Abstract

In multispectral imaging system, one of the most important tasks is to accurately reconstruct the spectral reflectance from system responses. We propose such a new method by combing three most frequently used techniques, i.e., wiener estimation, pseudo-inverse, and finite-dimensional modeling. The weightings of these techniques are calculated by minimizing the combined standard deviation of both spectral errors and colorimetric errors. Experimental results show that, in terms of color difference error, the performance of the proposed method is better than those of the three techniques. It is found that the simple averaging of the reflectance estimates of these three techniques can also yield good color accuracy.

© 2007 Optical Society of America

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References

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  1. J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Superieure des Telecommunications, 1999).
  2. H. L. Shen and J. H. Xin, “Spectral characterization of a color scanner by adaptive estimation,” J. Opt. Soc. Am. A 21, 1125–1130 (2004).
    [Crossref]
  3. 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]
  4. 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]
  5. M. Shi and G. Healey, “Using reflectance models for color scanner calibration,” J. Opt. Soc. Am. A 19, 645–656 (2002).
    [Crossref]
  6. F. H. Imai and R. S. Berns, “Spectral estimation using trichromaitc digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999).
  7. M. Soriano, W. Oblefias, and C. Saloma, “Fluorescence spectrum estimation using multiple color images and minimum negativity constraint,” Opt. Express,  16, 1458–1464 (2002).
  8. V. Cardei and B. Funt, “Committee-based color constancy,” in Proc. IS&T/SID Seventh Color Imaging Conf: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Virginia, 1999), pp.311–313.
  9. H. Stokman and T. Gevers, “Selection and fusion of color models for image feature detection,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 371–381 (2007).
    [Crossref] [PubMed]
  10. K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
    [Crossref]
  11. W. K. Pratt, Digital Image Processing, 2nd ed. (Wiley, New York, 1991).
  12. L. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [Crossref] [PubMed]
  13. R. McDonald and K. J. Smith, “CIE94 - a new colour difference formaula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
    [Crossref]

2007 (1)

H. Stokman and T. Gevers, “Selection and fusion of color models for image feature detection,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 371–381 (2007).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2002 (3)

M. Shi and G. Healey, “Using reflectance models for color scanner calibration,” J. Opt. Soc. Am. A 19, 645–656 (2002).
[Crossref]

M. Soriano, W. Oblefias, and C. Saloma, “Fluorescence spectrum estimation using multiple color images and minimum negativity constraint,” Opt. Express,  16, 1458–1464 (2002).

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[Crossref]

2000 (1)

1995 (1)

R. McDonald and K. J. Smith, “CIE94 - a new colour difference formaula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

1986 (1)

Barnard, K.

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[Crossref]

Berns, R. S.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromaitc digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999).

Cardei, V.

V. Cardei and B. Funt, “Committee-based color constancy,” in Proc. IS&T/SID Seventh Color Imaging Conf: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Virginia, 1999), pp.311–313.

Cheung, V.

Connah, D.

Funt, B.

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[Crossref]

V. Cardei and B. Funt, “Committee-based color constancy,” in Proc. IS&T/SID Seventh Color Imaging Conf: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Virginia, 1999), pp.311–313.

Gevers, T.

H. Stokman and T. Gevers, “Selection and fusion of color models for image feature detection,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 371–381 (2007).
[Crossref] [PubMed]

Haneishi, H.

Hardeberg, J.

Hardeberg, J. Y.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Superieure des Telecommunications, 1999).

Hasegawa, T.

Healey, G.

Hosoi, A.

Imai, F. H.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromaitc digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999).

Li, C.

Maloney, L.

McDonald, R.

R. McDonald and K. J. Smith, “CIE94 - a new colour difference formaula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

Miyake, Y.

Oblefias, W.

M. Soriano, W. Oblefias, and C. Saloma, “Fluorescence spectrum estimation using multiple color images and minimum negativity constraint,” Opt. Express,  16, 1458–1464 (2002).

Pratt, W. K.

W. K. Pratt, Digital Image Processing, 2nd ed. (Wiley, New York, 1991).

Saloma, C.

M. Soriano, W. Oblefias, and C. Saloma, “Fluorescence spectrum estimation using multiple color images and minimum negativity constraint,” Opt. Express,  16, 1458–1464 (2002).

Shen, H. L.

Shi, M.

Smith, K. J.

R. McDonald and K. J. Smith, “CIE94 - a new colour difference formaula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

Soriano, M.

M. Soriano, W. Oblefias, and C. Saloma, “Fluorescence spectrum estimation using multiple color images and minimum negativity constraint,” Opt. Express,  16, 1458–1464 (2002).

Stokman, H.

H. Stokman and T. Gevers, “Selection and fusion of color models for image feature detection,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 371–381 (2007).
[Crossref] [PubMed]

Tsumura, N.

Westland, S.

Xin, J. H.

Yokoyama, Y.

Appl. Opt. (1)

Color Res. Appl. (1)

K. Barnard and B. Funt, “Camera characterization for color research,” Color Res. Appl. 27, 152–163 (2002).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

H. Stokman and T. Gevers, “Selection and fusion of color models for image feature detection,” IEEE Trans. Pattern Anal. Mach. Intell. 29, 371–381 (2007).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (4)

J. Soc. Dyers Colour. (1)

R. McDonald and K. J. Smith, “CIE94 - a new colour difference formaula,” J. Soc. Dyers Colour. 111, 376–379 (1995).
[Crossref]

Opt. Express (1)

M. Soriano, W. Oblefias, and C. Saloma, “Fluorescence spectrum estimation using multiple color images and minimum negativity constraint,” Opt. Express,  16, 1458–1464 (2002).

Other (4)

V. Cardei and B. Funt, “Committee-based color constancy,” in Proc. IS&T/SID Seventh Color Imaging Conf: Color Science, Systems, and Applications (Society for Imaging Science and Technology, Virginia, 1999), pp.311–313.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Superieure des Telecommunications, 1999).

F. H. Imai and R. S. Berns, “Spectral estimation using trichromaitc digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, Chiba, Japan, 1999).

W. K. Pratt, Digital Image Processing, 2nd ed. (Wiley, New York, 1991).

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Figures (2)

Fig. 1.
Fig. 1.

Distribution of colorimetric errors ΔE* 94 under D65 and spectral errors obtained using the objective function (16) with respect to different c values. The green square-symbol curve represents colorimetric errors, and the blue circle-symbol curve represents spectral rms errors.

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Fig. 2.
Fig. 2.

Reconstructed spectral reflectances of the proposed method using objective function (16). (a) the best case, with ΔE* 94=0.11 under D65, (b) the worst case, with ΔE* 94=3.68 under D65

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Tables (1)

Tables Icon

Table 1. Spectral and colorimetric error statistics of 6 methods when c=0.2: wiener estimation, pseudo-inverse method, finite-dimensional modeling method, simple averaging method, and the proposed methods.

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Equations (22)

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v L × 1 = M L × N r N × 1 + b L × 1 + n L × 1 ,
r ̂ = Wu .
W = K r M T ( MK r M T + K n ) − 1 ,
W = RU + = RU T ( UU T ) − ,
r = ∑ j = 1 J a j b j ,
u = Mr = ∑ j = 1 J a j Mb j .
x = ∑ k = 1 K w k x k ,
E ( x ) = ∑ k = 1 K w k E ( x k ) ,
σ 2 ( x ) = ∑ k = 1 K ∑ l = 1 K w k w l σ ( x k , x l ) ,
δr k = ( ( r − r ̂ k ) T ( r − r ̂ k ) N ) 1 2 ,
δr = ∑ k = 1 K w k δr k .
δe k = Δ E 94 * ( r , r ̂ k ) ,
δe = ∑ k = 1 K w k δe k .
E ( δ ) = c ∑ k = 1 K w k E ( δr k ) + ( 1 − c ) ∑ k = 1 K w k E ( δe k )
= c E r T w + ( 1 − c ) E e T w ,
σ 2 ( δ ) = c ∑ k = 1 K ∑ l = 1 K w k w l σ ( δr k , δr l ) + ( 1 − c ) ∑ k = 1 K ∑ l = 1 K w k w l σ ( δe k , δe l )
= c w T ∑ r w + ( 1 − c ) w T ∑ e w ,
minimize σ 2 ( δ ) ,
minimize σ 2 ( δ ) + E ( δ ) .
∑ k = 1 K w k = 1 ,
0 ≤ w k ≤ 1 .
r ̂ = ∑ k = 1 K w k r ̂ k .

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