Abstract

The correlated color temperature (CCT) provides a simple and useful descriptor for a given spectral power distribution as well as an approximation of the full spectrum of the measured illuminant. But typically, the CCT is calculated on the basis of distance in the chromaticity plane. Here we suggest that, while familiar, this metric is not the most effective for actually generating a useful spectral approximation. Given the recent interest in whole- spectrum calculations, we consider what optimization would be most sensible for identifying the nearest Planckian in terms of the whole-spectrum RMS error; in that case, we are calculating a variant of the distribution temperature, another simple descriptor. This effectively means that instead of one value T, we instead describe a spectrum in terms of both T and an intensity I. In general, we wish to balance the need for (i) a best mapping of the whole spectrum and (ii) the smallest CIELAB error. As a first step, we show how to calculate the spectrum analytically in the case when RMS spectral-error minimization is the sole goal. Generalizing, we consider an optimization that tries to minimize a balance of RMS and CIELAB error, leading to a family of solutions. Finally, we suggest a specific optimization that arguably forms a best trade-off of these two objectives, which we denote the Planckian regression temperature. Results are shown for some standard test illuminants and then for a further 102 measured spectra, with results separately reported for fluorescent and nonfluorescent illuminants.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. Wyszecki and W. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, 1982).
  2. A. Robertson, “Computation of correlated color temperature and distribution temperature,” J. Opt. Soc. Am. 58, 1528–1535(1968).
    [CrossRef]
  3. N. Tsumura, “Appearance reproduction and multispectral imaging,” Color Res. Appl. 31, 270–277 (2006).
    [CrossRef]
  4. E. Angelopoulou, “Objective colour from multispectral imaging,” in Proceedings of ECCV 2000: European Conference on Computer Vision (Springer, 2000), pp. 359–374.
    [CrossRef]
  5. M. Drew and G. Finlayson, “Multispectral processing without spectra,” J. Opt. Soc. Am. A 20, 1181–1193 (2003).
    [CrossRef]
  6. D. Brainard and P. Longere, “Simulation of digital camera images from hyperspectral input,” in Vision Models and Applications to Image and Video Processing, C.van den Branden Lambrecht, ed. (Springer, 2001), http://color.psych.ucsb.edu/simchapter/index.html.
  7. P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
    [CrossRef]
  8. D. Socolinsky and L. Wolff, “Multispectral image visualization through first-order fusion,” IEEE Trans. Image Process. 11, 923–931 (2002).
    [CrossRef]
  9. M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
    [CrossRef]
  10. Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
    [CrossRef]
  11. T. Jääskeläinen and J. Parkkinen, University of Eastern Finland Color Group, http://www.multispectral.org/.
  12. J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
    [CrossRef] [PubMed]
  13. S. Bergner, M. Drew, and T. Möller, “A tool to create illuminant and reflectance spectra for light-driven graphics and visualization,” ACM Trans. Graph. 28, 5 (2009).
    [CrossRef]
  14. S. Bergner, T. Möller, M. Drew, and G. Finlayson, “Interactive spectral volume rendering,” in IEEE Visualization (IEEE, 2002), pp. 101–108, selected for proceedings cover.
  15. CIE, International Lighting Vocabulary, 4th ed., CIE-17.4-1987 (Joint publication CIE/IEC, 1987).
  16. D. Judd, “Sensibility to color-temperature change as a function of temperature,” J. Opt. Soc. Am. 23, 7–14 (1933).
    [CrossRef]
  17. C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144(1992).
    [CrossRef]
  18. C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates: erratum,” Color Res. Appl. 18, 150 (1993).
    [CrossRef]
  19. J. Hernández-Andrés, R. Lee, and J. Romero, “Calculating correlated color temperatures across the entire gamut of daylight and skylight chromaticities,” Appl. Opt. 38, 5703–5709 (1999).
    [CrossRef]
  20. Y. Ohno and M. Jergens, “Results of the intercomparison of correlated color temperature calculation,” Council for Optical Radiation Measurements, CORM Subcommittee CR3 Photometry (1999).
  21. D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
    [CrossRef]
  22. M. D. Fairchild, Color Appearance Models (Addison-Wesley, 1998).
  23. J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
    [CrossRef]
  24. J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).
  25. P. Vora and H. Trussell, “Measure of goodness of a set of color-scanning filters,” J. Opt. Soc. Am. A 10, 1499–1508 (1993).
    [CrossRef]
  26. K. Barnard, http://www.cs.sfu.ca/~colour/data/.
  27. M. S. Drew and H. R. Vaezi Jose, http://www.cs.sfu.ca/~mark/ftp/PRT/.
  28. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection (Wiley, 1987).
    [CrossRef]

2010 (1)

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

2009 (1)

S. Bergner, M. Drew, and T. Möller, “A tool to create illuminant and reflectance spectra for light-driven graphics and visualization,” ACM Trans. Graph. 28, 5 (2009).
[CrossRef]

2007 (1)

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).

2006 (1)

N. Tsumura, “Appearance reproduction and multispectral imaging,” Color Res. Appl. 31, 270–277 (2006).
[CrossRef]

2005 (1)

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

2003 (1)

2002 (1)

D. Socolinsky and L. Wolff, “Multispectral image visualization through first-order fusion,” IEEE Trans. Image Process. 11, 923–931 (2002).
[CrossRef]

2001 (1)

P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

1999 (1)

1998 (1)

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

1993 (2)

P. Vora and H. Trussell, “Measure of goodness of a set of color-scanning filters,” J. Opt. Soc. Am. A 10, 1499–1508 (1993).
[CrossRef]

C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates: erratum,” Color Res. Appl. 18, 150 (1993).
[CrossRef]

1992 (1)

C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144(1992).
[CrossRef]

1989 (1)

D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
[CrossRef]

1968 (1)

1933 (1)

Alman, D.

D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
[CrossRef]

Amira, A.

M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
[CrossRef]

Amyot, F.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Angelopoulou, E.

E. Angelopoulou, “Objective colour from multispectral imaging,” in Proceedings of ECCV 2000: European Conference on Computer Vision (Springer, 2000), pp. 359–374.
[CrossRef]

Barnard, K.

K. Barnard, http://www.cs.sfu.ca/~colour/data/.

Bergner, S.

S. Bergner, M. Drew, and T. Möller, “A tool to create illuminant and reflectance spectra for light-driven graphics and visualization,” ACM Trans. Graph. 28, 5 (2009).
[CrossRef]

S. Bergner, T. Möller, M. Drew, and G. Finlayson, “Interactive spectral volume rendering,” in IEEE Visualization (IEEE, 2002), pp. 101–108, selected for proceedings cover.

Berns, R.

D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
[CrossRef]

Bouridane, A.

M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
[CrossRef]

Brainard, D.

P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

D. Brainard and P. Longere, “Simulation of digital camera images from hyperspectral input,” in Vision Models and Applications to Image and Video Processing, C.van den Branden Lambrecht, ed. (Springer, 2001), http://color.psych.ucsb.edu/simchapter/index.html.

Chernomordik, V.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Demos, S.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Diamond, J.

M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
[CrossRef]

Drew, M.

S. Bergner, M. Drew, and T. Möller, “A tool to create illuminant and reflectance spectra for light-driven graphics and visualization,” ACM Trans. Graph. 28, 5 (2009).
[CrossRef]

M. Drew and G. Finlayson, “Multispectral processing without spectra,” J. Opt. Soc. Am. A 20, 1181–1193 (2003).
[CrossRef]

S. Bergner, T. Möller, M. Drew, and G. Finlayson, “Interactive spectral volume rendering,” in IEEE Visualization (IEEE, 2002), pp. 101–108, selected for proceedings cover.

Drew, M. S.

M. S. Drew and H. R. Vaezi Jose, http://www.cs.sfu.ca/~mark/ftp/PRT/.

Ehler, M.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Fairchild, M. D.

M. D. Fairchild, Color Appearance Models (Addison-Wesley, 1998).

Farrell, J.

P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Finlayson, G.

M. Drew and G. Finlayson, “Multispectral processing without spectra,” J. Opt. Soc. Am. A 20, 1181–1193 (2003).
[CrossRef]

S. Bergner, T. Möller, M. Drew, and G. Finlayson, “Interactive spectral volume rendering,” in IEEE Visualization (IEEE, 2002), pp. 101–108, selected for proceedings cover.

Gandjbakhche, A.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Hassan, M.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Hernández-Andrés, J.

Hitzenberger, C.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Jääskeläinen, T.

T. Jääskeläinen and J. Parkkinen, University of Eastern Finland Color Group, http://www.multispectral.org/.

Jergens, M.

Y. Ohno and M. Jergens, “Results of the intercomparison of correlated color temperature calculation,” Council for Optical Radiation Measurements, CORM Subcommittee CR3 Photometry (1999).

Judd, D.

Kainerstorfer, J.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Ke, H.

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

Lagarias, J.

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Larson, W.

D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
[CrossRef]

Lee, R.

Leroy, A. M.

P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection (Wiley, 1987).
[CrossRef]

Longere, P.

D. Brainard and P. Longere, “Simulation of digital camera images from hyperspectral input,” in Vision Models and Applications to Image and Video Processing, C.van den Branden Lambrecht, ed. (Springer, 2001), http://color.psych.ucsb.edu/simchapter/index.html.

McCamy, C.

C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates: erratum,” Color Res. Appl. 18, 150 (1993).
[CrossRef]

C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144(1992).
[CrossRef]

Miller, P.

M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
[CrossRef]

Möller, T.

S. Bergner, M. Drew, and T. Möller, “A tool to create illuminant and reflectance spectra for light-driven graphics and visualization,” ACM Trans. Graph. 28, 5 (2009).
[CrossRef]

S. Bergner, T. Möller, M. Drew, and G. Finlayson, “Interactive spectral volume rendering,” in IEEE Visualization (IEEE, 2002), pp. 101–108, selected for proceedings cover.

Ohno, Y.

Y. Ohno and M. Jergens, “Results of the intercomparison of correlated color temperature calculation,” Council for Optical Radiation Measurements, CORM Subcommittee CR3 Photometry (1999).

Parkkinen, J.

T. Jääskeläinen and J. Parkkinen, University of Eastern Finland Color Group, http://www.multispectral.org/.

Reeds, J.

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Riley, J.

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

Robertson, A.

Romero, J.

Roula, M.

M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
[CrossRef]

Rousseeuw, P. J.

P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection (Wiley, 1987).
[CrossRef]

Snyder, G.

D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
[CrossRef]

Socolinsky, D.

D. Socolinsky and L. Wolff, “Multispectral image visualization through first-order fusion,” IEEE Trans. Image Process. 11, 923–931 (2002).
[CrossRef]

Stiles, W.

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

Tietz, J.

P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

Trussell, H.

Tsumura, N.

N. Tsumura, “Appearance reproduction and multispectral imaging,” Color Res. Appl. 31, 270–277 (2006).
[CrossRef]

Vaezi Jose, H. R.

M. S. Drew and H. R. Vaezi Jose, http://www.cs.sfu.ca/~mark/ftp/PRT/.

Vora, P.

P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

P. Vora and H. Trussell, “Measure of goodness of a set of color-scanning filters,” J. Opt. Soc. Am. A 10, 1499–1508 (1993).
[CrossRef]

Wolff, L.

D. Socolinsky and L. Wolff, “Multispectral image visualization through first-order fusion,” IEEE Trans. Image Process. 11, 923–931 (2002).
[CrossRef]

Wright, M.

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Wright, P.

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Wu, Q.

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

Wyszecki, G.

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

Xie, W.

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

Zeng, L.

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

Zhang, Y.

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

Zheng, H.

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

Color Res. Appl. (1)

C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates: erratum,” Color Res. Appl. 18, 150 (1993).
[CrossRef]

ACM Trans. Graph. (1)

S. Bergner, M. Drew, and T. Möller, “A tool to create illuminant and reflectance spectra for light-driven graphics and visualization,” ACM Trans. Graph. 28, 5 (2009).
[CrossRef]

Appl. Opt. (1)

Color Res. Appl. (3)

C. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144(1992).
[CrossRef]

N. Tsumura, “Appearance reproduction and multispectral imaging,” Color Res. Appl. 31, 270–277 (2006).
[CrossRef]

D. Alman, R. Berns, G. Snyder, and W. Larson, “Performance testing of color difference metrics using a color-tolerance dataset,” Color Res. Appl. 21, 174–188 (1989).
[CrossRef]

IEEE Trans. Image Process. (2)

P. Vora, J. Farrell, J. Tietz, and D. Brainard, “Image capture: simulation of sensor responses from hyperspectral images,” IEEE Trans. Image Process. 10, 307–316 (2001).
[CrossRef]

D. Socolinsky and L. Wolff, “Multispectral image visualization through first-order fusion,” IEEE Trans. Image Process. 11, 923–931 (2002).
[CrossRef]

J. Biomed. Opt. (1)

J. Kainerstorfer, M. Ehler, F. Amyot, M. Hassan, S. Demos, V. Chernomordik, C. Hitzenberger, A. Gandjbakhche, and J. Riley, “Principal component model of multispectral data for near real-time skin chromophore mapping,” J. Biomed. Opt. 15, 046007(2010).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Proc. SPIE (1)

Q. Wu, L. Zeng, H. Ke, W. Xie, H. Zheng, and Y. Zhang, “Analysis of blood and bone marrow smears using multispectral imaging analysis techniques,” Proc. SPIE 5747, 1872–1882 (2005).
[CrossRef]

SIAM J. Optim. (2)

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

J. Lagarias, J. Reeds, M. Wright, and P. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions: erratum,” SIAM J. Optim. 18, 150 (2007).

Other (12)

M. D. Fairchild, Color Appearance Models (Addison-Wesley, 1998).

D. Brainard and P. Longere, “Simulation of digital camera images from hyperspectral input,” in Vision Models and Applications to Image and Video Processing, C.van den Branden Lambrecht, ed. (Springer, 2001), http://color.psych.ucsb.edu/simchapter/index.html.

E. Angelopoulou, “Objective colour from multispectral imaging,” in Proceedings of ECCV 2000: European Conference on Computer Vision (Springer, 2000), pp. 359–374.
[CrossRef]

Y. Ohno and M. Jergens, “Results of the intercomparison of correlated color temperature calculation,” Council for Optical Radiation Measurements, CORM Subcommittee CR3 Photometry (1999).

T. Jääskeläinen and J. Parkkinen, University of Eastern Finland Color Group, http://www.multispectral.org/.

M. Roula, J. Diamond, A. Bouridane, P. Miller, and A. Amira, “A multispectral computer vision system for automatic grading of prostatic neoplasia,” in Proceedings of the International Symposium on Biomedical Imaging (2002), pp. 193–196.
[CrossRef]

S. Bergner, T. Möller, M. Drew, and G. Finlayson, “Interactive spectral volume rendering,” in IEEE Visualization (IEEE, 2002), pp. 101–108, selected for proceedings cover.

CIE, International Lighting Vocabulary, 4th ed., CIE-17.4-1987 (Joint publication CIE/IEC, 1987).

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

K. Barnard, http://www.cs.sfu.ca/~colour/data/.

M. S. Drew and H. R. Vaezi Jose, http://www.cs.sfu.ca/~mark/ftp/PRT/.

P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection (Wiley, 1987).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

(a) Input spectrum (solid blue curve), closest Planckian according to T from Eq. (3) (dashed red curve) [ T = 9354 K ], and closest Planckian according to the best CIELAB optimization Eq. (5) (dotted–dashed magenta curve) [ T = 7617 K ]. (b) Part of input spectrum in the HVS (dashed red curve).

Fig. 2
Fig. 2

Input spectrum [solid blue curve (black in print], closest Planckian according to T from Eq. (3) (dashed red curve) [ T = 9354 K ], closest Planckian according to a DT optimization Eq. (8) (dotted–dashed magenta curve) [ T = 5378.1 K ], and best RMS error optimization Eq. (9) [solid green curve (gray in print)] [ T = 7255.6 K ].

Fig. 3
Fig. 3

The blue curve is the result of the optimization [Eq. (10)] for values of μ from 0 (emphasizing minimizing RMS spectral error) to 100 (emphasizing minimizing CIELAB error). The red (upper) ball shows the result for μ = 0 , and the green (lower) ball shows the result for an optimization for CIELAB error alone. The yellow (middle) ball shows a single representative solution (Subsection 5B). The black (lower) square shows error values using the chromaticity-based formula [Eq. (2)], and the magenta (upper) square shows values for Eq. (3).

Fig. 4
Fig. 4

Derivative value of spectral-RMS error over all multiplier values μ: the maximum derivative occurs at μ = 3 (red dashed line).

Fig. 5
Fig. 5

Input spectrum [blue (most spiked) curve] and Planckian optimization solutions over all values of multiplier μ. Green (upper) curve, best CIELAB solution [ T = 7617 K ]; red (lower) curve, best spectral-error solution [ T = 7256 K ].

Fig. 6
Fig. 6

(a) Black square, { x , y } coordinates for input spectrum; red diamond, closest to Planckian locus (dashed black curve), solution of Eq. (3); green downward triangle, best CIELAB optimization; blue star, best representative optimization. (b) Detailed view.

Fig. 7
Fig. 7

(a) CIELAB versus RMS spectral errors, for illuminant D65. (b) Range of Planckian spectrum solutions, from best CIELAB at top (green) to best spectral at bottom (red).

Fig. 8
Fig. 8

(a) Histogram of amounts by which spectral-RMS errors for 102 illuminants are less than those using Eq. (3). Red (upper) shows errors for fluorescent, and blue (lower) shows errors for nonfluorescent illuminants in both histograms. The more negative is the amount shown, the better the PRT has performed compared to the CCT. (b) Histogram of amounts by which CIELAB errors are smaller using proposed algorithm.

Tables (2)

Tables Icon

Table 1 T, I Pairs and Errors for Methods Using Eq. (3), Sections 3, 4, and Subsection 5B

Tables Icon

Table 2 Comparison of Mean CIELAB Errors and Mean RMS Errors, Collectively and Separately for Fluorescent and Nonfluorescent Lights over 102 Test Illuminants a

Equations (22)

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

P ( λ ) = k 1 λ 5 [ exp ( k 2 T λ ) 1 ] 1 ,
n = ( x x e ) / ( y y e ) , x e = 0.3320 , y e = 0.1858 , T ( x , y ) = 449 n 3 + 3525 n 2 6823.3 n + 5520.33 ,
n = ( x x e ) / ( y y e ) , x e = 0.3366 , y e = 0.1735 , T ( x , y ) = A 0 + A 1 exp ( n / t 1 ) + A 2 exp ( n / t 2 ) + A 3 exp ( n / t 3 ) ,
I = ( ( P ( λ ) ) T P ( λ ) ) 1 ( P ( λ ) ) T E ( λ ) ,
min T , I LAB P LAB E 2 .
Let     P ( T , λ ) = I · P ^ ( T , λ ) .
X Y Z E = Q T E ( λ ) , X Y Z P = Q T P ( T , λ ) ,
LAB E = CIELAB ( E ( λ ) , D 65 ) , LAB P = CIELAB ( P ( T , λ ) , D 65 ) ,
E HVS ( λ ) = Q ( Q T Q ) 1 Q T E ( λ ) ,
RMS = 100 · { [ E ( λ ) I · P ( T , λ ) ] 2 } 1 / 2 / { [ E ( λ ) ] 2 } 1 / 2 ,
min T , I [ 1 E ( λ ) I · P ( λ ) ] 2 d λ .
min T , I E ( λ ) I · P ( T , λ ) 2 .
min T , I { λ [ E ( λ ) I · P ( T , λ ) ] 2 } / { λ [ E ( λ ) ] 2 } + μ { [ LAB E LAB P ] 2 } / { [ LAB E ] 2 } ,
P ^ ( λ , T ) I k 1 λ 5 e k 2 T λ .
min I , T P ^ E 2
min I , T I = [ I λ 5 e k 2 T λ E ( λ ) ] 2 d λ .
I = [ log I 5 log λ k 2 τ λ log E ] 2 d λ .
0 1 2 I log I = [ log I 5 log λ log E k 2 τ λ ] d λ ,
log I d λ = 5 log λ d λ + log E d λ + k 2 τ λ d λ .
log I = 5 log λ ¯ + log E ¯ + ( k 2 τ λ ) ¯ .
I = { ( 5 log λ ¯ 5 log λ ) + ( log E ¯ log E ) + τ [ ( k 2 λ ) ¯ ( k 2 λ ) ] } 2 d λ ,
0 1 2 I τ = { [ ( k 2 λ ) ¯ ( k 2 λ ) ] ( 5 log λ ¯ 5 log λ + log E ¯ log E ) } d λ + τ { [ 1 ϵ ] [ ( k 2 λ ) ¯ ( k 2 λ ) ] 2 d λ } ,

Metrics