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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 9 — Sep. 1, 2013
  • pp: 1806–1813

Eigenvectors of optimal color spectra

Mika Flinkman, Hannu Laamanen, Jukka Tuomela, Pasi Vahimaa, and Markku Hauta-Kasari  »View Author Affiliations


JOSA A, Vol. 30, Issue 9, pp. 1806-1813 (2013)
http://dx.doi.org/10.1364/JOSAA.30.001806


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Abstract

Principal component analysis (PCA) and weighted PCA were applied to spectra of optimal colors belonging to the outer surface of the object-color solid or to so-called MacAdam limits. The correlation matrix formed from this data is a circulant matrix whose biggest eigenvalue is simple and the corresponding eigenvector is constant. All other eigenvalues are double, and the eigenvectors can be expressed with trigonometric functions. Found trigonometric functions can be used as a general basis to reconstruct all possible smooth reflectance spectra. When the spectral data are weighted with an appropriate weight function, the essential part of the color information is compressed to the first three components and the shapes of the first three eigenvectors correspond to one achromatic response function and to two chromatic response functions, the latter corresponding approximately to Munsell opponent-hue directions 9YR-9B and 2BG-2R.

© 2013 Optical Society of America

OCIS Codes
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.1690) Vision, color, and visual optics : Color

ToC Category:
Vision, Color, and Visual Optics

History
Original Manuscript: February 12, 2013
Revised Manuscript: June 18, 2013
Manuscript Accepted: July 29, 2013
Published: August 21, 2013

Virtual Issues
Vol. 8, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Mika Flinkman, Hannu Laamanen, Jukka Tuomela, Pasi Vahimaa, and Markku Hauta-Kasari, "Eigenvectors of optimal color spectra," J. Opt. Soc. Am. A 30, 1806-1813 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-9-1806


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References

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