Abstract

Linear models in color constancy theory face, at least, five major problems different in nature, to be solved as a prerequisite for a satisfactory theory of the phenomenon. Solutions are proposed.

© 2007 Optical Society of America

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References

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  1. H. E. Ives, "The relation between the color of the illuminant and the color of the illuminated object," Trans. Illum. Eng. Soc. 7, 62-72 (1912).
  2. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 1982).
  3. H-C. Lee, "Method for computing the scene-illuminant chromaticity from specular highlights," J. Opt. Soc. Am. 3, 1694-1699 (1986).
    [CrossRef]
  4. D. Jameson and L. M. Hurvich, "Essay concerning color constancy," Annu. Rev. Psychol. 40, 1-22 (1989).
    [CrossRef] [PubMed]
  5. C. van Trigt, "Illuminant-dependence of von Kries type quotients," Int. J. Comput. Vis. 61, 5-30 (2005). In this paper P(λ) and p1(λ) denote the achromatic A(λ) and a(λ) here.
    [CrossRef]
  6. D. A. Forsyth, "A novel algorithm for color constancy," Int. J. Comput. Vis. 5, 5-36 (1990).
    [CrossRef]
  7. H. v. Helmholtz, Physiological Optics, J.P. C.Southall, ed. (Optical Society of America, 1924), Vol. 2.
  8. E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms (Pitman, 1979).
  9. G. Buchsbaum, "A spatial processor model for object color perception," J. Franklin Inst. 310, 1-26 (1980).
    [CrossRef]
  10. E. H. Land and J. J. McCann, "Lightness and retinex theory," J. Opt. Soc. Am. 61, 1-11 (1971).
    [CrossRef] [PubMed]
  11. G. Szegö, Orthogonal Polynomials (American Mathematical Society, 1967).
  12. C. van Trigt, "Smoothest reflectance functions. I. Definition and main results," J. Opt. Soc. Am. A 7, 2208-2222 (1990).
    [CrossRef]
  13. C. van Trigt, "Smoothest reflectance functions. II. Complete results," J. Opt. Soc. Am. A 7, 2208-2222 (1990).
    [CrossRef]
  14. C. Fox, An Introduction to the Calculus of Variations (Oxford U. Press, 1954).
  15. C. van Trigt, "Metameric blacks and estimating reflectance," J. Opt. Soc. Am. A 11, 1003-1024 (1994).
    [CrossRef]
  16. D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives (Kluwer Academic, 1991).
  17. L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small number of parameters," J. Opt. Soc. Am. A 10, 1673-1683 (1986).
    [CrossRef]
  18. D. H. Marrimont and B. A. Wandell, "Linear models of surface and illuminant spectra," J. Opt. Soc. Am. A 9, 1905-1913 (1992).
    [CrossRef]
  19. M. D'Zmura and G. Iverson, "Color constancy. I. Basic theory of two stage recovery of spectral lights for lights and surfaces," J. Opt. Soc. Am. A 10, 2148-2165 (1993).
    [CrossRef]
  20. J. M. Troost and C. M. M. de Weert, "Techniques for simulating object color under changing illuminant conditions on electronic displays," Color Res. Appl. 17, 316-327 (1992).
    [CrossRef]
  21. R. R. Goldberg, Fourier Transforms (Cambridge U. Press, 1970).
  22. N. Y. Vilenkin, Functional Analysis (Wolters-Noordhof, 1972).

2005 (1)

C. van Trigt, "Illuminant-dependence of von Kries type quotients," Int. J. Comput. Vis. 61, 5-30 (2005). In this paper P(λ) and p1(λ) denote the achromatic A(λ) and a(λ) here.
[CrossRef]

1994 (1)

1993 (1)

1992 (2)

J. M. Troost and C. M. M. de Weert, "Techniques for simulating object color under changing illuminant conditions on electronic displays," Color Res. Appl. 17, 316-327 (1992).
[CrossRef]

D. H. Marrimont and B. A. Wandell, "Linear models of surface and illuminant spectra," J. Opt. Soc. Am. A 9, 1905-1913 (1992).
[CrossRef]

1990 (3)

1989 (1)

D. Jameson and L. M. Hurvich, "Essay concerning color constancy," Annu. Rev. Psychol. 40, 1-22 (1989).
[CrossRef] [PubMed]

1986 (2)

L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small number of parameters," J. Opt. Soc. Am. A 10, 1673-1683 (1986).
[CrossRef]

H-C. Lee, "Method for computing the scene-illuminant chromaticity from specular highlights," J. Opt. Soc. Am. 3, 1694-1699 (1986).
[CrossRef]

1980 (1)

G. Buchsbaum, "A spatial processor model for object color perception," J. Franklin Inst. 310, 1-26 (1980).
[CrossRef]

1971 (1)

1912 (1)

H. E. Ives, "The relation between the color of the illuminant and the color of the illuminated object," Trans. Illum. Eng. Soc. 7, 62-72 (1912).

Buchsbaum, G.

G. Buchsbaum, "A spatial processor model for object color perception," J. Franklin Inst. 310, 1-26 (1980).
[CrossRef]

de Weert, C. M. M.

J. M. Troost and C. M. M. de Weert, "Techniques for simulating object color under changing illuminant conditions on electronic displays," Color Res. Appl. 17, 316-327 (1992).
[CrossRef]

D'Zmura, M.

Fink, A. M.

D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives (Kluwer Academic, 1991).

Forsyth, D. A.

D. A. Forsyth, "A novel algorithm for color constancy," Int. J. Comput. Vis. 5, 5-36 (1990).
[CrossRef]

Fox, C.

C. Fox, An Introduction to the Calculus of Variations (Oxford U. Press, 1954).

Goldberg, R. R.

R. R. Goldberg, Fourier Transforms (Cambridge U. Press, 1970).

Helmholtz, H. v.

H. v. Helmholtz, Physiological Optics, J.P. C.Southall, ed. (Optical Society of America, 1924), Vol. 2.

Horowitz, E.

E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms (Pitman, 1979).

Hurvich, L. M.

D. Jameson and L. M. Hurvich, "Essay concerning color constancy," Annu. Rev. Psychol. 40, 1-22 (1989).
[CrossRef] [PubMed]

Iverson, G.

Ives, H. E.

H. E. Ives, "The relation between the color of the illuminant and the color of the illuminated object," Trans. Illum. Eng. Soc. 7, 62-72 (1912).

Jameson, D.

D. Jameson and L. M. Hurvich, "Essay concerning color constancy," Annu. Rev. Psychol. 40, 1-22 (1989).
[CrossRef] [PubMed]

Land, E. H.

Lee, H-C.

H-C. Lee, "Method for computing the scene-illuminant chromaticity from specular highlights," J. Opt. Soc. Am. 3, 1694-1699 (1986).
[CrossRef]

Maloney, L. T.

L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small number of parameters," J. Opt. Soc. Am. A 10, 1673-1683 (1986).
[CrossRef]

Marrimont, D. H.

McCann, J. J.

Mitrinovic, D. S.

D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives (Kluwer Academic, 1991).

Pecaric, J. E.

D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives (Kluwer Academic, 1991).

Sahni, S.

E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms (Pitman, 1979).

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 1982).

Szegö, G.

G. Szegö, Orthogonal Polynomials (American Mathematical Society, 1967).

Troost, J. M.

J. M. Troost and C. M. M. de Weert, "Techniques for simulating object color under changing illuminant conditions on electronic displays," Color Res. Appl. 17, 316-327 (1992).
[CrossRef]

van Trigt, C.

Vilenkin, N. Y.

N. Y. Vilenkin, Functional Analysis (Wolters-Noordhof, 1972).

Wandell, B. A.

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 1982).

Annu. Rev. Psychol. (1)

D. Jameson and L. M. Hurvich, "Essay concerning color constancy," Annu. Rev. Psychol. 40, 1-22 (1989).
[CrossRef] [PubMed]

Color Res. Appl. (1)

J. M. Troost and C. M. M. de Weert, "Techniques for simulating object color under changing illuminant conditions on electronic displays," Color Res. Appl. 17, 316-327 (1992).
[CrossRef]

Int. J. Comput. Vis. (2)

C. van Trigt, "Illuminant-dependence of von Kries type quotients," Int. J. Comput. Vis. 61, 5-30 (2005). In this paper P(λ) and p1(λ) denote the achromatic A(λ) and a(λ) here.
[CrossRef]

D. A. Forsyth, "A novel algorithm for color constancy," Int. J. Comput. Vis. 5, 5-36 (1990).
[CrossRef]

J. Franklin Inst. (1)

G. Buchsbaum, "A spatial processor model for object color perception," J. Franklin Inst. 310, 1-26 (1980).
[CrossRef]

J. Opt. Soc. Am. (2)

H-C. Lee, "Method for computing the scene-illuminant chromaticity from specular highlights," J. Opt. Soc. Am. 3, 1694-1699 (1986).
[CrossRef]

E. H. Land and J. J. McCann, "Lightness and retinex theory," J. Opt. Soc. Am. 61, 1-11 (1971).
[CrossRef] [PubMed]

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

Trans. Illum. Eng. Soc. (1)

H. E. Ives, "The relation between the color of the illuminant and the color of the illuminated object," Trans. Illum. Eng. Soc. 7, 62-72 (1912).

Other (8)

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, 1982).

G. Szegö, Orthogonal Polynomials (American Mathematical Society, 1967).

C. Fox, An Introduction to the Calculus of Variations (Oxford U. Press, 1954).

D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives (Kluwer Academic, 1991).

H. v. Helmholtz, Physiological Optics, J.P. C.Southall, ed. (Optical Society of America, 1924), Vol. 2.

E. Horowitz and S. Sahni, Fundamentals of Computer Algorithms (Pitman, 1979).

R. R. Goldberg, Fourier Transforms (Cambridge U. Press, 1970).

N. Y. Vilenkin, Functional Analysis (Wolters-Noordhof, 1972).

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Equations (24)

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R ( λ , λ ) = 1 N k = 1 N ρ k ( λ ) ρ k ( λ ) .
ρ ( λ ) [ d h d λ ] d λ = [ d ρ d λ ] h ( λ ) d λ .
ρ e ( λ ) S e ( λ ) [ x ( λ ) , y ( λ ) , z ( λ ) ] d λ = ρ ( λ ) S ( λ ) [ x ( λ ) , y ( λ ) , z ( λ ) ] d λ ,
V ( ρ e ) = [ d ρ e d λ ] 2 d λ .
d ρ e d λ = C j = 1 3 μ j f j ( λ ) ,
[ f 1 ( λ ) , f 2 ( λ ) , f 3 ( λ ) ] = λ b λ [ x ( λ ) X 0 , y ( λ ) Y 0 , z ( λ ) Z 0 ] S e ( λ ) d λ ,
λ j 1 λ j [ ρ ( λ ) ρ e ( λ ) ] 2 d λ ( λ j λ j 1 ) 2 π 2 λ j 1 λ j [ d ρ d λ d ρ e d λ ] 2 d λ ,
ρ ( λ ) = ρ ( λ e ) + ( λ λ e ) [ ρ ( λ e ) ρ ( λ b ) ] ( λ e λ b ) ,
ρ ( λ ) S ( λ ) A ( λ ) d λ ρ ( λ ) A ( λ ) d λ S ( λ ) A ( λ ) d λ = Q ( ρ , S ) .
( λ λ c ) 2 A ( λ ) d λ .
d a d λ = ( λ c λ ) A ( λ ) ; a ( λ b ) = 0 .
a ( λ ) d λ = ( λ λ c ) 2 A ( λ ) d λ .
S ( λ c ) S ( λ ) = ( λ c λ ) [ d S d λ ] + λ c λ ( λ λ c ) [ d 2 S d λ 2 ] d λ ,
Q ( ρ , S ) = a ( λ ) [ d ρ d λ ] [ d S d λ ] d λ Q r ( ρ , S ) ,
Q ( ρ , S ) [ ( λ e λ b ) 2 V ( ρ ) V ( S ) ] 1 2 a ( λ ) d λ ( λ e λ b ) 2 .
X 1 X 2 ρ ( λ ) S 1 ( λ ) S 2 ( λ ) x ( λ ) d λ ε X .
ρ ( λ ) = ρ e ( λ ) + r ( λ ) ,
r ( λ ) S ( λ ) z ( λ ) d λ = 0 ,
exp [ i k λ b ] r ( λ ) exp [ i k λ ] E ( λ ) z ( λ ) d λ = 0 , for all k .
ρ ( λ ) B ( λ ) d λ = ρ e ( λ ) B ( λ ) d λ + r ( λ ) B ( λ ) d λ
[ ρ e ( λ ) A ( λ ) d λ ρ ( λ ) A ( λ ) d λ ] S ( λ ) A ( λ ) d λ = Q ( ρ , S ) Q ( ρ e , S e ) .
X X 0 = ρ e ( λ ) [ d f 1 d λ ] d λ = ρ e ( λ e ) [ d ρ e d λ ] f 1 ( λ ) d λ ,
ρ ( λ b ) = ρ ( λ e ) + C ( λ b λ e ) + 1 3 μ j f j ( λ ) d λ .
( [ d ρ d λ ] [ d ρ e d λ ] ) f j ( λ ) d λ = 0 .

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