Abstract

Reconstruction of spectral images from camera responses is investigated using an edge preserving spatio-spectral Wiener estimation. A Wiener denoising filter and a spectral reconstruction Wiener filter are combined into a single spatio-spectral filter using local propagation of the noise covariance matrix. To preserve edges the local mean and covariance matrix of camera responses is estimated by bilateral weighting of neighboring pixels. We derive the edge-preserving spatio-spectral Wiener estimation by means of Bayesian inference and show that it fades into the standard Wiener reflectance estimation shifted by a constant reflectance in case of vanishing noise. Simulation experiments conducted on a six-channel camera system and on multispectral test images show the performance of the filter, especially for edge regions. A test implementation of the method is provided as a MATLAB script at the first author’s website.

© 2009 Optical Society of America

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References

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  1. CIE Publication No. 142, “Improvement to Industrial Colour Difference Evaluation” (CIE Central Bureau, Vienna, 2001).
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    [CrossRef]
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  9. V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, “Characterization of trichromatic color cameras by using a new multispectral imaging technique,” J. Opt. Soc. Am. A 22, 1231-1240 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
  16. G. Sharma, “Targetless scanner color calibration,” J. Imaging Sci. Technol. 44, 301-307 (2000).
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    [CrossRef]
  18. Y. Murakami, K. Fukura, M. Yamaguchi, and N. Ohyama, “Color reproduction from low-SNR multispectral images using spatio-spectral Wiener estimation,” Opt. Express 16, 4106-4120 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  21. H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the spectral reflectance of art paintings,” Appl. Opt. 39, 6621-6632 (2000).
    [CrossRef]
  22. N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
    [CrossRef] [PubMed]
  23. S. H. J. Brauers and T. Aach, “Multispectral imaging with flash light sources,” in CGIV, 4th European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2008), pp. 608-612.
  24. A. Mohammad-Djafari, “Bayesian inference for inverse problems in signal and image processing and applications,” Int. J. Imaging Syst. Technol. 16, 209-214 (2006).
    [CrossRef]
  25. C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color Images,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 1998), pp. 839-846.
  26. Y. Zhao, “Image segmentation and pigment mapping of cultural heritage based on spectral imaging,” Ph.D. thesis (Rochester Institute of Technology, Rochester, New York, 2008).
  27. J. Viggiano, “Minimal-knowledge assumptions in digital still camera characterization I.: Uniform distribution, Toeplitz correlation,” in Proceedings of the IS&T/SID 9th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2001), pp. 332-336.
  28. University of Joensuu Color Group, “Spectral database,” http://spectral.joensuu.fi (June 2009).
  29. M. D. Fairchild and G. M. Johnson, “METACOW: A public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 239-245.

2008 (2)

2007 (4)

2006 (3)

P. Morovic and G. D. Finlayson, “Metamer-set-based approach to estimating surface reflectance from camera RGB,” J. Opt. Soc. Am. A 23, 1814-1822 (2006).
[CrossRef]

N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

A. Mohammad-Djafari, “Bayesian inference for inverse problems in signal and image processing and applications,” Int. J. Imaging Syst. Technol. 16, 209-214 (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (1)

2000 (3)

G. Sharma, “Targetless scanner color calibration,” J. Imaging Sci. Technol. 44, 301-307 (2000).

G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333-348 (2000).
[CrossRef]

H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the spectral reflectance of art paintings,” Appl. Opt. 39, 6621-6632 (2000).
[CrossRef]

1986 (1)

Aach, T.

S. H. J. Brauers and T. Aach, “Multispectral imaging with flash light sources,” in CGIV, 4th European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2008), pp. 608-612.

Attewell, D.

D. Attewell and R. J. Baddeley, “The distribution of reflectances within the visual environment,” Vision Res. 47, 548-554 (2007).
[CrossRef] [PubMed]

Baddeley, R. J.

D. Attewell and R. J. Baddeley, “The distribution of reflectances within the visual environment,” Vision Res. 47, 548-554 (2007).
[CrossRef] [PubMed]

Berns, R.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 59-64.

Berns, R. S.

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Chiba University, 1999), pp. 42-49.

P. Urban, M. R. Rosen, and R. S. Berns, “A spatially adaptive wiener filter for reflectance estimation,” in Proceedings of the IS&T/SID 16th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2008), pp. 279-284.

Brauers, S. H. J.

S. H. J. Brauers and T. Aach, “Multispectral imaging with flash light sources,” in CGIV, 4th European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2008), pp. 608-612.

Cheung, V.

Connah, D.

DiCarlo, J. M.

Fairchild, M. D.

M. D. Fairchild and G. M. Johnson, “METACOW: A public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 239-245.

Finlayson, G. D.

Fukura, K.

Haneishi, H.

Hardeberg, J.

Hardeberg, J. Y.

J. Y. Hardeberg, “On the spectral dimensionality of object colours,” in CGIV, First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 480-485.

Hasegawa, T.

Healey, G.

Hosoi, A.

Ietomi, K.

Imai, F. H.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Chiba University, 1999), pp. 42-49.

Johnson, G. M.

M. D. Fairchild and G. M. Johnson, “METACOW: A public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 239-245.

Li, C.

V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, “Characterization of trichromatic color cameras by using a new multispectral imaging technique,” J. Opt. Soc. Am. A 22, 1231-1240 (2005).
[CrossRef]

C. Li and M. R. Luo, “The estimation of spectral reflectances using the smoothness constraint condition,” in Proceedings of the IS&T/SID 9th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2001), pp. 62-67.

C. Li and M. R. Luo, “A novel approach for generating object spectral reflectance functions from digital cameras,” in Proceedings of the IS&T/SID 13th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2005), pp. 99-103.

Luo, M. R.

C. Li and M. R. Luo, “A novel approach for generating object spectral reflectance functions from digital cameras,” in Proceedings of the IS&T/SID 13th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2005), pp. 99-103.

C. Li and M. R. Luo, “The estimation of spectral reflectances using the smoothness constraint condition,” in Proceedings of the IS&T/SID 9th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2001), pp. 62-67.

Maloney, L. T.

Manduchi, R.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color Images,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 1998), pp. 839-846.

Miyake, Y.

Mohammad-Djafari, A.

A. Mohammad-Djafari, “Bayesian inference for inverse problems in signal and image processing and applications,” Int. J. Imaging Syst. Technol. 16, 209-214 (2006).
[CrossRef]

Mohammadi, M.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 59-64.

Morovic, P.

Murakami, Y.

Nezamabadi, M.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 59-64.

Ohyama, N.

Rosen, M. R.

P. Urban, M. R. Rosen, and R. S. Berns, “A spatially adaptive wiener filter for reflectance estimation,” in Proceedings of the IS&T/SID 16th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2008), pp. 279-284.

Shao, S. J.

Sharma, G.

G. Sharma, “Targetless scanner color calibration,” J. Imaging Sci. Technol. 44, 301-307 (2000).

G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333-348 (2000).
[CrossRef]

Shen, H. L.

Shi, M.

Shimano, N.

N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

Taplin, L.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 59-64.

Tomasi, C.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color Images,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 1998), pp. 839-846.

Tsumura, N.

Urban, P.

P. Urban, M. R. Rosen, and R. S. Berns, “A spatially adaptive wiener filter for reflectance estimation,” in Proceedings of the IS&T/SID 16th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2008), pp. 279-284.

Viggiano, J.

J. Viggiano, “Minimal-knowledge assumptions in digital still camera characterization I.: Uniform distribution, Toeplitz correlation,” in Proceedings of the IS&T/SID 9th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2001), pp. 332-336.

Wandell, B. A.

Westland, S.

Xin, J. H.

Xu, H.

Yamaguchi, M.

Yokoyama, Y.

Zhang, X.

Zhao, Y.

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

Y. Zhao, “Image segmentation and pigment mapping of cultural heritage based on spectral imaging,” Ph.D. thesis (Rochester Institute of Technology, Rochester, New York, 2008).

Appl. Opt. (2)

Color Res. Appl. (2)

G. Sharma, “Set theoretic estimation for problems in subtractive color,” Color Res. Appl. 25, 333-348 (2000).
[CrossRef]

Y. Zhao and R. S. Berns, “Image-based spectral reflectance reconstruction using the matrix R method,” Color Res. Appl. 32, 343-351 (2007).
[CrossRef]

IEEE Trans. Image Process. (1)

N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006).
[CrossRef] [PubMed]

Int. J. Imaging Syst. Technol. (1)

A. Mohammad-Djafari, “Bayesian inference for inverse problems in signal and image processing and applications,” Int. J. Imaging Syst. Technol. 16, 209-214 (2006).
[CrossRef]

J. Imaging Sci. Technol. (1)

G. Sharma, “Targetless scanner color calibration,” J. Imaging Sci. Technol. 44, 301-307 (2000).

J. Opt. Soc. Am. A (6)

Opt. Express (2)

Vision Res. (1)

D. Attewell and R. J. Baddeley, “The distribution of reflectances within the visual environment,” Vision Res. 47, 548-554 (2007).
[CrossRef] [PubMed]

Other (13)

P. Urban, M. R. Rosen, and R. S. Berns, “A spatially adaptive wiener filter for reflectance estimation,” in Proceedings of the IS&T/SID 16th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2008), pp. 279-284.

C. Li and M. R. Luo, “The estimation of spectral reflectances using the smoothness constraint condition,” in Proceedings of the IS&T/SID 9th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2001), pp. 62-67.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “Spectral imaging target development based on hierarchical cluster analysis,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 59-64.

J. Y. Hardeberg, “On the spectral dimensionality of object colours,” in CGIV, First European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2002), pp. 480-485.

CIE Publication No. 142, “Improvement to Industrial Colour Difference Evaluation” (CIE Central Bureau, Vienna, 2001).

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Chiba University, 1999), pp. 42-49.

C. Li and M. R. Luo, “A novel approach for generating object spectral reflectance functions from digital cameras,” in Proceedings of the IS&T/SID 13th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2005), pp. 99-103.

C. Tomasi and R. Manduchi, “Bilateral filtering for gray and color Images,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 1998), pp. 839-846.

Y. Zhao, “Image segmentation and pigment mapping of cultural heritage based on spectral imaging,” Ph.D. thesis (Rochester Institute of Technology, Rochester, New York, 2008).

J. Viggiano, “Minimal-knowledge assumptions in digital still camera characterization I.: Uniform distribution, Toeplitz correlation,” in Proceedings of the IS&T/SID 9th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2001), pp. 332-336.

University of Joensuu Color Group, “Spectral database,” http://spectral.joensuu.fi (June 2009).

M. D. Fairchild and G. M. Johnson, “METACOW: A public-domain, high-resolution, fully-digital, noise-free, metameric, extended-dynamic-range, spectral test target for imaging system analysis and simulation,” in Proceedings of the IS&T/SID 12th Color Imaging Conference (Society for Imaging Science and Technology/Society for Information Display, 2004), pp. 239-245.

S. H. J. Brauers and T. Aach, “Multispectral imaging with flash light sources,” in CGIV, 4th European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2008), pp. 608-612.

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Figures (9)

Fig. 1
Fig. 1

Combining spatial and range weights into bilateral weights.

Fig. 2
Fig. 2

Spectral images selected from the Joensuu Spectral Image Database [28] and rendered for illuminant CIE D65. Left: fruitandflowers, right: young̱girl.

Fig. 3
Fig. 3

METACOW image [29]. Top, rendered for illuminant CIE D65; bottom, rendered for illuminant CIE A.

Fig. 4
Fig. 4

Spectral image consisting of two nested rectangles with different reflectances. The image is rendered for CIE D65.

Fig. 5
Fig. 5

Normalized spectral sensitivities of the modified Sinar-based six-channel camera.

Fig. 6
Fig. 6

Average spectral RMS errors for the investigated images. Top row, errors for acquisition illuminant CIE D65; bottom row, errors for CIE F11.

Fig. 7
Fig. 7

Spectral reconstruction results for image young̱girl rendered for illuminant CIE D65. Top row, reconstructions from noise-free image; middle row, reconstructions from an image with low SNR; bottom row, reconstruction from an image with very low SNR.

Fig. 8
Fig. 8

Spectral reconstruction results for a cutout of image METACOW rendered for illuminant CIED65. Top row; reconstructions from noise-free image; middle row, reconstructions from an image with low SNR; bottom row; reconstruction from an image with very low SNR. The specified mean RMS values correspond to the whole image.

Fig. 9
Fig. 9

Spectral reconstructions of the rectangle image from an image with very low SNR ( SNR = 15.6497 ) . The reconstructed spectral images are rendered for illuminant CIE D65.

Tables (2)

Tables Icon

Table 1 Method Parameters Used in Experiments

Tables Icon

Table 2 Colorimetric and Spectral RMS Results for Acquisition Illuminant CIE D65

Equations (27)

Equations on this page are rendered with MathJax. Learn more.

c = D L r + ϵ = Ω r + ϵ ,
ϵ = G ( Ω r ) ϵ 1 + ϵ 2 ,
G ( Ω r ) = G ( ( ω 1 , , ω n ) T r ) = [ g ( ω 1 T r ) 0 0 g ( ω n T r ) ]
W = K r Ω T ( Ω K r Ω T + K ϵ ) 1 ,
W = P K r ( I m 2 Ω ) T [ ( I m 2 Ω ) K r ( I m 2 Ω ) T + K ϵ ] 1 ,
K r = K x K r ,
R ( ρ ) = [ ρ 0 ρ 1 ρ m 1 ρ 1 ρ 0 ρ m 2 ρ m 1 ρ m 2 ρ 0 ] ,
c = c ́ + ϵ ,
p ( c | c ́ ) = N ( c ́ , K ϵ ) .
c ́ ( i , j ) = M ( i , j ) w ( i , j ) ,
w spatial [ ( k , l ) , ( i , j ) ] = exp [ ( i k ) 2 + ( j l ) 2 2 σ spatial 2 ] ,
w range [ ( k , l ) , ( i , j ) ] = exp [ c ( k , l ) c ( i , j ) 2 2 2 σ range 2 ] ,
w bilateral [ ( k , l ) , ( i , j ) ] = w spatial [ ( k , l ) , ( i , j ) ] w range [ ( k , l ) , ( i , j ) ] ( α , β ) C ( i , j ) w spatial [ ( α , β ) , ( i , j ) ] w range [ ( α , β ) , ( i , j ) ] .
( k , l ) C ( i , j ) : w ¯ ( k , l ) ( i , j ) = w bilateral [ ( k , l ) , ( i , j ) ] ,
c ¯ ( i , j ) = M ( i , j ) w ¯ ( i , j ) .
c ̌ ( k , l ) = w bilateral [ ( k , l ) , ( i , j ) ] c ( k , l ) .
c ¯ ( i , j ) = M ( i , j ) w ¯ ( i , j ) = ( k , l ) C ( i , j ) c ̌ ( k , l ) ,
K ( i , j ) = M ( i , j ) K w ( i , j ) M ( i , j ) T = C ̌ ( i , j ) C ̌ ( i , j ) T ,
p ( c ́ ( i , j ) ) = N ( c ¯ ( i , j ) , K ( i , j ) ) .
p ( c ́ ( i , j ) | c ( i , j ) ) = p ( c ́ ( i , j ) ) p ( c ( i , j ) | c ́ ( i , j ) ) p ( c ( i , j ) ) = N ( W d ( i , j ) [ c ( i , j ) c ¯ ( i , j ) ] + c ¯ ( i , j ) , K ( i , j ) W d ( i , j ) K ( i , j ) ) ,
W d ( i , j ) = K ( i , j ) [ K ( i , j ) + K ϵ ] 1
c ́ ( i , j ) = Ω r ( i , j ) + ϵ ̂ ,
p ( c ́ ( i , j ) | r ( i , j ) ) = N ( Ω r ( i , j ) , K ( i , j ) W ( i , j ) K ( i , j ) ) ,
p ( r ) = N ( μ r , K r ) .
p ( r ( i , j ) | c ́ ( i , j ) ) = p ( r ( i , j ) ) p ( c ́ ( i , j ) | r ( i , j ) ) p ( c ́ ( i , j ) ) = N ( W r ( i , j ) [ c ́ ( i , j ) Ω μ r ] + μ r , K r W r ( i , j ) Ω K r ) ,
W r ( i , j ) = K r Ω T [ Ω K r Ω T + K ( i , j ) W d ( i , j ) K ( i , j ) ] 1
r estimate ( i , j ) = W r ( i , j ) { W d ( i , j ) [ c ( i , j ) c ¯ ( i , j ) ] + c ¯ ( i , j ) Ω μ r } + μ r ,

Metrics