Abstract

We investigate methods for the recovery of reflectance spectra from the responses of trichromatic camera systems and the application of these methods to the problem of camera characterization. The recovery of reflectance from colorimetric data is an ill-posed problem, and a unique solution requires additional constraints. We introduce a novel method for reflectance recovery that finds the smoothest spectrum consistent with both the colorimetric data and a linear model of reflectance. Four multispectral methods were tested using data from a real trichromatic camera system. The new method gave the lowest maximum colorimetric error in terms of camera characterization with test data that were independent of the training data. However, the average colorimetric performances of the four multispectral methods were statistically indistinguishable from each other but were significantly worse than conventional methods for camera characterization such as polynomial transforms.

© 2005 Optical Society of America

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References

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    [CrossRef]
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  3. W. Wu, J. P. Allebach, M. Analoui, “Imaging colorimetry using a digital camera,” J. Imaging Sci. Technol. 44, 267–279 (2000).
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    [CrossRef]
  5. G. D. Finlayson, P. M. Morovic, “Metamer constrained color correction,” in Proceedings of the 7th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1999).
  6. G. Hong, M. R. Luo, P. A. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
    [CrossRef]
  7. S. Westland, C. Ripamonti, Computational Colour Science: Using MATLAB (Wiley, Chichester, UK, 2004).
  8. F. H. Imai, S Quan, M. R. Rosen, R. S. Berns, “Digital camera filter design for colorimetric and spectral accuracy,” in Proceedings of the 3rd International Conference on Multispectral Color Science (Joensuu, Finland), 23–26 (2001).
  9. J. Y. Hardeberg, “Acquisition and reproduction of colour images: colorimetric and multispectral approaches,” Ph.D. thesis (Ecole Nationale Supérieure des Télécommunica- tions, Paris, 1999).
  10. H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  25. Q. Sun, M. D. Fairchild, “Statistical characterization of spectral reflectances in human portraiture,” Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).
  26. Q. Chen, “Estimation of digital camera’s spectral sensitivity,” M.Sc. dissertation, (University of Derby, Derby, UK 2001).
  27. G. D. Finlayson, S. D. Hordley, P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of the 6th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1998).
  28. G. J. Borse, Numerical Methods with MATLAB: A Resource for Scientists and Engineers (PWS, London, 1997).
  29. G. Upton, I. Cook, Understanding Statistics (Oxford U. Press, Oxford, UK, 1996).
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2004 (3)

V. Cheung, S. Westland, D. Connah, C. Ripamonti, “A comparative study of characterization of color cameras using neural networks and polynomial transforms,” Coloration Technol 120, 19–25 (2004).
[CrossRef]

V. Cheung, S. Westland, M. G.A. Thomson, “Accurate estimation of the non-linearity of input-output response for color cameras,” Color Res. Appl. 29, 406–412 (2004).
[CrossRef]

H. -L. Shen, J. H. Xin, “Spectral characterization of a color scanner by adaptive estimation,” J. Opt. Soc. Am. A 21, 1125–1130 (2004).
[CrossRef]

2002 (1)

2001 (3)

M. G.A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

G. Hong, M. R. Luo, P. A. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

D. Connah, S. Westland, M. G.A. Thomson, “Recovering spectral information using digital camera systems,” Coloration Technol 117, 309–312 (2001).
[CrossRef]

2000 (1)

W. Wu, J. P. Allebach, M. Analoui, “Imaging colorimetry using a digital camera,” J. Imaging Sci. Technol. 44, 267–279 (2000).

1996 (1)

T. Johnson, “Methods for characterising color scanners and digital cameras,” Displays 16, 183–191 (1996).
[CrossRef]

1995 (1)

R. S. Berns, M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[CrossRef]

1993 (1)

B. A. Wandell, J. E. Farrell, “Water into wine: converting scanner RGB to tristimulus XYZ,” in “Device-independent color image and imaging systems integration,” R. J. Motta and H. A. Berberian, eds., Proc. SPIE 1909, 92–101 (1993).
[CrossRef]

1990 (2)

1986 (2)

Allebach, J. P.

W. Wu, J. P. Allebach, M. Analoui, “Imaging colorimetry using a digital camera,” J. Imaging Sci. Technol. 44, 267–279 (2000).

Analoui, M.

W. Wu, J. P. Allebach, M. Analoui, “Imaging colorimetry using a digital camera,” J. Imaging Sci. Technol. 44, 267–279 (2000).

Berns, R. S.

R. S. Berns, M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[CrossRef]

F. H. Imai, R. S. Berns, “Spectral estimation using trichromatic 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).

F. H. Imai, S Quan, M. R. Rosen, R. S. Berns, “Digital camera filter design for colorimetric and spectral accuracy,” in Proceedings of the 3rd International Conference on Multispectral Color Science (Joensuu, Finland), 23–26 (2001).

Borse, G. J.

G. J. Borse, Numerical Methods with MATLAB: A Resource for Scientists and Engineers (PWS, London, 1997).

Chen, Q.

Q. Chen, “Estimation of digital camera’s spectral sensitivity,” M.Sc. dissertation, (University of Derby, Derby, UK 2001).

Cheung, V.

V. Cheung, S. Westland, D. Connah, C. Ripamonti, “A comparative study of characterization of color cameras using neural networks and polynomial transforms,” Coloration Technol 120, 19–25 (2004).
[CrossRef]

V. Cheung, S. Westland, M. G.A. Thomson, “Accurate estimation of the non-linearity of input-output response for color cameras,” Color Res. Appl. 29, 406–412 (2004).
[CrossRef]

Connah, D.

V. Cheung, S. Westland, D. Connah, C. Ripamonti, “A comparative study of characterization of color cameras using neural networks and polynomial transforms,” Coloration Technol 120, 19–25 (2004).
[CrossRef]

D. Connah, S. Westland, M. G.A. Thomson, “Recovering spectral information using digital camera systems,” Coloration Technol 117, 309–312 (2001).
[CrossRef]

Cook, I.

G. Upton, I. Cook, Understanding Statistics (Oxford U. Press, Oxford, UK, 1996).

Fairchild, M. D.

Q. Sun, M. D. Fairchild, “Statistical characterization of spectral reflectances in human portraiture,” Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).

Farrell, J. E.

B. A. Wandell, J. E. Farrell, “Water into wine: converting scanner RGB to tristimulus XYZ,” in “Device-independent color image and imaging systems integration,” R. J. Motta and H. A. Berberian, eds., Proc. SPIE 1909, 92–101 (1993).
[CrossRef]

J. E. Farrell, D. Sherman, B. A. Wandell, “How to turn your scanner into a colorimeter,” in Proceedings of the 10th International Conference on Advances in Non-impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1994).

Finlayson, G. D.

G. D. Finlayson, P. M. Morovic, “Metamer constrained color correction,” in Proceedings of the 7th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1999).

G. D. Finlayson, S. D. Hordley, P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of the 6th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1998).

Hardeberg, J. Y.

J. Y. Hardeberg, “Acquisition and reproduction of colour images: colorimetric and multispectral approaches,” Ph.D. thesis (Ecole Nationale Supérieure des Télécommunica- tions, Paris, 1999).

J. Y. Hardeberg, “On the spectral dimensionality of object colors,” in Proceedings of the 1st European Conference on Color in Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002).

Hayashi, J.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).

Healey, G.

Hong, G.

G. Hong, M. R. Luo, P. A. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

Hordley, S. D.

G. D. Finlayson, S. D. Hordley, P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of the 6th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1998).

Hubel, P. M.

G. D. Finlayson, S. D. Hordley, P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of the 6th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1998).

Imai, F. H.

F. H. Imai, S Quan, M. R. Rosen, R. S. Berns, “Digital camera filter design for colorimetric and spectral accuracy,” in Proceedings of the 3rd International Conference on Multispectral Color Science (Joensuu, Finland), 23–26 (2001).

F. H. Imai, R. S. Berns, “Spectral estimation using trichromatic 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).

Johnson, T.

T. Johnson, “Methods for characterising color scanners and digital cameras,” Displays 16, 183–191 (1996).
[CrossRef]

Kuno, T.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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. J.

C. J. Li, M. R. Luo, “The estimation of spectral reflectances using the smoothness constraint condition,” in Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).

Luo, M. R.

G. Hong, M. R. Luo, P. A. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

C. J. Li, M. R. Luo, “The estimation of spectral reflectances using the smoothness constraint condition,” in Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).

Maloney, L. T.

Matoba, N.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).

Miyake, Y.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).

Morovic, P.

P. Morovič, “Metamer sets,” Ph.D. thesis, (University of East Anglia, Norwich, UK, 2002).

Morovic, P. M.

G. D. Finlayson, P. M. Morovic, “Metamer constrained color correction,” in Proceedings of the 7th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1999).

Quan, S

F. H. Imai, S Quan, M. R. Rosen, R. S. Berns, “Digital camera filter design for colorimetric and spectral accuracy,” in Proceedings of the 3rd International Conference on Multispectral Color Science (Joensuu, Finland), 23–26 (2001).

Rhodes, P. A.

G. Hong, M. R. Luo, P. A. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

Ripamonti, C.

V. Cheung, S. Westland, D. Connah, C. Ripamonti, “A comparative study of characterization of color cameras using neural networks and polynomial transforms,” Coloration Technol 120, 19–25 (2004).
[CrossRef]

S. Westland, C. Ripamonti, Computational Colour Science: Using MATLAB (Wiley, Chichester, UK, 2004).

Rosen, M. R.

F. H. Imai, S Quan, M. R. Rosen, R. S. Berns, “Digital camera filter design for colorimetric and spectral accuracy,” in Proceedings of the 3rd International Conference on Multispectral Color Science (Joensuu, Finland), 23–26 (2001).

Shen, H. -L.

Sherman, D.

J. E. Farrell, D. Sherman, B. A. Wandell, “How to turn your scanner into a colorimeter,” in Proceedings of the 10th International Conference on Advances in Non-impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1994).

Shi, M.

Shyu, M. J.

R. S. Berns, M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[CrossRef]

Sugiura, H.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).

Sun, Q.

Q. Sun, M. D. Fairchild, “Statistical characterization of spectral reflectances in human portraiture,” Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).

Thomson, M. G.A.

V. Cheung, S. Westland, M. G.A. Thomson, “Accurate estimation of the non-linearity of input-output response for color cameras,” Color Res. Appl. 29, 406–412 (2004).
[CrossRef]

D. Connah, S. Westland, M. G.A. Thomson, “Recovering spectral information using digital camera systems,” Coloration Technol 117, 309–312 (2001).
[CrossRef]

M. G.A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

Upton, G.

G. Upton, I. Cook, Understanding Statistics (Oxford U. Press, Oxford, UK, 1996).

van Trigt, C.

Wandell, B. A.

B. A. Wandell, J. E. Farrell, “Water into wine: converting scanner RGB to tristimulus XYZ,” in “Device-independent color image and imaging systems integration,” R. J. Motta and H. A. Berberian, eds., Proc. SPIE 1909, 92–101 (1993).
[CrossRef]

L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
[CrossRef] [PubMed]

J. E. Farrell, D. Sherman, B. A. Wandell, “How to turn your scanner into a colorimeter,” in Proceedings of the 10th International Conference on Advances in Non-impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1994).

Watanabe, N.

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).

Westland, S.

V. Cheung, S. Westland, M. G.A. Thomson, “Accurate estimation of the non-linearity of input-output response for color cameras,” Color Res. Appl. 29, 406–412 (2004).
[CrossRef]

V. Cheung, S. Westland, D. Connah, C. Ripamonti, “A comparative study of characterization of color cameras using neural networks and polynomial transforms,” Coloration Technol 120, 19–25 (2004).
[CrossRef]

M. G.A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

D. Connah, S. Westland, M. G.A. Thomson, “Recovering spectral information using digital camera systems,” Coloration Technol 117, 309–312 (2001).
[CrossRef]

S. Westland, C. Ripamonti, Computational Colour Science: Using MATLAB (Wiley, Chichester, UK, 2004).

Wu, W.

W. Wu, J. P. Allebach, M. Analoui, “Imaging colorimetry using a digital camera,” J. Imaging Sci. Technol. 44, 267–279 (2000).

Xin, J. H.

Color Res. Appl. (3)

G. Hong, M. R. Luo, P. A. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modelling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

M. G.A. Thomson, S. Westland, “Color-imager calibration by parametric fitting of sensor responses,” Color Res. Appl. 26, 442–449 (2001).
[CrossRef]

V. Cheung, S. Westland, M. G.A. Thomson, “Accurate estimation of the non-linearity of input-output response for color cameras,” Color Res. Appl. 29, 406–412 (2004).
[CrossRef]

Coloration Technol (2)

V. Cheung, S. Westland, D. Connah, C. Ripamonti, “A comparative study of characterization of color cameras using neural networks and polynomial transforms,” Coloration Technol 120, 19–25 (2004).
[CrossRef]

D. Connah, S. Westland, M. G.A. Thomson, “Recovering spectral information using digital camera systems,” Coloration Technol 117, 309–312 (2001).
[CrossRef]

Displays (1)

T. Johnson, “Methods for characterising color scanners and digital cameras,” Displays 16, 183–191 (1996).
[CrossRef]

J. Electron. Imaging (1)

R. S. Berns, M. J. Shyu, “Colorimetric characterization of a desktop drum scanner using a spectral model,” J. Electron. Imaging 4, 360–372 (1995).
[CrossRef]

J. Imaging Sci. Technol. (1)

W. Wu, J. P. Allebach, M. Analoui, “Imaging colorimetry using a digital camera,” J. Imaging Sci. Technol. 44, 267–279 (2000).

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

Proc. SPIE (1)

B. A. Wandell, J. E. Farrell, “Water into wine: converting scanner RGB to tristimulus XYZ,” in “Device-independent color image and imaging systems integration,” R. J. Motta and H. A. Berberian, eds., Proc. SPIE 1909, 92–101 (1993).
[CrossRef]

Other (15)

J. E. Farrell, D. Sherman, B. A. Wandell, “How to turn your scanner into a colorimeter,” in Proceedings of the 10th International Conference on Advances in Non-impact Printing Technologies (Society for Imaging Science and Technology, Springfield, Va., 1994).

G. D. Finlayson, P. M. Morovic, “Metamer constrained color correction,” in Proceedings of the 7th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1999).

S. Westland, C. Ripamonti, Computational Colour Science: Using MATLAB (Wiley, Chichester, UK, 2004).

F. H. Imai, S Quan, M. R. Rosen, R. S. Berns, “Digital camera filter design for colorimetric and spectral accuracy,” in Proceedings of the 3rd International Conference on Multispectral Color Science (Joensuu, Finland), 23–26 (2001).

J. Y. Hardeberg, “Acquisition and reproduction of colour images: colorimetric and multispectral approaches,” Ph.D. thesis (Ecole Nationale Supérieure des Télécommunica- tions, Paris, 1999).

H. Sugiura, T. Kuno, N. Watanabe, N. Matoba, J. Hayashi, Y. Miyake, “Development of highly accurate multispectral 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).

Q. Sun, M. D. Fairchild, “Statistical characterization of spectral reflectances in human portraiture,” Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).

Q. Chen, “Estimation of digital camera’s spectral sensitivity,” M.Sc. dissertation, (University of Derby, Derby, UK 2001).

G. D. Finlayson, S. D. Hordley, P. M. Hubel, “Recovering device sensitivities with quadratic programming,” in Proceedings of the 6th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 1998).

G. J. Borse, Numerical Methods with MATLAB: A Resource for Scientists and Engineers (PWS, London, 1997).

G. Upton, I. Cook, Understanding Statistics (Oxford U. Press, Oxford, UK, 1996).

J. Y. Hardeberg, “On the spectral dimensionality of object colors,” in Proceedings of the 1st European Conference on Color in Graphics, Image and Vision (Society for Imaging Science and Technology, Springfield, Va., 2002).

F. H. Imai, R. S. Berns, “Spectral estimation using trichromatic 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).

C. J. Li, M. R. Luo, “The estimation of spectral reflectances using the smoothness constraint condition,” in Proceedings of the 9th Color Imaging Science Conference (Society for Imaging Science and Technology, Springfield, Va., 2001).

P. Morovič, “Metamer sets,” Ph.D. thesis, (University of East Anglia, Norwich, UK, 2002).

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Figures (11)

Fig. 1
Fig. 1

Luminance reflectance factors ( Y ) of 13 achromatic patches plotted against the spatially averaged camera channel RGB responses (circles) for each patch and third-order polynomial fit (solid lines) (left column) and the linearized camera responses (circles) converted from the polynomial fit (right column). The circles in the right-column graphs should lie along the straight line if the linearization process is perfect. All data are shown normalized in the range 0–1.

Fig. 2
Fig. 2

Color distributions of 166 Macbeth ColorChecker DC (circles) and 50 NCS samples (asterisks) in CIELAB a * b * space.

Fig. 3
Fig. 3

Estimated camera spectral sensitivities of the blue (solid curve), green (dashed curve), and red (dotted curve) channels of the Agfa StudioCam (estimations by Chen[26]).

Fig. 4
Fig. 4

First three basis functions (first component, solid curve; second component, dashed curve; third component, dotted curve) of the Macbeth ColorChecker DC training samples.

Fig. 5
Fig. 5

Example of spectral-reflectance recovery for a NCS sample (1070 R20B, solid curve) with the Maloney-Wandell (dashed curve) and Imai–Berns (dotted curve) methods.

Fig. 6
Fig. 6

Effect of training size of the reflectance recovery with the Maloney–Wandell method. The median CIELAB errors are plotted for the training (diamonds) set and for the ColorChecker (triangles) and NCS (circles) test sets.

Fig. 7
Fig. 7

Effect of training size of the reflectance recovery with the Imai–Berns method. The median CIELAB errors are plotted for the training (diamonds) set and for the ColorChecker (triangles) and NCS (circles) test sets.

Fig. 8
Fig. 8

Examples of spectral-reflectance recovery for a NCS sample (1070 R20B, solid curve) by use of Shi–Healey method (dashed curve) with between 4 and 12 basis functions (estimation with 4 basis functions in top-left figure; number of basis functions increases left to right and then for each row).

Fig. 9
Fig. 9

Example of spectral reflectance recovery for a NCS sample (1070 R20B, solid curve) by use of Li-Luo method (dashed curve) with between 4 and 12 basis functions (estimation with 4 basis functions in top-left figure; number of basis functions increases left to right and then for each row).

Fig. 10
Fig. 10

Effect of training size of the reflectance recovery with the Shi–Healey method. The median CIELAB errors are plotted for the training (diamonds) set and for the ColorChecker (triangles) and NCS (circles) test sets.

Fig. 11
Fig. 11

Effect of training size of the reflectance recovery with the Li–Luo method. The median CIELAB errors are plotted for the training (diamonds) set and for the ColorChecker (triangles) and NCS (circles) test sets.

Tables (3)

Tables Icon

Table 1 Characterization Performance (Median CIELAB Δ E with Maximum Values in Parentheses) of Maloney–Wandell and Imai–Berns Methods for Different Training-Set Size

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Table 2 Characterization Performance (Median CIELAB Δ E with Maximum Values in Parentheses) of Shi–Healey and Li–Luo Methods with Different Numbers of Basis Functions a

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Table 3 Characterization Performance (Median CIELAB Δ E with Maximum Values in Parentheses) Using the Best Polynomial ( 3 × 20 Model) and Neural Networks (18 Hidden Units) Methods for Different Training-Set Sizes a

Equations (11)

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P = B W ,
C = M T P ,
C = Λ W ,
W = Λ + C ,
Λ = C W + ,
P = B 1 W 1 + B 2 W 2 ,
C = M T B 1 W 1 + M T B 2 W 2 .
W 1 = ( M T B 1 ) 1 C ( M T B 1 ) 1 M T B 2 W 2 .
P = B 1 ( ( M T B 1 ) 1 C ( M T B 1 ) 1 M T B 2 W 2 ) + B 2 W 2 ,
P = B 1 ( M T B 1 ) 1 C + ( B 2 B 1 ( M T B 1 ) 1 M T B 2 ) W 2 ,
R S i = ( R W R B ) × ( R i R B i ) ( R W i R B i ) ,

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