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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 11, Iss. 7 — Jul. 1, 1994
  • pp: 1970–1975

Criteria for color constancy in trichromatic bilinear models

Geoffrey Iverson and Michael D’Zmura  »View Author Affiliations

JOSA A, Vol. 11, Issue 7, pp. 1970-1975 (1994)

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We examine conditions under which the spectral properties of lights and surfaces may be recovered by a trichromatic visual system that uses bilinear models. We derive criteria for perfect recovery, formulated in terms of invariant properties of model matrices, for situations in which either two or three lights are shone sequentially on a set of surfaces.

© 1994 Optical Society of America

Original Manuscript: July 20, 1993
Revised Manuscript: January 26, 1994
Manuscript Accepted: January 26, 1994
Published: July 1, 1994

Geoffrey Iverson and Michael D’Zmura, "Criteria for color constancy in trichromatic bilinear models," J. Opt. Soc. Am. A 11, 1970-1975 (1994)

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  1. M. D’Zmura, “Color constancy: surface color from changing illumination,”J. Opt. Soc. Am. A 9, 490–493 (1992). [CrossRef]
  2. M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993). [CrossRef]
  3. M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993). [CrossRef]
  4. D. H. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992). [CrossRef] [PubMed]
  5. G. J. Iverson, M. D’Zmura, “Criteria for color constancy in trichromatic bilinear models,” presented at the Twenty-Fifth Annual Mathematical Psychology Meeting, Stanford University, Palo Alto, Calif., August 1992.
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  11. Note that our notion of decomposability is often referred to in the linear algebra literature as reducibility, e.g., P. R. Halmos, Finite-Dimensional Vector Spaces, 2nd ed. (Van Nostrand, Princeton, N.J., 1958),and S. K. Berberian, Linear Algebra (Oxford U. Press, New York, 1992).Our usage agrees with terminology used in the theory of group representations, e.g., M. Hamermesh, Group Theory and Its Application to Physical Problems (Addison-Wesley, Reading, Mass., 1962).
  12. S. Lang, Linear Algebra, 2nd ed. (Addison-Wesley, Reading, Mass., 1971).
  13. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, A. DuCroz, S. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, D. Sorensen, lapack User’s Guide (SIAM, Philadelphia, 1992).
  14. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975). [CrossRef] [PubMed]
  15. L. M. Hurvich, D. Jameson, “Some quantitative aspects of an opponent-colors theory. II. Brightness, saturation, and hue in normal and dichromatic vision,”J. Opt. Soc. Am. 45, 602–616 (1955). [CrossRef] [PubMed]
  16. G. Wyszecki, W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulas, 2nd ed. (Wiley, New York, 1982).

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