Abstract

We present criticism of signal-processing arguments recently used to explain the trichromacy of color vision. In particular, we note that illuminant spectral power distributions (SPD’s) can be metameric even when the signal-processing arguments state that trichromatic vision represents such SPD’s without ambiguity. Being statistical in nature, these arguments need not apply to each individual SPD; however, further use of the arguments calls for attributing them to some ensemble of SPD’s and then testing whether the ensemble satisfies the underlying statistical assumptions.

© 1985 Optical Society of America

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References

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  1. H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–644 (1982).
    [CrossRef] [PubMed]
  2. G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
    [CrossRef]
  3. G. Buchsbaum, A. Gottschalk, “Chromaticity coordinates of frequency-limited functions,” J. Opt. Soc. Am. A 1, 885–887 (1984).
    [CrossRef] [PubMed]
  4. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978), pp. 189–194.
  5. H. Van Trees, Detection, Estimation, and Modulation Theory, Vol. I (Wiley, New York, 1968), p. 192.
  6. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [CrossRef]
  7. G. Buchsbaum, “The chromaticity coordinates of frequency-limited functions: erratum,” J. Opt. Soc. Am. A 2, 95 (1985).
    [CrossRef]
  8. Over appropriate ϕ domains, sinusoidal SPD’s with low values of f are nonnegative over x ∈[a, b] for values of m that violate the constraint m≤ 1. For example, sometimes m≥ 0 is sufficient to ensure that S(x) ≥ 0 over [a, b].
  9. H. Wolter, “Physikalische Begriindung eines Farbenkreises und Anzätze einer physikalischen Farbenlehre,” Ann. Phys. (Leipzig) Ser. 6 8, 11–29 (1950).
    [CrossRef]
  10. M. H. Brill, T. Benzsehawel, “Spectral phase modulation transfer function as a test for models of color vision,” J. Opt. Soc. Am. 72, 1741 (A) (1982). Note that on line 5, “where” should be changed to “else.”

1985 (1)

1984 (1)

1983 (1)

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[CrossRef]

1982 (2)

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–644 (1982).
[CrossRef] [PubMed]

M. H. Brill, T. Benzsehawel, “Spectral phase modulation transfer function as a test for models of color vision,” J. Opt. Soc. Am. 72, 1741 (A) (1982). Note that on line 5, “where” should be changed to “else.”

1964 (1)

1950 (1)

H. Wolter, “Physikalische Begriindung eines Farbenkreises und Anzätze einer physikalischen Farbenlehre,” Ann. Phys. (Leipzig) Ser. 6 8, 11–29 (1950).
[CrossRef]

Barlow, H. B.

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–644 (1982).
[CrossRef] [PubMed]

Benzsehawel, T.

M. H. Brill, T. Benzsehawel, “Spectral phase modulation transfer function as a test for models of color vision,” J. Opt. Soc. Am. 72, 1741 (A) (1982). Note that on line 5, “where” should be changed to “else.”

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978), pp. 189–194.

Brill, M. H.

M. H. Brill, T. Benzsehawel, “Spectral phase modulation transfer function as a test for models of color vision,” J. Opt. Soc. Am. 72, 1741 (A) (1982). Note that on line 5, “where” should be changed to “else.”

Buchsbaum, G.

Gottschalk, A.

G. Buchsbaum, A. Gottschalk, “Chromaticity coordinates of frequency-limited functions,” J. Opt. Soc. Am. A 1, 885–887 (1984).
[CrossRef] [PubMed]

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[CrossRef]

Judd, D. B.

MacAdam, D. L.

Van Trees, H.

H. Van Trees, Detection, Estimation, and Modulation Theory, Vol. I (Wiley, New York, 1968), p. 192.

Wolter, H.

H. Wolter, “Physikalische Begriindung eines Farbenkreises und Anzätze einer physikalischen Farbenlehre,” Ann. Phys. (Leipzig) Ser. 6 8, 11–29 (1950).
[CrossRef]

Wyszecki, G.

Ann. Phys. (Leipzig) Ser. 6 (1)

H. Wolter, “Physikalische Begriindung eines Farbenkreises und Anzätze einer physikalischen Farbenlehre,” Ann. Phys. (Leipzig) Ser. 6 8, 11–29 (1950).
[CrossRef]

J. Opt. Soc. Am. (2)

M. H. Brill, T. Benzsehawel, “Spectral phase modulation transfer function as a test for models of color vision,” J. Opt. Soc. Am. 72, 1741 (A) (1982). Note that on line 5, “where” should be changed to “else.”

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[CrossRef]

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

Proc. R. Soc. London Ser. B (1)

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colours coding and optimum colour information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[CrossRef]

Vision Res. (1)

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–644 (1982).
[CrossRef] [PubMed]

Other (3)

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, New York, 1978), pp. 189–194.

H. Van Trees, Detection, Estimation, and Modulation Theory, Vol. I (Wiley, New York, 1968), p. 192.

Over appropriate ϕ domains, sinusoidal SPD’s with low values of f are nonnegative over x ∈[a, b] for values of m that violate the constraint m≤ 1. For example, sometimes m≥ 0 is sufficient to ensure that S(x) ≥ 0 over [a, b].

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Figures (1)

Fig. 1
Fig. 1

Loci of chromaticities of fully modulated (i.e., m = 1.0) sinusoidal illuminant spectral power distributions as functions of phase (0 ≤ ϕ ≤ 2π) for spectral frequencies of 0.00333, 0.00422, and 0.00500 cycle/nm.

Equations (6)

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

S ( x ) = E 0 [ 1 + m sin ( 2 π f x + ϕ ) ] for a x b , else S ( x ) = 0 .
K ( x 1 , x 2 ) = ψ ( x 1 ) ψ ( x 2 ) ψ ( x 1 ) ψ ( x 2 ) = P [ sin α ( x 1 x 2 ) α ( x 1 x 2 ) ] ,
Q j = E 0 [ q j ( x ) + m q j ( x ) cos 2 π f x × sin ϕ + m q j ( x ) sin 2 π f x cos ϕ ] ,
Q = E 0 A [ 1 m sin ϕ m cos ϕ ] ,
Q = E 0 [ 1 m sin ϕ m cos ϕ ] = [ Q 1 Q 2 Q 3 ] .
S ( x ) = E 0 [ F ( x ) + G ( x ) sin ϕ + H ( x ) cos ϕ ] .

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