vaart, “Posterior convergence rates of Dirichlet mixtures at smooth densities,” Ann. Stat. 35, 697–723 (2007).
[CrossRef]

Appl. Opt.

Arch. Ophthalmol.

C. L. Wilkerson, N. A. Syed, M. R. Fisher, N. L. Robinson, I. H. L. Wallow, and D. M. Albert, “Melanocytes and iris color: light-microscopic findings,” Arch. Ophthalmol. 114, 437–442 (1996).
[CrossRef]

IEEE Geosci. Remote Sens. Lett.

B. Guo, S. R. Gunn, R. I. Damper, and J. D. B. Nelson, “Band selection for hyperspectral image classification using mutual information,” IEEE Geosci. Remote Sens. Lett. 3, 522–526 (2006).
[CrossRef]

IEEE Trans. Syst. Man Cybern. B

W. Zuo, D. Zhang, and K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition,” IEEE Trans. Syst. Man Cybern. B 36, 863–872(2006).
[CrossRef]

J. Daugman, “New methods in iris recognition,” IEEE Trans. Syst. Man Cybern. B 37, 1167–1175 (IEEE, 2007).
[CrossRef]

J. Opt.

L. Franssen, J. E. Coppens, and T. J. T. P. van den Berg, “Grading of iris color with an extended photographic reference set,” J. Opt. 1, 36–40 (2008).
[CrossRef]

J. Real-Time Image Proc.

H. Wang and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Proc. 1, 109–121 (2006).
[CrossRef]

J. Real-Time Image Process.

H. Wang, and E. Angelopoulou, “Sensor band selection for multispectral imaging via average normalized information,” J. Real-Time Image Process. 1, 109–121 (2006).
[CrossRef]

Opt. Eng.

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Figures (9)

Fig. 1.
Fig. 1.

Structure of the multispectral iris acquisition system.

Fig. 2.
Fig. 2.

Sample images obtained at wavelengths of a. 420 nm, b. 490 nm, c. 545 nm, d. 590 nm, e. 635 nm, f. 665 nm, g. 700 nm, h. 730 nm, i. 780 nm, j. 810 nm, k. 850 nm, and l. 940 nm.

Fig. 3.
Fig. 3.

Structure of the image-indexed dissimilarity matrix A.

Fig. 4.
Fig. 4.

Two types of principle components generated from specified and joint eigenstructures and the correspondence with the dissimilarity data of matrix A.

Fig. 5.
Fig. 5.

Diagram of agglomerative clustering.

Fig. 6.
Fig. 6.

Diagram of the proposed method.

Fig. 7.
Fig. 7.

Image-indexed dissimilarity matrix A.

Fig. 8.
Fig. 8.

Dendrogram from the clustering hierarchy.

Fig. 9.
Fig. 9.

Wavelength versus EER.

Tables (2)

Tables Icon

Table 1. Clustering Result of Three Clusters

Tables Icon

Table 2. Fusion Result for Different Numbers of Wavelength Clusters

Equations (20)

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A(i,j)=d(Ti,Tj),i,j=1,,N,N=S×B.
G1b+b=12Ss=12S(Xsb+bX¯b+b)T(Xsb+bX¯b+b),G2b+b=12Ss=12S(Xsb+bX¯b+b)(Xsb+bX¯b+b)T,
X¯b+b=12Ss=12SXsb+b.
jc=1k1b+bλ1jcb+b/jc=1Icλ1jcb+bCu,
jr=1k2b+bλ2jrb+b/jr=1Irλ2jrb+bCu,
db+b=T^bT^b=V2b+bTTbV1b+bV2b+bTTbV1b+b.
G1b=1Ss=1S(XsbX¯b)T(XsbX¯b),G2b=1Ss=1S(XsbX¯b)(XsbX¯b)T,
DKL(PQ)=iP(i)lnP(i)Q(i).
DKL(P,Q)=12[DKL(PQ)+DKL(QP)].
dseg(pi,pj)=exp(-DKL(pi,pj)),dseg(pi,pj)(0,1].
As(i,j)=dseg(pi,pj),i,j=1,,K.
dcross(b,b)=p=1Sq=1db+b(Xpb,Xqb),
dave(b)=1N1n=1N1dcross(b,n).
C={i|argmindave(i)},i=1,2,,N.
|AB|=|A|+|B|-|AB|,
|i=1nAi|=i=1n|Ai|i,j:1ijn|AiAj|+i,j,k:1ijkn|AiAjAk|+(1)n1|A1An|.
HDraw,t(A,B)=(codeA,icodeB,i)maskA,imaskB,imaskA,imaskB,i.
HDsum(1,2)(A,B)=HDraw,1(A,B)+HDraw,2(A,B)HDraw,1(A,B)+HDraw,2(A,B)2×P1,2(A,B),
P1,2(A,B)=1((codeA,1codeA,2)maskA,1maskA,2maskA,1maskA,2+(codeB,1codeB,2)maskB,1maskB,2maskB,1maskB,2)×12,
HDsum(1,2,3)(A,B)=HDraw,1(A,B)+HDraw,2(A,B)+HDraw,3(A,B)HDraw,1(A,B)+HDraw,2(A,B)2×P1,2(A,B)HDraw,1(A,B)+HDraw,3(A,B)2×P1,3(A,B)HDraw,2(A,B)+HDraw,3(A,B)2×P2,3(A,B)HDraw,1(A,B)+HDraw,2(A,B)+HDraw,3(A,B)2×P1,2,3(A,B).

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