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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 9 — Sep. 1, 2011
  • pp: 1954–1961

Planckian regression temperature for least spectral error and least CIELAB error

Mark S. Drew and Hamid Reza Vaezi Joze  »View Author Affiliations

JOSA A, Vol. 28, Issue 9, pp. 1954-1961 (2011)

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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

OCIS Codes
(330.1690) Vision, color, and visual optics : Color
(330.1715) Vision, color, and visual optics : Color, rendering and metamerism

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: March 28, 2011
Revised Manuscript: June 20, 2011
Manuscript Accepted: July 29, 2011
Published: August 31, 2011

Virtual Issues
Vol. 6, Iss. 10 Virtual Journal for Biomedical Optics

Mark S. Drew and Hamid Reza Vaezi Joze, "Planckian regression temperature for least spectral error and least CIELAB error," J. Opt. Soc. Am. A 28, 1954-1961 (2011)

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  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]

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