Abstract

This paper introduces a new approach in narrow-band imaging (NBI). Existing NBI techniques generate images by selecting discrete bands over the full visible spectrum or an even wider spectral range. In contrast, here we perform the sampling with filters covering a tight spectral window. This image acquisition method, named narrow spectral imaging, can be particularly useful when optical information is only available within a narrow spectral window, such as in the case of deep-water transmittance, which constitutes the principal motivation of this work. In this study we demonstrate the potential of the proposed photographic technique on nonunderwater scenes recorded under controlled conditions. To this end three multilayer narrow bandpass filters were employed, which transmit at 440, 456, and 470 nm bluish wavelengths, respectively. Since the differences among the images captured in such a narrow spectral window can be extremely small, both image acquisition and visualization require a novel approach. First, high-bit-depth images were acquired with multilayer narrow-band filters either placed in front of the illumination or mounted on the camera lens. Second, a color-mapping method is proposed, using which the input data can be transformed onto the entire display color gamut with a continuous and perceptually nearly uniform mapping, while ensuring optimally high information content for human perception.

© 2013 Optical Society of America

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2011

Z. Mahmood and P. Scheunders, “Enhanced visualization of hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 8, 869–873 (2011).
[CrossRef]

2010

J. Rigau, M. Feixas, and M. Sbert, “Image information in digital photography,” Lect. Notes Comput. Sci. 6469, 122–131 (2010).
[CrossRef]

D. Pál, B. Poczos, and C. Szepesvari, “Estimation of Renyi entropy and mutual information based on generalized nearest-neighbor graphs,” Adv. Neural Inform. Process. Syst. 23, 1849–1857 (2010).

2009

M. Cui, A. Razdan, J. Hu, and P. Wonka, “Interactive hyperspectral image visualization using convex optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1673–1684 (2009).
[CrossRef]

2008

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

2007

K. Hoshino, F. Nielsen, and T. Nishimura, “Noise reduction in CMOS image sensors for high quality imaging: the autocorrelation function filter on burst image sequences,” ICGST-GVIP J. 7(3), 17–24 (2007).

2006

V. Tsagaris and V. Anastassopoulos, “Global measure for assessing image fusion methods,” Opt. Eng. 45, 026201 (2006).
[CrossRef]

K. Kuznetsov, R. Lambert, and J.-F. Rey, “Narrow-band imaging: potential and limitations,” Endoscopy 38, 76–81 (2006).
[CrossRef]

J. Wang and I. C. Chein, “Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis,” IEEE Trans. Geosci. Remote Sens. 44, 1586–1600 (2006).
[CrossRef]

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

2004

P. M. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng. 61, 67–81 (2004).
[CrossRef]

2003

J. S. Tyo, A. Konsolakis, D. I. Diersen, and R. C. Olsen, “Principal-components-based display strategy for spectral imagery,” IEEE Trans. Geosci. Remote Sens. 41, 708–718 (2003).
[CrossRef]

2002

J. Morovic, J. Shaw, and P. Sun, “A fast, non-iterative, and exact histogram matching algorithm,” Pattern Recogn. Lett. 23, 127–135 (2002).
[CrossRef]

1998

1990

W. Li, “Mutual information functions versus correlation functions,” J. Stat. Phys. 60, 823–837 (1990).
[CrossRef]

1960

S. Watanabe, “Information theoretical analysis of multivariate correlation,” IBM J. Res. Dev. 4, 66–82 (1960).
[CrossRef]

1954

W. J. McGill, “Multivariate information transmission,” Psychometrika 19, 97–116 (1954).

Anastassopoulos, V.

V. Tsagaris and V. Anastassopoulos, “Global measure for assessing image fusion methods,” Opt. Eng. 45, 026201 (2006).
[CrossRef]

Anderson, R. B.

J. F. Bell, R. B. Anderson, K. Kressler, M. J. Wolff, and B. Cantor, “Color mosaics and multispectral analyses of Mars reconnaissance orbit mars color imager (MARCI) observations,” in Proceedings of American Geophysical Union (AGU) Fall Meeting Abstracts (2008), paper P32B-08.

Bell, A. J.

A. J. Bell, “The co-information lattice,” in Proceedings of 4th International Symposium on Independent Component Analysis and Blind Source Separation (Springer-Verlag, 2003), pp. 921–926.

Bell, J. F.

J. F. Bell, R. B. Anderson, K. Kressler, M. J. Wolff, and B. Cantor, “Color mosaics and multispectral analyses of Mars reconnaissance orbit mars color imager (MARCI) observations,” in Proceedings of American Geophysical Union (AGU) Fall Meeting Abstracts (2008), paper P32B-08.

Cantor, B.

J. F. Bell, R. B. Anderson, K. Kressler, M. J. Wolff, and B. Cantor, “Color mosaics and multispectral analyses of Mars reconnaissance orbit mars color imager (MARCI) observations,” in Proceedings of American Geophysical Union (AGU) Fall Meeting Abstracts (2008), paper P32B-08.

Chan, D. E.

P. M. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng. 61, 67–81 (2004).
[CrossRef]

Chein, I. C.

J. Wang and I. C. Chein, “Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis,” IEEE Trans. Geosci. Remote Sens. 44, 1586–1600 (2006).
[CrossRef]

Chen, H.

Y. Zhu, P. K. Varshney, and H. Chen, “Evaluation of ICA based fusion of hyperspectral images for color display,” in Proceedings of 10th International Conference on Information Fusion (IEEE, 2007), pp. 1–7.

Chen, Y.-R.

P. M. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng. 61, 67–81 (2004).
[CrossRef]

Chiao, C. C.

Cover, T. M.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, 2006).

Cronin, T. W.

Cui, G.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

Cui, M.

M. Cui, A. Razdan, J. Hu, and P. Wonka, “Interactive hyperspectral image visualization using convex optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1673–1684 (2009).
[CrossRef]

Debevec, P.

P. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in ACM Computer Graphics, Proceedings of SIGGRAPH (ACM, 1997), pp. 369–378.

Dera, J.

B. Wozniak and J. Dera, Light Absorption in Sea Water (Springer, 2007).

Diersen, D. I.

J. S. Tyo, A. Konsolakis, D. I. Diersen, and R. C. Olsen, “Principal-components-based display strategy for spectral imagery,” IEEE Trans. Geosci. Remote Sens. 41, 708–718 (2003).
[CrossRef]

Ebert, M.-O.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Feixas, M.

J. Rigau, M. Feixas, and M. Sbert, “Image information in digital photography,” Lect. Notes Comput. Sci. 6469, 122–131 (2010).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2006).

Hoshino, K.

K. Hoshino, F. Nielsen, and T. Nishimura, “Noise reduction in CMOS image sensors for high quality imaging: the autocorrelation function filter on burst image sequences,” ICGST-GVIP J. 7(3), 17–24 (2007).

Hu, J.

M. Cui, A. Razdan, J. Hu, and P. Wonka, “Interactive hyperspectral image visualization using convex optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1673–1684 (2009).
[CrossRef]

Hunt, R. W. G.

R. W. G. Hunt, Measuring Colour, 3rd ed. (Fountain, 2001).

Jockusch, S.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Kim, M. S.

P. M. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng. 61, 67–81 (2004).
[CrossRef]

Konsolakis, A.

J. S. Tyo, A. Konsolakis, D. I. Diersen, and R. C. Olsen, “Principal-components-based display strategy for spectral imagery,” IEEE Trans. Geosci. Remote Sens. 41, 708–718 (2003).
[CrossRef]

Kräutler, B.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Kressler, K.

J. F. Bell, R. B. Anderson, K. Kressler, M. J. Wolff, and B. Cantor, “Color mosaics and multispectral analyses of Mars reconnaissance orbit mars color imager (MARCI) observations,” in Proceedings of American Geophysical Union (AGU) Fall Meeting Abstracts (2008), paper P32B-08.

Kuznetsov, K.

K. Kuznetsov, R. Lambert, and J.-F. Rey, “Narrow-band imaging: potential and limitations,” Endoscopy 38, 76–81 (2006).
[CrossRef]

Lambert, R.

K. Kuznetsov, R. Lambert, and J.-F. Rey, “Narrow-band imaging: potential and limitations,” Endoscopy 38, 76–81 (2006).
[CrossRef]

Li, C.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

Li, W.

W. Li, “Mutual information functions versus correlation functions,” J. Stat. Phys. 60, 823–837 (1990).
[CrossRef]

Luo, M. R.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

Mahmood, Z.

Z. Mahmood and P. Scheunders, “Enhanced visualization of hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 8, 869–873 (2011).
[CrossRef]

Malik, J.

P. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” in ACM Computer Graphics, Proceedings of SIGGRAPH (ACM, 1997), pp. 369–378.

Matkovic, K.

K. Matkovic, A. Neumann, L. Neumann, T. Psik, and W. Purgathofer, “Global contrast factor—a new approach to image contrast,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, L. Neumann, M. Sbert, B. Gooch, and W. Purgathofer, eds. (Eurographics Book Series, 2005), pp. 159–167.

McGill, W. J.

W. J. McGill, “Multivariate information transmission,” Psychometrika 19, 97–116 (1954).

Mehl, P. M.

P. M. Mehl, Y.-R. Chen, M. S. Kim, and D. E. Chan, “Development of hyperspectral imaging technique for the detection of apple surface defects and contaminations,” J. Food Eng. 61, 67–81 (2004).
[CrossRef]

Morovic, J.

J. Morovic, J. Shaw, and P. Sun, “A fast, non-iterative, and exact histogram matching algorithm,” Pattern Recogn. Lett. 23, 127–135 (2002).
[CrossRef]

Moser, S.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Müller, T.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Neumann, A.

K. Matkovic, A. Neumann, L. Neumann, T. Psik, and W. Purgathofer, “Global contrast factor—a new approach to image contrast,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, L. Neumann, M. Sbert, B. Gooch, and W. Purgathofer, eds. (Eurographics Book Series, 2005), pp. 159–167.

L. Neumann and A. Neumann, “Color style transfer techniques using hue, lightness and saturation histogram matching,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging (Springer-Verlag, 2005), pp. 111–122.

Neumann, L.

L. Neumann and A. Neumann, “Color style transfer techniques using hue, lightness and saturation histogram matching,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging (Springer-Verlag, 2005), pp. 111–122.

K. Matkovic, A. Neumann, L. Neumann, T. Psik, and W. Purgathofer, “Global contrast factor—a new approach to image contrast,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, L. Neumann, M. Sbert, B. Gooch, and W. Purgathofer, eds. (Eurographics Book Series, 2005), pp. 159–167.

Nielsen, F.

K. Hoshino, F. Nielsen, and T. Nishimura, “Noise reduction in CMOS image sensors for high quality imaging: the autocorrelation function filter on burst image sequences,” ICGST-GVIP J. 7(3), 17–24 (2007).

Nishimura, T.

K. Hoshino, F. Nielsen, and T. Nishimura, “Noise reduction in CMOS image sensors for high quality imaging: the autocorrelation function filter on burst image sequences,” ICGST-GVIP J. 7(3), 17–24 (2007).

Olsen, R. C.

J. S. Tyo, A. Konsolakis, D. I. Diersen, and R. C. Olsen, “Principal-components-based display strategy for spectral imagery,” IEEE Trans. Geosci. Remote Sens. 41, 708–718 (2003).
[CrossRef]

Pál, D.

D. Pál, B. Poczos, and C. Szepesvari, “Estimation of Renyi entropy and mutual information based on generalized nearest-neighbor graphs,” Adv. Neural Inform. Process. Syst. 23, 1849–1857 (2010).

Poczos, B.

D. Pál, B. Poczos, and C. Szepesvari, “Estimation of Renyi entropy and mutual information based on generalized nearest-neighbor graphs,” Adv. Neural Inform. Process. Syst. 23, 1849–1857 (2010).

Psik, T.

K. Matkovic, A. Neumann, L. Neumann, T. Psik, and W. Purgathofer, “Global contrast factor—a new approach to image contrast,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, L. Neumann, M. Sbert, B. Gooch, and W. Purgathofer, eds. (Eurographics Book Series, 2005), pp. 159–167.

Purgathofer, W.

K. Matkovic, A. Neumann, L. Neumann, T. Psik, and W. Purgathofer, “Global contrast factor—a new approach to image contrast,” in First Eurographics Workshop on Computational Aesthetics in Graphics, Visualization and Imaging, L. Neumann, M. Sbert, B. Gooch, and W. Purgathofer, eds. (Eurographics Book Series, 2005), pp. 159–167.

Rancourt, J. D.

J. D. Rancourt, Optical Thin Films: User Handbook (SPIE, 1996).

Razdan, A.

M. Cui, A. Razdan, J. Hu, and P. Wonka, “Interactive hyperspectral image visualization using convex optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1673–1684 (2009).
[CrossRef]

Rey, J.-F.

K. Kuznetsov, R. Lambert, and J.-F. Rey, “Narrow-band imaging: potential and limitations,” Endoscopy 38, 76–81 (2006).
[CrossRef]

Rigau, J.

J. Rigau, M. Feixas, and M. Sbert, “Image information in digital photography,” Lect. Notes Comput. Sci. 6469, 122–131 (2010).
[CrossRef]

Ruderman, D. L.

Sbert, M.

J. Rigau, M. Feixas, and M. Sbert, “Image information in digital photography,” Lect. Notes Comput. Sci. 6469, 122–131 (2010).
[CrossRef]

Scheunders, P.

Z. Mahmood and P. Scheunders, “Enhanced visualization of hyperspectral images,” IEEE Geosci. Remote Sens. Lett. 8, 869–873 (2011).
[CrossRef]

Shaw, J.

J. Morovic, J. Shaw, and P. Sun, “A fast, non-iterative, and exact histogram matching algorithm,” Pattern Recogn. Lett. 23, 127–135 (2002).
[CrossRef]

Sun, P.

J. Morovic, J. Shaw, and P. Sun, “A fast, non-iterative, and exact histogram matching algorithm,” Pattern Recogn. Lett. 23, 127–135 (2002).
[CrossRef]

Szepesvari, C.

D. Pál, B. Poczos, and C. Szepesvari, “Estimation of Renyi entropy and mutual information based on generalized nearest-neighbor graphs,” Adv. Neural Inform. Process. Syst. 23, 1849–1857 (2010).

Thomas, J. A.

T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley-Interscience, 2006).

Tsagaris, V.

V. Tsagaris and V. Anastassopoulos, “Global measure for assessing image fusion methods,” Opt. Eng. 45, 026201 (2006).
[CrossRef]

Turro, N. J.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Tyo, J. S.

J. S. Tyo, A. Konsolakis, D. I. Diersen, and R. C. Olsen, “Principal-components-based display strategy for spectral imagery,” IEEE Trans. Geosci. Remote Sens. 41, 708–718 (2003).
[CrossRef]

van de Cruys, T. V.

T. V. van de Cruys, “Two multivariate generalizations of pointwise mutual information,” presented at DiSCO 2011: Workshop on Distributional Semantics and Compositionality (DiSCo at ACL-HLT 2011), Portland, Oregon, June 24, 2011.

Varshney, P. K.

Y. Zhu, P. K. Varshney, and H. Chen, “Evaluation of ICA based fusion of hyperspectral images for color display,” in Proceedings of 10th International Conference on Information Fusion (IEEE, 2007), pp. 1–7.

Wang, J.

J. Wang and I. C. Chein, “Independent component analysis-based dimensionality reduction with applications in hyperspectral image analysis,” IEEE Trans. Geosci. Remote Sens. 44, 1586–1600 (2006).
[CrossRef]

Watanabe, S.

S. Watanabe, “Information theoretical analysis of multivariate correlation,” IBM J. Res. Dev. 4, 66–82 (1960).
[CrossRef]

Wolff, M. J.

J. F. Bell, R. B. Anderson, K. Kressler, M. J. Wolff, and B. Cantor, “Color mosaics and multispectral analyses of Mars reconnaissance orbit mars color imager (MARCI) observations,” in Proceedings of American Geophysical Union (AGU) Fall Meeting Abstracts (2008), paper P32B-08.

Wonka, P.

M. Cui, A. Razdan, J. Hu, and P. Wonka, “Interactive hyperspectral image visualization using convex optimization,” IEEE Trans. Geosci. Remote Sens. 47, 1673–1684 (2009).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2006).

Wozniak, B.

B. Wozniak and J. Dera, Light Absorption in Sea Water (Springer, 2007).

Yeung, R. W.

R. W. Yeung, Information Theory and Network Coding (Springer, 2008).

Zhu, Y.

Y. Zhu, P. K. Varshney, and H. Chen, “Evaluation of ICA based fusion of hyperspectral images for color display,” in Proceedings of 10th International Conference on Information Fusion (IEEE, 2007), pp. 1–7.

Adv. Neural Inform. Process. Syst.

D. Pál, B. Poczos, and C. Szepesvari, “Estimation of Renyi entropy and mutual information based on generalized nearest-neighbor graphs,” Adv. Neural Inform. Process. Syst. 23, 1849–1857 (2010).

Angew. Chem. Int. Ed. Engl., Suppl.

S. Moser, T. Müller, M.-O. Ebert, S. Jockusch, N. J. Turro, and B. Kräutler, “Blue luminescence of ripening bananas,” Angew. Chem. Int. Ed. Engl., Suppl. 47, 8954–8957 (2008).
[CrossRef]

Color Res. Appl.

M. R. Luo, G. Cui, and C. Li, “Uniform colour spaces based on CIECAM02 colour appearance model,” Color Res. Appl. 31, 320–330 (2006).
[CrossRef]

Endoscopy

K. Kuznetsov, R. Lambert, and J.-F. Rey, “Narrow-band imaging: potential and limitations,” Endoscopy 38, 76–81 (2006).
[CrossRef]

IBM J. Res. Dev.

S. Watanabe, “Information theoretical analysis of multivariate correlation,” IBM J. Res. Dev. 4, 66–82 (1960).
[CrossRef]

ICGST-GVIP J.

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Figures (9)

Fig. 1.
Fig. 1.

(A) Absorption coefficient of clean waters in the Sargasso Sea versus wavelength. The measured data was extracted from Wozniak and Dera [5]. (B) Calculated relative transmittance in Sargasso Sea with respect to the peak transmittance near 500 nm at various distances from 1 to 200 m traversed by the light in the medium.

Fig. 2.
Fig. 2.

(A) Spectral transmittance of the applied three narrow-band filters with central wavelengths 440, 456, and 470 nm, respectively. (B)–(D) Still-life composition of fruits as seen through the narrow-band filters at 440, 456, and 470 nm, respectively.

Fig. 3.
Fig. 3.

Venn diagram of (A) two random variables X1 and X2 and (B) three random variables L, u, v, demonstrating the relation among applicable entropy, joint entropy, conditional entropy, mutual information, and conditional mutual information measures.

Fig. 4.
Fig. 4.

Boundary of the AdobeRGB gamut within CIELuv color space at L=50, displayed at the uv plane. The red dots show the loci of the red, green, and blue primaries. Note that the blue primary cannot be realized at this luminance level, so it falls outside the boundary.

Fig. 5.
Fig. 5.

Image of a still-life composition of fruits: (A) naked-eye image (visible spectrum); narrow spectral data, (B) standard RGB false colorized, and (C) color mapped by the proposed algorithm. Pixels that either were overexposed in any of the source images or belonged to areas that did not remain static during the exposure sequence (leaves) were excluded from the color-mapping process and therefore rendered gray by setting their CIELuv u and v coordinates to zero.

Fig. 6.
Fig. 6.

Same as Fig. 5, for image of a piece of petrified tree trunk.

Fig. 7.
Fig. 7.

Image of a simulated document forgery: (A) naked-eye image (visible spectrum) and (B) narrow spectral data color mapped by the proposed algorithm.

Fig. 8.
Fig. 8.

Image of the Sun courtesy of NASA SDO in the UV range, recorded in narrow bands at 171, 193, and 211 nm central wavelengths, respectively. (A) Standard RGB false colorized and (B) color mapped by the proposed algorithm.

Fig. 9.
Fig. 9.

Image of an underwater scene in coastal waters along Costa Brava, Spain. (A) Naked-eye image and (B) Bayer-filtered RGB channels color mapped by the proposed algorithm.

Tables (1)

Tables Icon

Table 1. Values of TUI T and Tchrom and of Average Local Neighbor Color Differences E and Echrom (See Definitions in Section 2.C) for Various Input Data and Display Methodsa

Equations (20)

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P1*=mm1P1,P2*=mm2P2,P3*=mm3P3,
Y=l1P1*+l2P2*+l3P3*L=L(Y),according toXYZLuvformula,u=cu1P1N+cu2P2N+cu3P3N,v=cv1P1N+cv2P2N+cv3P3N.
r(L,u)=E(Lu)E(L)E(u)σLσu=E(Lu)σLσu=0,r(L,v)=E(Lv)E(L)E(v)σLσv=E(Lv)σLσv=0,r(u,v)=E(uv)E(u)E(v)σuσv=E(uv)σuσv=0,
Acu1+Bcu2+Ccu3=0,cu1+cu2+cu3=1,Acv1+Bcv2+Ccv3=0,cv1+cv2+cv3=1.
cu1=α1cu3+β1,cu2=α2cu3+β2,cv1=α1cv3+β1,cv2=α2cv3+β2,whereα1=B1AB,β1=BAB,α2=A1AB,β2=AAB,
cu1cv1+cu2cv2+cu3cv3+H(cu1cv2+cu2cv1)+I(cu1cv3+cu3cv1)+J(cu2cv3+cu3cv2)=0,
H=i=1KP1N(i)P2N(i);I=i=1KP1N(i)P3N(i);J=i=1KP2N(i)P3N(i).
T+Ucu3+Ucv3+Vcv3cu3=0,whereT=β12+β22+2Hβ1β2,U=(H+1)(α1β2+α2β1)+Iβ1+Jβ2,V=1+α12+α22+2Hα1α2+2Iα1+2Jα2.
cv3=T+Ucu3U+Vcu3.
H(X)=xχp(x)logp(x).
H(X1,X2)=x1χ1x2χ2p(x1,x2)logp(x1,x2),
H(X1|X2)=x2χ2p(x2)x1χ1p(x1|x2)logp(x1|x2),
I(X1,X2)=x1χ1x2χ2p(x1,x2)logp(x1,x2)p(x1)p(x2).
T(L,u,v)=H(L|u,v)+H(u|L,v)+H(v|L,u)=H(L,u,v)(I(L,u,v)+I(L,u|v)+I(L,v|u)+I(u,v|L)),
T(L,u,v)=3·H(L,u,v)(H(L,u)+H(L,v)+H(u,v)).
(uFi*(φ,t)vFi*(φ,t))=C*·DG(L,h)·(uRM[Fi](φ,t)vRM[Fi](φ,t)),where(uRM[Fi](φ,t)vRM[Fi](φ,t))=R(φ)M(t)(uFivFi).
(Ffinφfintfin)=argmaxFfin{F1FZc}φfin[0,2π]tfin{1,1}T(L,uFfin*(φfin,tfin),vFfin*(φfin,tfin)).
TChrom(L,u,v)=H(u|L,v)+H(v|L,u)=2·H(L,u,v)(H(L,u)+H(L,v)).
E=1KR(i=1XR1j=1YR(Li+1,jLi,j)2+(ui+1,jui,j)2+(vi+1,jvi,j)2+i=1XRj=1YR1(Li,j+1Li,j)2+(ui,j+1ui,j)2+(vi,j+1vi,j)2),
Echrom=1KR(i=1XR1j=1YR(ui+1,jui,j)2+(vi+1,jvi,j)2+i=1XRj=1YR1(ui,j+1ui,j)2+(vi,j+1vi,j)2),

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