Abstract

It is often the case that multiplications of whole spectra, component by component, must be carried out, for example when light reflects from or is transmitted through materials. This leads to particularly taxing calculations, especially in spectrally based ray tracing or radiosity in graphics, making a full-spectrum method prohibitively expensive. Nevertheless, using full spectra is attractive because of the many important phenomena that can be modeled only by using all the physics at hand. We apply to the task of spectral multiplication a method previously used in modeling RGB-based light propagation. We show that we can often multiply spectra without carrying out spectral multiplication. In previous work [J. Opt. Soc. Am. A 11, 1553 (1994)] we developed a method called spectral sharpening, which took camera RGBs to a special sharp basis that was designed to render illuminant change simple to model. Specifically, in the new basis, one can effectively model illuminant change by using a diagonal matrix rather than the 3×3 linear transform that results from a three-component finite-dimensional model [G. Healey and D. Slater, J. Opt. Soc. Am. A 11, 3003 (1994)]. We apply this idea of sharpening to the set of principal components vectors derived from a representative set of spectra that might reasonably be encountered in a given application. With respect to the sharp spectral basis, we show that spectral multiplications can be modeled as the multiplication of the basis coefficients. These new product coefficients applied to the sharp basis serve to accurately reconstruct the spectral product. Although the method is quite general, we show how to use spectral modeling by taking advantage of metameric surfaces, ones that match under one light but not another, for tasks such as volume rendering. The use of metamers allows a user to pick out or merge different volume structures in real time simply by changing the lighting.

© 2003 Optical Society of America

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References

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  1. P. Robertson, J. Shönhut, eds. Special issue, “Color in Computer Graphics,” in IEEE Comput. Graphics Appl.19, July/August, 18–67 (1999).
    [CrossRef]
  2. C. F. Borges, “Trichromatic approximation method for surface illumination,” J. Opt. Soc. Am. A 8, 1319–1323 (1991).
    [CrossRef]
  3. M. S. Peercy, “Linear color representations for full spectral rendering,” in Comput. Graph. (SIGGRAPH’93) 27, 191–198 (1993).
  4. G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
    [CrossRef]
  5. L. Arend, A. Reeves, “Simultaneous color constancy,” J. Opt. Soc. Am. A 3, 1743–1751 (1986).
    [CrossRef] [PubMed]
  6. 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]
  7. D. A. Forsyth, “A novel approach to color constancy,” presented at the International Conference on Computer Vision ’88, Tarpon Springs, Fla., Dec. 5–8, 1988.
  8. D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
    [CrossRef]
  9. D. H. Foster, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
    [CrossRef]
  10. D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
    [CrossRef]
  11. G. Buchsbaum, “Color signal coding: color vision and color television,” Color Res. Appl. 12, 266–269 (1987).
    [CrossRef]
  12. P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).
  13. M. S. Drew, G. D. Finlayson, “Spectral sharpening with positivity,” J. Opt. Soc. Am. A 17, 1361–1370 (2000).
    [CrossRef]
  14. M. S. Drew, G. D. Finlayson, “Representation of colour in a colour display system,” UK Patent Application No. 0206916.9. Under review, British Patent Office, March23, 2002.
  15. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982).
  16. M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).
  17. M. S. Drew, B. V. Funt, “Natural metamers,” CVGIP: Image Understand. 56, 139–151 (1992).
    [CrossRef]
  18. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [CrossRef]
  19. M. Stokes, M. D. Fairchild, R. S. Berns, “Precision requirements for digital color reproduction,” ACM Trans. Graphics 11, 406–422 (1992).
    [CrossRef]
  20. C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. App. Photog. Eng. 2, 95–99 (1976).
  21. Y. Sun, F. D. Fracchia, M. S. Drew, T. W. Calvert, “Rendering iridescent colors of optical disks,” in Proceedings of the 11th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2000), pp. 341–352.
  22. G. M. Johnson, M. D. Fairchild, “Full-spectral color calculations in realistic image synthesis,” IEEE Comput. Graphics Appl. 19, (July/August), 47–53 (1999).
    [CrossRef]
  23. A colour version of all figures may be found at http://www.cs.sfu.ca/∼mark/ftp/Josa03 .
  24. G. D. Finlayson, “Coefficient color constancy,” Ph.D. thesis (Simon Fraser University, Vancouver, B.C., Canada, 1995).
  25. G. Ward, E. Eydelberg-Vileshin, “Picture perfect RGB rendering using spectral prefiltering and sharp color primaries,” in Proceedings of the 13th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2002), pp. 117–124.
  26. G. W. Meyer, “Wavelength selection for synthetic image generation,” Comput. Vision Graph. Image Process. 41, 57–79 (1988).
    [CrossRef]
  27. S. Bergner, T. Möller, M. S. Drew, G. D. Finlayson, “Interactive spectral volume rendering,” in Proceedings of the IEEE Conference on Visualization (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 101–108. Selected for proceedings cover.
  28. C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
    [CrossRef]
  29. H. J. Noordmans, H. T. M. van der Voort, A. W. M. Smeulders, “Spectral volume rendering,” IEEE Trans. Visualz. Comput. Graphics 6, 196–207 (2000).
    [CrossRef]

2000 (2)

H. J. Noordmans, H. T. M. van der Voort, A. W. M. Smeulders, “Spectral volume rendering,” IEEE Trans. Visualz. Comput. Graphics 6, 196–207 (2000).
[CrossRef]

M. S. Drew, G. D. Finlayson, “Spectral sharpening with positivity,” J. Opt. Soc. Am. A 17, 1361–1370 (2000).
[CrossRef]

1999 (1)

G. M. Johnson, M. D. Fairchild, “Full-spectral color calculations in realistic image synthesis,” IEEE Comput. Graphics Appl. 19, (July/August), 47–53 (1999).
[CrossRef]

1997 (1)

1994 (3)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

D. H. Foster, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

1993 (2)

M. S. Peercy, “Linear color representations for full spectral rendering,” in Comput. Graph. (SIGGRAPH’93) 27, 191–198 (1993).

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[CrossRef]

1992 (2)

M. Stokes, M. D. Fairchild, R. S. Berns, “Precision requirements for digital color reproduction,” ACM Trans. Graphics 11, 406–422 (1992).
[CrossRef]

M. S. Drew, B. V. Funt, “Natural metamers,” CVGIP: Image Understand. 56, 139–151 (1992).
[CrossRef]

1991 (1)

1988 (1)

G. W. Meyer, “Wavelength selection for synthetic image generation,” Comput. Vision Graph. Image Process. 41, 57–79 (1988).
[CrossRef]

1987 (1)

G. Buchsbaum, “Color signal coding: color vision and color television,” Color Res. Appl. 12, 266–269 (1987).
[CrossRef]

1986 (2)

1984 (1)

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
[CrossRef]

1976 (1)

C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. App. Photog. Eng. 2, 95–99 (1976).

1964 (1)

Arend, L.

Battaile, B.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
[CrossRef]

Bergner, S.

S. Bergner, T. Möller, M. S. Drew, G. D. Finlayson, “Interactive spectral volume rendering,” in Proceedings of the IEEE Conference on Visualization (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 101–108. Selected for proceedings cover.

Berns, R. S.

M. Stokes, M. D. Fairchild, R. S. Berns, “Precision requirements for digital color reproduction,” ACM Trans. Graphics 11, 406–422 (1992).
[CrossRef]

Borges, C. F.

Brainard, D. H.

D. H. Brainard, W. T. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
[CrossRef]

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[CrossRef]

Buchsbaum, G.

G. Buchsbaum, “Color signal coding: color vision and color television,” Color Res. Appl. 12, 266–269 (1987).
[CrossRef]

Calvert, T. W.

Y. Sun, F. D. Fracchia, M. S. Drew, T. W. Calvert, “Rendering iridescent colors of optical disks,” in Proceedings of the 11th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2000), pp. 341–352.

Chichilnisky, E.-J.

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[CrossRef]

Davidson, J. G.

C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. App. Photog. Eng. 2, 95–99 (1976).

Drew, M. S.

M. S. Drew, G. D. Finlayson, “Spectral sharpening with positivity,” J. Opt. Soc. Am. A 17, 1361–1370 (2000).
[CrossRef]

G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

M. S. Drew, B. V. Funt, “Natural metamers,” CVGIP: Image Understand. 56, 139–151 (1992).
[CrossRef]

Y. Sun, F. D. Fracchia, M. S. Drew, T. W. Calvert, “Rendering iridescent colors of optical disks,” in Proceedings of the 11th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2000), pp. 341–352.

S. Bergner, T. Möller, M. S. Drew, G. D. Finlayson, “Interactive spectral volume rendering,” in Proceedings of the IEEE Conference on Visualization (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 101–108. Selected for proceedings cover.

M. S. Drew, G. D. Finlayson, “Representation of colour in a colour display system,” UK Patent Application No. 0206916.9. Under review, British Patent Office, March23, 2002.

Eydelberg-Vileshin, E.

G. Ward, E. Eydelberg-Vileshin, “Picture perfect RGB rendering using spectral prefiltering and sharp color primaries,” in Proceedings of the 13th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2002), pp. 117–124.

Fairchild, M. D.

G. M. Johnson, M. D. Fairchild, “Full-spectral color calculations in realistic image synthesis,” IEEE Comput. Graphics Appl. 19, (July/August), 47–53 (1999).
[CrossRef]

M. Stokes, M. D. Fairchild, R. S. Berns, “Precision requirements for digital color reproduction,” ACM Trans. Graphics 11, 406–422 (1992).
[CrossRef]

Finlayson, G. D.

M. S. Drew, G. D. Finlayson, “Spectral sharpening with positivity,” J. Opt. Soc. Am. A 17, 1361–1370 (2000).
[CrossRef]

G. D. Finlayson, M. S. Drew, B. V. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[CrossRef]

M. S. Drew, G. D. Finlayson, “Representation of colour in a colour display system,” UK Patent Application No. 0206916.9. Under review, British Patent Office, March23, 2002.

S. Bergner, T. Möller, M. S. Drew, G. D. Finlayson, “Interactive spectral volume rendering,” in Proceedings of the IEEE Conference on Visualization (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 101–108. Selected for proceedings cover.

G. D. Finlayson, “Coefficient color constancy,” Ph.D. thesis (Simon Fraser University, Vancouver, B.C., Canada, 1995).

Forsyth, D. A.

D. A. Forsyth, “A novel approach to color constancy,” presented at the International Conference on Computer Vision ’88, Tarpon Springs, Fla., Dec. 5–8, 1988.

Foster, D. H.

D. H. Foster, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

Fracchia, F. D.

Y. Sun, F. D. Fracchia, M. S. Drew, T. W. Calvert, “Rendering iridescent colors of optical disks,” in Proceedings of the 11th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2000), pp. 341–352.

Freeman, W. T.

Funt, B. V.

Gershon, R.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Gill, P. E.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

Goral, C. M.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
[CrossRef]

Greenberg, D. P.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
[CrossRef]

Iwan, L. S.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Johnson, G. M.

G. M. Johnson, M. D. Fairchild, “Full-spectral color calculations in realistic image synthesis,” IEEE Comput. Graphics Appl. 19, (July/August), 47–53 (1999).
[CrossRef]

Judd, D. B.

MacAdam, D. L.

Maloney, L. T.

Marcus, H.

C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. App. Photog. Eng. 2, 95–99 (1976).

McCamy, C. S.

C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. App. Photog. Eng. 2, 95–99 (1976).

Meyer, G. W.

G. W. Meyer, “Wavelength selection for synthetic image generation,” Comput. Vision Graph. Image Process. 41, 57–79 (1988).
[CrossRef]

Möller, T.

S. Bergner, T. Möller, M. S. Drew, G. D. Finlayson, “Interactive spectral volume rendering,” in Proceedings of the IEEE Conference on Visualization (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 101–108. Selected for proceedings cover.

Murray, W.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

Nascimento, S. M. C.

D. H. Foster, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

Noordmans, H. J.

H. J. Noordmans, H. T. M. van der Voort, A. W. M. Smeulders, “Spectral volume rendering,” IEEE Trans. Visualz. Comput. Graphics 6, 196–207 (2000).
[CrossRef]

Peercy, M. S.

M. S. Peercy, “Linear color representations for full spectral rendering,” in Comput. Graph. (SIGGRAPH’93) 27, 191–198 (1993).

Reeves, A.

Smeulders, A. W. M.

H. J. Noordmans, H. T. M. van der Voort, A. W. M. Smeulders, “Spectral volume rendering,” IEEE Trans. Visualz. Comput. Graphics 6, 196–207 (2000).
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982).

Stokes, M.

M. Stokes, M. D. Fairchild, R. S. Berns, “Precision requirements for digital color reproduction,” ACM Trans. Graphics 11, 406–422 (1992).
[CrossRef]

Sun, Y.

Y. Sun, F. D. Fracchia, M. S. Drew, T. W. Calvert, “Rendering iridescent colors of optical disks,” in Proceedings of the 11th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2000), pp. 341–352.

Torrance, K. E.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
[CrossRef]

van der Voort, H. T. M.

H. J. Noordmans, H. T. M. van der Voort, A. W. M. Smeulders, “Spectral volume rendering,” IEEE Trans. Visualz. Comput. Graphics 6, 196–207 (2000).
[CrossRef]

Vrhel, M. J.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Wandell, B. A.

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (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]

Ward, G.

G. Ward, E. Eydelberg-Vileshin, “Picture perfect RGB rendering using spectral prefiltering and sharp color primaries,” in Proceedings of the 13th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2002), pp. 117–124.

Wright, M. H.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

Wyszecki, G.

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982).

ACM Trans. Graphics (1)

M. Stokes, M. D. Fairchild, R. S. Berns, “Precision requirements for digital color reproduction,” ACM Trans. Graphics 11, 406–422 (1992).
[CrossRef]

Color Res. Appl. (2)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

G. Buchsbaum, “Color signal coding: color vision and color television,” Color Res. Appl. 12, 266–269 (1987).
[CrossRef]

Comput. Graph. (1)

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modeling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 213–222 (1984).
[CrossRef]

Comput. Graph. (SIGGRAPH’93) (1)

M. S. Peercy, “Linear color representations for full spectral rendering,” in Comput. Graph. (SIGGRAPH’93) 27, 191–198 (1993).

Comput. Vision Graph. Image Process. (1)

G. W. Meyer, “Wavelength selection for synthetic image generation,” Comput. Vision Graph. Image Process. 41, 57–79 (1988).
[CrossRef]

Curr. Dir. Psychol. Sci. (1)

D. H. Brainard, B. A. Wandell, E.-J. Chichilnisky, “Color constancy: from physics to appearance,” Curr. Dir. Psychol. Sci. 2, 165–170 (1993).
[CrossRef]

CVGIP: Image Understand. (1)

M. S. Drew, B. V. Funt, “Natural metamers,” CVGIP: Image Understand. 56, 139–151 (1992).
[CrossRef]

IEEE Comput. Graphics Appl. (1)

G. M. Johnson, M. D. Fairchild, “Full-spectral color calculations in realistic image synthesis,” IEEE Comput. Graphics Appl. 19, (July/August), 47–53 (1999).
[CrossRef]

IEEE Trans. Visualz. Comput. Graphics (1)

H. J. Noordmans, H. T. M. van der Voort, A. W. M. Smeulders, “Spectral volume rendering,” IEEE Trans. Visualz. Comput. Graphics 6, 196–207 (2000).
[CrossRef]

J. App. Photog. Eng. (1)

C. S. McCamy, H. Marcus, J. G. Davidson, “A color-rendition chart,” J. App. Photog. Eng. 2, 95–99 (1976).

J. Opt. Soc. Am. (1)

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

Proc. R. Soc. London Ser. B (1)

D. H. Foster, S. M. C. Nascimento, “Relational colour constancy from invariant cone-excitation ratios,” Proc. R. Soc. London Ser. B 257, 115–121 (1994).
[CrossRef]

Other (10)

D. A. Forsyth, “A novel approach to color constancy,” presented at the International Conference on Computer Vision ’88, Tarpon Springs, Fla., Dec. 5–8, 1988.

A colour version of all figures may be found at http://www.cs.sfu.ca/∼mark/ftp/Josa03 .

G. D. Finlayson, “Coefficient color constancy,” Ph.D. thesis (Simon Fraser University, Vancouver, B.C., Canada, 1995).

G. Ward, E. Eydelberg-Vileshin, “Picture perfect RGB rendering using spectral prefiltering and sharp color primaries,” in Proceedings of the 13th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2002), pp. 117–124.

Y. Sun, F. D. Fracchia, M. S. Drew, T. W. Calvert, “Rendering iridescent colors of optical disks,” in Proceedings of the 11th Eurographics Workshop on Rendering (Eurographics/ACM, New York, 2000), pp. 341–352.

S. Bergner, T. Möller, M. S. Drew, G. D. Finlayson, “Interactive spectral volume rendering,” in Proceedings of the IEEE Conference on Visualization (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 101–108. Selected for proceedings cover.

M. S. Drew, G. D. Finlayson, “Representation of colour in a colour display system,” UK Patent Application No. 0206916.9. Under review, British Patent Office, March23, 2002.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982).

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

P. Robertson, J. Shönhut, eds. Special issue, “Color in Computer Graphics,” in IEEE Comput. Graphics Appl.19, July/August, 18–67 (1999).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) First five SVD vectors, (b) sharpened version of basis vectors.

Fig. 2
Fig. 2

(a) One bounce. Exact, solid curves; best least squares, dotted curves; spectral factor model, dashed curves. (b) Two bounces. (c) Three bounces.

Fig. 3
Fig. 3

Three pairs of metameric surface spectral reflectance functions.

Fig. 4
Fig. 4

Color signals for the three metameric pairs, under tungsten lighting (solid curves) with the spectral factor model approximation (dashed curves).

Fig. 5
Fig. 5

Spheres painted with metameric surface reflectance functions. Top row, results under D65, bottom row, results under illuminant A. Left column, results from use of full-spectrum reflectances and illuminants in a full-spectrum 31-component ray tracer; middle column, results from use of the present spectral factor model approach agree with those in the left column; right column, results from use of standard three-component graphics, with very different results. (Color versions of figures may be viewed at http://www.cs.sfu.ca/∼mark/ftp/Josa03.)

Fig. 6
Fig. 6

Color signals for one to six bounces of lights D65 [(a)–(f)] and A [(g)–(l)] from the six metameric reflectances in order, accumulating the signal over bounces. Solid curves, actual color signal; dashed curves, spectral factor model approximation.

Fig. 7
Fig. 7

Volume rendering of three-dimensional biological data. (a) Under illuminant D65, most materials are metameric. (b) Under illuminant A, most structures fade from view and just the stomach is prominent (image shown in inverse color).

Tables (5)

Tables Icon

Table 1 Median CIELAB ΔE Values for 170 Object Reflectances Comparing the Best Spectral Approximation from Use of a Finite-Dimensional Basis Set with the Spectral Factor Model Approach, Accumulating over 1 to 5 Recursive Reflections a

Tables Icon

Table 2 Ninetieth Percentile Level for CIELAB ΔE Values over 170 Object Reflectances with Randomly Chosen Lights

Tables Icon

Table 3 Rms Percentage Errors for Whole Spectra over 170 Object Reflectances with Randomly Chosen Lights

Tables Icon

Table 4 CIELAB Errors from Use of Specialized Seven-Dimensional Basis from Lights D65 and A Applied to the Metamer Reflectances over Both Lights and Six Bounces, Accumulating the Signal over Bounces

Tables Icon

Table 5 Rms Whole-Spectrum Percentage Errors for Lights D65 and A Applied to the Metamer Reflectances over Both Lights and Six Bounces, Accumulating the Signal over Bounces

Equations (29)

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

rx=f(x, λ)E(λ)Sx(λ)q(λ)dλ,
bE(λ)S(λ)q(λ)dλ.
C̲=E̲×S̲,
C̲=diag(E̲)S̲.
b=QTdiag(E̲)S̲=QTC̲.
bkskek/wk,k=13,
s=QTS̲,
e=QTE̲.
w=QT1̲,
Q˜=QT.
minλϕk[Q(λ)t]2+μλω[Q(λ)t]2-1,
k=13,
minλϕk[Q(λ)t]2,k=13
λω[Q(λ)t]2=1,L2 normalizationQ(λ)t0,nonnegativesensorresult.
bb=QTdiag(E̲)S̲QTdiag(E̲)S̲QTdiag(E̲)S̲refQTdiag(E̲)S̲ref.
b˜b˜Q˜Tdiag(E̲)S̲refQ˜Tdiag(E̲)S̲ref=b˜refb˜ref.
b˜=Q˜Tdiag(E̲)S̲=[Q˜TE̲][Q˜TS̲]Q˜Tdiag(1̲).
b˜=[Q˜Tdiag(E̲)S̲ref][Q˜Tdiag(E̲w)S̲]Q˜Tdiag(E̲w)S̲ref=b˜refb˜b˜ref,
b˜b˜=b˜refb˜ref.
c=Q˜TC̲.
s=Q˜TS̲.
Cˆ̲=Q˜+c,
Q˜+Q˜(Q˜TQ˜)-1.
Sˆ̲=Q˜+s.
vkcksk,k=1p.
v=diag(c)s.
spectrum=Q˜+v,vk=cksk.
bT=C_TR,
b=RTC̲=(RTQ˜+)cUc,

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