Abstract

In color theory and perceptual practice, two color naming combinations are forbidden—reddish greens and bluish yellows—however, when multicolored images are stabilized on the retina, their borders fade and filling-in mechanisms can create forbidden colors. The sole report of such events found that only some observers saw forbidden colors, while others saw illusory multicolored patterns. We found that when colors were equiluminant, subjects saw reddish greens, bluish yellows, or a multistable spatial color exchange (an entirely novel perceptual phenomena); when the colors were nonequiluminant, subjects saw spurious pattern formation. To make sense of color opponency violations, we created a soft-wired model of cortical color opponency (based on winner-take-all competition) whose opponency can be disabled.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. D. Crane, T. P. Piantanida, “On seeing reddish green and yellowish blue,” Science 221, 1078–1080 (1983).
    [CrossRef] [PubMed]
  2. For a review see P. Cavanagh, “Vision at equiluminance,” in Limits of Vision, Vol. 5 of Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, I. J. Murray, eds. (CRC Press, Boca Raton, Fla., 1991), pp. 234–250.
  3. R. L. De Valois, K. K. De Valois, “A multistage vision model,” Vision Res. 33, 1053–1065 (1993).
    [CrossRef] [PubMed]
  4. N. C. Cottaris, R. L. De Valois, “Temporal dynamics of chromatic tuning in macaque primary visual cortex,” Nature 395, 896–900 (1998).
    [CrossRef] [PubMed]
  5. V. A. Billock, “A chaos theory approach to some intractable problems in color vision,” Invest. Ophthalmol. Visual Sci. 38, 254 (1997).
  6. V. A. Billock, A. J. Vingrys, P. E. King-Smith, “Opponent color detection threshold asymmetries may result from reduction of ganglion cell subpopulations,” Visual Neurosci. 11, 99–109 (1994).
    [CrossRef]
  7. R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
    [CrossRef] [PubMed]
  8. Stabilized images often fragment upon stabilization; the fragments fade and revive in groupings that obey Gestalt-like laws. R. M. Prichard, W. Heron, D. O. Hebb, “Visual perception approached by the method of stabilized images,” Can. J. Psychol. 14, 67–77 (1960).
    [CrossRef]
  9. S. L. Buck, F. Frome, R. M. Boynton, “Initial distinctness and subsequent fading of minimally distinct borders,” J. Opt. Soc. Am. 67, 1126–1128 (1977).
    [CrossRef]
  10. D. H. Kelly, “Disappearance of stabilized chromatic gratings,” Science 214, 1257–1258 (1981).
    [CrossRef] [PubMed]
  11. We used a Generation 5 dual Purkinje image eye tracker (Fourward Technologies, El Cajon, Calif.), which transduces moving infrared reflections from cornea and lens. This signal is fed back to a servo-driven mirror to stabilize the image of a stimulus reflected therein (see Ref. 1). The primary subjects were two of the authors, but five additional observers, including outside color researchers, also participated. Because Ref. 1 reported difficulty characterizing non-Hering colors, we used only extremely experienced observers (all but one—a doctoral candidate in color vision—are professional psychophysicists). All subjects had normal color vision (gauged by anomaloscope and F2 tritan test plates). Experiments were in accord with U.S. Air Force human-use protocols. Subjects were fixed by forehead and chin rests, with their left eyes patched and their right pupils dilated by 1 drop of 1% Tropicamide to facilitate tracking of the 4th Purkinje image. Red/green and blue/yellow bipartite fields were presented on a photometrically and colorimetrically calibrated VisionWorks (VRG, Inc., Durham, NH) display system. The two sides of the field could be equated for luminance by flicker photometry. The standard red field had CIE chromaticity coordinates of (0.631, 0.338) and a CIE luminance of 13.8 cd/m2. The green field flicker matched to it had coordinates (0.287, 0.604). The blue field was (0.151, 0.061) and had a luminance of 8 cd/m2(the maximum available). The yellow field flicker matched to it consisted of equal mixtures of the red and green guns. Its CIE coordinates were (0.393, 0.525), which is considered a greenish-yellow location in CIE space but which appeared golden under experimental conditions. Refractive error and monitor distance were optically compensated. To achieve stabilization, subjects controlled mirror deflection circuit gain. Stabilization was checked by observations of eye movement effects on the position of colored borders relative to the unstabilized aperture. As in Ref. 1, the stabilized bipartite fields were viewed through unstabilized vertical occluders to reduce the incidence of image fading (which is otherwise severe). The visible stimulus subtended 14° horizontal×24° vertical.
  12. The transparency effects are reminiscent of superimposition effects sometimes seen in binocular color mixtures (two subjects report luster effects similar to binocular luster). J. Hovis, “Review of dichoptic color mixing,” Optom. Vision Sci. 66, 181–190 (1989).
    [CrossRef]
  13. The gradient effect is seen for steadily fixated color pairs whose border stimulates only S cones. B. W. Tansley, R. M. Boynton, “A line, not a space, represents visual distinctness of borders formed by different colors,” J. Opt. Soc. Am. 71, 145–150 (1981). However, we found that gradients can be produced from any pair of equiluminous colors if stabilized.
  14. Although image stabilization often induces gradual fading, most of our subjects (6 out of 7) reported simultaneously binocular abrupt transitions to pitch blackness or to complete loss of any visual sense; one psychophysicist characterized it as like the optic nerve being cut; another compared it with the visual blackout that accompanies manual carotid strangulation in the martial arts. This strikingly unnatural phenomenon is believed to be mediated by central mechanisms. R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, UK, 1973).
  15. D. Hume, Treatise on Human Nature (Oxford U. Press, Oxford, UK, 1739/1955).
  16. O. W. Sacks, An Anthropologist on Mars: Seven Paradoxical Tales (Vintage, New York, 1995).
  17. One rationale for low-pass filtering (pooling) and rectification can be found in demultiplexing theory: V. A. Billock, “Cortical simple cells can extract achromatic information from the multiplexed chromatic and achromatic signals in the parvocellular pathway,” Vision Res. 35, 2359–2369 (1995). Other evidence is found in psychophysical data of subjects with low ganglion cell densities (Ref. 6). See Ref. 3 for a different but related approach.
    [CrossRef] [PubMed]
  18. V. A. Billock, “Consequences of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996).
    [CrossRef] [PubMed]
  19. P. E. Lennie, P. W. Haake, D. R. Williams, “The design of chromatically opponent receptive fields,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 71–82.
  20. S. Zeki, “Color coding in the cerebral cortex,” Neuroscience (N.Y.) 9, 741–756 (1983).
    [CrossRef]
  21. H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
    [PubMed]
  22. P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).
  23. This is a highly modified version of the Lotka–Volterra population dynamics model; for review see S. Grossberg, “Nonlinear neural networks,” Neural Networks 1, 17–61 (1988).
    [CrossRef]
  24. H. R. Wilson, Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience (Oxford U. Press, Oxford, UK, 1999).
  25. Data of D. Jameson, L. M. Hurvich, “Some quantitative aspects of an opponent-colors theory. I. Chromatic responses and spectral saturation,” J. Opt. Soc. Am. 45, 546–552 (1955), digitized from Ref. 26. Cone fundamentals from Ref. 27. Equations (4)–(6) were integrated using an adaptive fourth-order Runge–Kutta routine (Scientist, MicroMath Research, Salt Lake City, UT) and fitted to the average of Jameson and Hurvich’s data. The fit was done in ascending steps of 10 nm, with an adaptive integration step size between increments. Parameters a, d, and h were determined by linear stability analysis; the remaining six parameters were fit by least squares (see Table 1). No physiological significance should be vested in their values; they are not a unique solution, nor are they likely to be a global minimum, and are strictly of illustrative value.
    [CrossRef]
  26. J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. I. Red/green equilibria,” Vision Res. 14, 1127–1140 (1974).
    [CrossRef] [PubMed]
  27. A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
    [CrossRef]
  28. For example Eq. 4 could be modified to  ∂ωR/∂t=ωR[LC*(λ)-(aωR+bωG+cωv)]+DR(∂2ωR/∂x2+∂2ωR/∂y2), a Lotka–Volterra (LV) version of a reaction–diffusion (RD) equation. We take diffusion to be the prototypical filling-in mechanism (see Refs. 29 and 30). Both RD and diffusive LV systems are capable of spatiotemporal pattern formation (morphogenesis) for some parameterizations (in general, ωR,ωG,ωV would need different diffusion rates or asymmetrical coupling, or cross diffusion). Such models give rise to transient or stable stationary spatial structures.A. Okubo, Diffusion and Ecological Problems: Mathematical Models (Springer, Berlin, 1980).
  29. A. A. Baloch, S. Grossberg, “A neural model of high level motion processing,” Vision Res. 37, 3037–3059 (1997).
    [CrossRef]
  30. A good physical analogy is two separated reservoirs respectively filled with infinite supplies of red and green ink (at fixed concentrations). If connected by a long clear pipe, Eqs. (9) and (10) give the concentrations of red and green ink along the length of the pipe (at steady state). At steady state, the values of the diffusion rate constants are irrelevant. For a brief discussion of related issues see J. M. Smith, Mathematical Ideas in Biology (Cambridge U. Press, Cambridge, UK, 1971).
  31. R. T. Eskew, “The gap effect revisited: Slow changes in chromatic sensitivity as affected by luminance and chromatic borders,” Vision Res. 29, 717–729 (1989).
    [CrossRef] [PubMed]
  32. For a review of related models of drug- and migraine-induced geometric hallucinations see O. W. Sacks, R. M. Siegal, “Migraine aura and hallucinatory constants,” in Migraine, O. W. Sacks, ed. (Picador, London, 1992), pp. 273–297.
  33. We can however speculate. Niebur et al.’s model of competition interactions uses frequency-gated inhibition; e.g., there is no inhibition unless the neural activity into the inhibitory mechanism falls within a particular spike rate (centered around gamma-band spike rates in the Niebur et al. model). E. Niebur, C. Koch, C. Rosin, “An oscillation-based model for the neuronal basis of attention,” Vision Res. 33, 2789–2802 (1993). It is an interesting coincidence that during image stabilization, when stabilized images fade or fragment, the power ratio of alpha rhythm to higher-frequency components in the electroencephalogram (EEG) drastically increases just before and during image fading or fragmentation and wanes when images reappear (see Refs. 34 and 35). Why this happens is unclear, but if stabilization somehow eliminates higher-frequency neural activity, then it should also be expected to eliminate frequency-gated cortical competition. Such an analysis depends on drawing a tighter relationship between EEG spectra and the neural activity in specific cortical units [like those modeled in Eq. (4)–(6)] than we currently can.
    [CrossRef] [PubMed]
  34. D. Lehmann, G. W. Beeler, D. H. Fender, “Changes in patterns of the human electroencephalogram during fluctuations of perception of stabilized retinal images,” Electroencephalogr. Clin. Neurophysiol. 19, 336–343 (1965).
    [CrossRef] [PubMed]
  35. U. T. Keesey, D. J. Nichols, “Fluctuations in target visibility as related to the alpha component of the electroencephalogram,” Vision Res. 7, 859–879 (1967).
    [CrossRef]
  36. T. Poggio, E. B. Gamble, L. T. Little, “Parallel integration of visual modules,” Science 242, 436–440 (1988).
    [CrossRef] [PubMed]
  37. M. Barinaga, “Listening in on the brain,” Science 280, 376–378 (1998).
    [CrossRef] [PubMed]

1998 (3)

N. C. Cottaris, R. L. De Valois, “Temporal dynamics of chromatic tuning in macaque primary visual cortex,” Nature 395, 896–900 (1998).
[CrossRef] [PubMed]

P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).

M. Barinaga, “Listening in on the brain,” Science 280, 376–378 (1998).
[CrossRef] [PubMed]

1997 (3)

A. A. Baloch, S. Grossberg, “A neural model of high level motion processing,” Vision Res. 37, 3037–3059 (1997).
[CrossRef]

V. A. Billock, “A chaos theory approach to some intractable problems in color vision,” Invest. Ophthalmol. Visual Sci. 38, 254 (1997).

R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
[CrossRef] [PubMed]

1996 (1)

V. A. Billock, “Consequences of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996).
[CrossRef] [PubMed]

1995 (1)

One rationale for low-pass filtering (pooling) and rectification can be found in demultiplexing theory: V. A. Billock, “Cortical simple cells can extract achromatic information from the multiplexed chromatic and achromatic signals in the parvocellular pathway,” Vision Res. 35, 2359–2369 (1995). Other evidence is found in psychophysical data of subjects with low ganglion cell densities (Ref. 6). See Ref. 3 for a different but related approach.
[CrossRef] [PubMed]

1994 (1)

V. A. Billock, A. J. Vingrys, P. E. King-Smith, “Opponent color detection threshold asymmetries may result from reduction of ganglion cell subpopulations,” Visual Neurosci. 11, 99–109 (1994).
[CrossRef]

1993 (3)

R. L. De Valois, K. K. De Valois, “A multistage vision model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef] [PubMed]

A. Stockman, D. I. A. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[CrossRef]

We can however speculate. Niebur et al.’s model of competition interactions uses frequency-gated inhibition; e.g., there is no inhibition unless the neural activity into the inhibitory mechanism falls within a particular spike rate (centered around gamma-band spike rates in the Niebur et al. model). E. Niebur, C. Koch, C. Rosin, “An oscillation-based model for the neuronal basis of attention,” Vision Res. 33, 2789–2802 (1993). It is an interesting coincidence that during image stabilization, when stabilized images fade or fragment, the power ratio of alpha rhythm to higher-frequency components in the electroencephalogram (EEG) drastically increases just before and during image fading or fragmentation and wanes when images reappear (see Refs. 34 and 35). Why this happens is unclear, but if stabilization somehow eliminates higher-frequency neural activity, then it should also be expected to eliminate frequency-gated cortical competition. Such an analysis depends on drawing a tighter relationship between EEG spectra and the neural activity in specific cortical units [like those modeled in Eq. (4)–(6)] than we currently can.
[CrossRef] [PubMed]

1992 (1)

H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
[PubMed]

1989 (2)

The transparency effects are reminiscent of superimposition effects sometimes seen in binocular color mixtures (two subjects report luster effects similar to binocular luster). J. Hovis, “Review of dichoptic color mixing,” Optom. Vision Sci. 66, 181–190 (1989).
[CrossRef]

R. T. Eskew, “The gap effect revisited: Slow changes in chromatic sensitivity as affected by luminance and chromatic borders,” Vision Res. 29, 717–729 (1989).
[CrossRef] [PubMed]

1988 (2)

T. Poggio, E. B. Gamble, L. T. Little, “Parallel integration of visual modules,” Science 242, 436–440 (1988).
[CrossRef] [PubMed]

This is a highly modified version of the Lotka–Volterra population dynamics model; for review see S. Grossberg, “Nonlinear neural networks,” Neural Networks 1, 17–61 (1988).
[CrossRef]

1983 (2)

S. Zeki, “Color coding in the cerebral cortex,” Neuroscience (N.Y.) 9, 741–756 (1983).
[CrossRef]

H. D. Crane, T. P. Piantanida, “On seeing reddish green and yellowish blue,” Science 221, 1078–1080 (1983).
[CrossRef] [PubMed]

1981 (2)

1977 (1)

1974 (1)

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. I. Red/green equilibria,” Vision Res. 14, 1127–1140 (1974).
[CrossRef] [PubMed]

1967 (1)

U. T. Keesey, D. J. Nichols, “Fluctuations in target visibility as related to the alpha component of the electroencephalogram,” Vision Res. 7, 859–879 (1967).
[CrossRef]

1965 (1)

D. Lehmann, G. W. Beeler, D. H. Fender, “Changes in patterns of the human electroencephalogram during fluctuations of perception of stabilized retinal images,” Electroencephalogr. Clin. Neurophysiol. 19, 336–343 (1965).
[CrossRef] [PubMed]

1960 (1)

Stabilized images often fragment upon stabilization; the fragments fade and revive in groupings that obey Gestalt-like laws. R. M. Prichard, W. Heron, D. O. Hebb, “Visual perception approached by the method of stabilized images,” Can. J. Psychol. 14, 67–77 (1960).
[CrossRef]

1955 (1)

Baloch, A. A.

A. A. Baloch, S. Grossberg, “A neural model of high level motion processing,” Vision Res. 37, 3037–3059 (1997).
[CrossRef]

Barinaga, M.

M. Barinaga, “Listening in on the brain,” Science 280, 376–378 (1998).
[CrossRef] [PubMed]

Beeler, G. W.

D. Lehmann, G. W. Beeler, D. H. Fender, “Changes in patterns of the human electroencephalogram during fluctuations of perception of stabilized retinal images,” Electroencephalogr. Clin. Neurophysiol. 19, 336–343 (1965).
[CrossRef] [PubMed]

Billock, V. A.

V. A. Billock, “A chaos theory approach to some intractable problems in color vision,” Invest. Ophthalmol. Visual Sci. 38, 254 (1997).

V. A. Billock, “Consequences of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996).
[CrossRef] [PubMed]

One rationale for low-pass filtering (pooling) and rectification can be found in demultiplexing theory: V. A. Billock, “Cortical simple cells can extract achromatic information from the multiplexed chromatic and achromatic signals in the parvocellular pathway,” Vision Res. 35, 2359–2369 (1995). Other evidence is found in psychophysical data of subjects with low ganglion cell densities (Ref. 6). See Ref. 3 for a different but related approach.
[CrossRef] [PubMed]

V. A. Billock, A. J. Vingrys, P. E. King-Smith, “Opponent color detection threshold asymmetries may result from reduction of ganglion cell subpopulations,” Visual Neurosci. 11, 99–109 (1994).
[CrossRef]

Boynton, R. M.

Buck, S. L.

Cavanagh, P.

For a review see P. Cavanagh, “Vision at equiluminance,” in Limits of Vision, Vol. 5 of Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, I. J. Murray, eds. (CRC Press, Boca Raton, Fla., 1991), pp. 234–250.

Cicerone, C. M.

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. I. Red/green equilibria,” Vision Res. 14, 1127–1140 (1974).
[CrossRef] [PubMed]

Cottaris, N. C.

N. C. Cottaris, R. L. De Valois, “Temporal dynamics of chromatic tuning in macaque primary visual cortex,” Nature 395, 896–900 (1998).
[CrossRef] [PubMed]

Crane, H. D.

H. D. Crane, T. P. Piantanida, “On seeing reddish green and yellowish blue,” Science 221, 1078–1080 (1983).
[CrossRef] [PubMed]

De Valois, K. K.

R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
[CrossRef] [PubMed]

R. L. De Valois, K. K. De Valois, “A multistage vision model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef] [PubMed]

De Valois, R. L.

N. C. Cottaris, R. L. De Valois, “Temporal dynamics of chromatic tuning in macaque primary visual cortex,” Nature 395, 896–900 (1998).
[CrossRef] [PubMed]

R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
[CrossRef] [PubMed]

R. L. De Valois, K. K. De Valois, “A multistage vision model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef] [PubMed]

Ditchburn, R. W.

Although image stabilization often induces gradual fading, most of our subjects (6 out of 7) reported simultaneously binocular abrupt transitions to pitch blackness or to complete loss of any visual sense; one psychophysicist characterized it as like the optic nerve being cut; another compared it with the visual blackout that accompanies manual carotid strangulation in the martial arts. This strikingly unnatural phenomenon is believed to be mediated by central mechanisms. R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, UK, 1973).

Eskew, R. T.

R. T. Eskew, “The gap effect revisited: Slow changes in chromatic sensitivity as affected by luminance and chromatic borders,” Vision Res. 29, 717–729 (1989).
[CrossRef] [PubMed]

Fender, D. H.

D. Lehmann, G. W. Beeler, D. H. Fender, “Changes in patterns of the human electroencephalogram during fluctuations of perception of stabilized retinal images,” Electroencephalogr. Clin. Neurophysiol. 19, 336–343 (1965).
[CrossRef] [PubMed]

Friedman, H.

P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).

Frome, F.

Gamble, E. B.

T. Poggio, E. B. Gamble, L. T. Little, “Parallel integration of visual modules,” Science 242, 436–440 (1988).
[CrossRef] [PubMed]

Grossberg, S.

A. A. Baloch, S. Grossberg, “A neural model of high level motion processing,” Vision Res. 37, 3037–3059 (1997).
[CrossRef]

This is a highly modified version of the Lotka–Volterra population dynamics model; for review see S. Grossberg, “Nonlinear neural networks,” Neural Networks 1, 17–61 (1988).
[CrossRef]

Haake, P. W.

P. E. Lennie, P. W. Haake, D. R. Williams, “The design of chromatically opponent receptive fields,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 71–82.

Hebb, D. O.

Stabilized images often fragment upon stabilization; the fragments fade and revive in groupings that obey Gestalt-like laws. R. M. Prichard, W. Heron, D. O. Hebb, “Visual perception approached by the method of stabilized images,” Can. J. Psychol. 14, 67–77 (1960).
[CrossRef]

Heron, W.

Stabilized images often fragment upon stabilization; the fragments fade and revive in groupings that obey Gestalt-like laws. R. M. Prichard, W. Heron, D. O. Hebb, “Visual perception approached by the method of stabilized images,” Can. J. Psychol. 14, 67–77 (1960).
[CrossRef]

Hovis, J.

The transparency effects are reminiscent of superimposition effects sometimes seen in binocular color mixtures (two subjects report luster effects similar to binocular luster). J. Hovis, “Review of dichoptic color mixing,” Optom. Vision Sci. 66, 181–190 (1989).
[CrossRef]

Hume, D.

D. Hume, Treatise on Human Nature (Oxford U. Press, Oxford, UK, 1739/1955).

Hurvich, L. M.

Ideura, Y.

H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
[PubMed]

Jameson, D.

Johnson, N. E.

Kaji, S.

H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
[PubMed]

Kaloudis, P.

P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).

Keesey, U. T.

U. T. Keesey, D. J. Nichols, “Fluctuations in target visibility as related to the alpha component of the electroencephalogram,” Vision Res. 7, 859–879 (1967).
[CrossRef]

Kelly, D. H.

D. H. Kelly, “Disappearance of stabilized chromatic gratings,” Science 214, 1257–1258 (1981).
[CrossRef] [PubMed]

King-Smith, P. E.

V. A. Billock, A. J. Vingrys, P. E. King-Smith, “Opponent color detection threshold asymmetries may result from reduction of ganglion cell subpopulations,” Visual Neurosci. 11, 99–109 (1994).
[CrossRef]

Koch, C.

We can however speculate. Niebur et al.’s model of competition interactions uses frequency-gated inhibition; e.g., there is no inhibition unless the neural activity into the inhibitory mechanism falls within a particular spike rate (centered around gamma-band spike rates in the Niebur et al. model). E. Niebur, C. Koch, C. Rosin, “An oscillation-based model for the neuronal basis of attention,” Vision Res. 33, 2789–2802 (1993). It is an interesting coincidence that during image stabilization, when stabilized images fade or fragment, the power ratio of alpha rhythm to higher-frequency components in the electroencephalogram (EEG) drastically increases just before and during image fading or fragmentation and wanes when images reappear (see Refs. 34 and 35). Why this happens is unclear, but if stabilization somehow eliminates higher-frequency neural activity, then it should also be expected to eliminate frequency-gated cortical competition. Such an analysis depends on drawing a tighter relationship between EEG spectra and the neural activity in specific cortical units [like those modeled in Eq. (4)–(6)] than we currently can.
[CrossRef] [PubMed]

Komatsu, H.

H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
[PubMed]

Krantz, D. H.

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. I. Red/green equilibria,” Vision Res. 14, 1127–1140 (1974).
[CrossRef] [PubMed]

Larimer, J.

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. I. Red/green equilibria,” Vision Res. 14, 1127–1140 (1974).
[CrossRef] [PubMed]

Lehmann, D.

D. Lehmann, G. W. Beeler, D. H. Fender, “Changes in patterns of the human electroencephalogram during fluctuations of perception of stabilized retinal images,” Electroencephalogr. Clin. Neurophysiol. 19, 336–343 (1965).
[CrossRef] [PubMed]

Lennie, P. E.

P. E. Lennie, P. W. Haake, D. R. Williams, “The design of chromatically opponent receptive fields,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 71–82.

Little, L. T.

T. Poggio, E. B. Gamble, L. T. Little, “Parallel integration of visual modules,” Science 242, 436–440 (1988).
[CrossRef] [PubMed]

MacLeod, D. I. A.

Mahon, L.

R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
[CrossRef] [PubMed]

Nichols, D. J.

U. T. Keesey, D. J. Nichols, “Fluctuations in target visibility as related to the alpha component of the electroencephalogram,” Vision Res. 7, 859–879 (1967).
[CrossRef]

Niebur, E.

We can however speculate. Niebur et al.’s model of competition interactions uses frequency-gated inhibition; e.g., there is no inhibition unless the neural activity into the inhibitory mechanism falls within a particular spike rate (centered around gamma-band spike rates in the Niebur et al. model). E. Niebur, C. Koch, C. Rosin, “An oscillation-based model for the neuronal basis of attention,” Vision Res. 33, 2789–2802 (1993). It is an interesting coincidence that during image stabilization, when stabilized images fade or fragment, the power ratio of alpha rhythm to higher-frequency components in the electroencephalogram (EEG) drastically increases just before and during image fading or fragmentation and wanes when images reappear (see Refs. 34 and 35). Why this happens is unclear, but if stabilization somehow eliminates higher-frequency neural activity, then it should also be expected to eliminate frequency-gated cortical competition. Such an analysis depends on drawing a tighter relationship between EEG spectra and the neural activity in specific cortical units [like those modeled in Eq. (4)–(6)] than we currently can.
[CrossRef] [PubMed]

Okubo, A.

For example Eq. 4 could be modified to  ∂ωR/∂t=ωR[LC*(λ)-(aωR+bωG+cωv)]+DR(∂2ωR/∂x2+∂2ωR/∂y2), a Lotka–Volterra (LV) version of a reaction–diffusion (RD) equation. We take diffusion to be the prototypical filling-in mechanism (see Refs. 29 and 30). Both RD and diffusive LV systems are capable of spatiotemporal pattern formation (morphogenesis) for some parameterizations (in general, ωR,ωG,ωV would need different diffusion rates or asymmetrical coupling, or cross diffusion). Such models give rise to transient or stable stationary spatial structures.A. Okubo, Diffusion and Ecological Problems: Mathematical Models (Springer, Berlin, 1980).

Piantanida, T. P.

H. D. Crane, T. P. Piantanida, “On seeing reddish green and yellowish blue,” Science 221, 1078–1080 (1983).
[CrossRef] [PubMed]

Poggio, T.

T. Poggio, E. B. Gamble, L. T. Little, “Parallel integration of visual modules,” Science 242, 436–440 (1988).
[CrossRef] [PubMed]

Prichard, R. M.

Stabilized images often fragment upon stabilization; the fragments fade and revive in groupings that obey Gestalt-like laws. R. M. Prichard, W. Heron, D. O. Hebb, “Visual perception approached by the method of stabilized images,” Can. J. Psychol. 14, 67–77 (1960).
[CrossRef]

Rosin, C.

We can however speculate. Niebur et al.’s model of competition interactions uses frequency-gated inhibition; e.g., there is no inhibition unless the neural activity into the inhibitory mechanism falls within a particular spike rate (centered around gamma-band spike rates in the Niebur et al. model). E. Niebur, C. Koch, C. Rosin, “An oscillation-based model for the neuronal basis of attention,” Vision Res. 33, 2789–2802 (1993). It is an interesting coincidence that during image stabilization, when stabilized images fade or fragment, the power ratio of alpha rhythm to higher-frequency components in the electroencephalogram (EEG) drastically increases just before and during image fading or fragmentation and wanes when images reappear (see Refs. 34 and 35). Why this happens is unclear, but if stabilization somehow eliminates higher-frequency neural activity, then it should also be expected to eliminate frequency-gated cortical competition. Such an analysis depends on drawing a tighter relationship between EEG spectra and the neural activity in specific cortical units [like those modeled in Eq. (4)–(6)] than we currently can.
[CrossRef] [PubMed]

Sacks, O. W.

For a review of related models of drug- and migraine-induced geometric hallucinations see O. W. Sacks, R. M. Siegal, “Migraine aura and hallucinatory constants,” in Migraine, O. W. Sacks, ed. (Picador, London, 1992), pp. 273–297.

O. W. Sacks, An Anthropologist on Mars: Seven Paradoxical Tales (Vintage, New York, 1995).

Shigeru, Y.

H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
[PubMed]

Siegal, R. M.

For a review of related models of drug- and migraine-induced geometric hallucinations see O. W. Sacks, R. M. Siegal, “Migraine aura and hallucinatory constants,” in Migraine, O. W. Sacks, ed. (Picador, London, 1992), pp. 273–297.

Smith, J. M.

A good physical analogy is two separated reservoirs respectively filled with infinite supplies of red and green ink (at fixed concentrations). If connected by a long clear pipe, Eqs. (9) and (10) give the concentrations of red and green ink along the length of the pipe (at steady state). At steady state, the values of the diffusion rate constants are irrelevant. For a brief discussion of related issues see J. M. Smith, Mathematical Ideas in Biology (Cambridge U. Press, Cambridge, UK, 1971).

Stockman, A.

Switkes, E.

R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
[CrossRef] [PubMed]

Tansley, B. W.

Vemuri, C.

P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).

Vingrys, A. J.

V. A. Billock, A. J. Vingrys, P. E. King-Smith, “Opponent color detection threshold asymmetries may result from reduction of ganglion cell subpopulations,” Visual Neurosci. 11, 99–109 (1994).
[CrossRef]

von der Heydt, R.

P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).

Williams, D. R.

P. E. Lennie, P. W. Haake, D. R. Williams, “The design of chromatically opponent receptive fields,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 71–82.

Wilson, H. R.

H. R. Wilson, Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience (Oxford U. Press, Oxford, UK, 1999).

Zeki, S.

S. Zeki, “Color coding in the cerebral cortex,” Neuroscience (N.Y.) 9, 741–756 (1983).
[CrossRef]

Can. J. Psychol. (1)

Stabilized images often fragment upon stabilization; the fragments fade and revive in groupings that obey Gestalt-like laws. R. M. Prichard, W. Heron, D. O. Hebb, “Visual perception approached by the method of stabilized images,” Can. J. Psychol. 14, 67–77 (1960).
[CrossRef]

Electroencephalogr. Clin. Neurophysiol. (1)

D. Lehmann, G. W. Beeler, D. H. Fender, “Changes in patterns of the human electroencephalogram during fluctuations of perception of stabilized retinal images,” Electroencephalogr. Clin. Neurophysiol. 19, 336–343 (1965).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (2)

V. A. Billock, “A chaos theory approach to some intractable problems in color vision,” Invest. Ophthalmol. Visual Sci. 38, 254 (1997).

P. Kaloudis, H. Friedman, C. Vemuri, R. von der Heydt, “Color selectivity of metacontrast masking,” Invest. Ophthalmol. Visual Sci. 39, 407 (1998).

J. Neurosci. (1)

H. Komatsu, Y. Ideura, S. Kaji, Y. Shigeru, “Color selectivity of neurons in the inferior temporal cortex of awake macaque monkey,” J. Neurosci. 12, 408–424 (1992).
[PubMed]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

Nature (1)

N. C. Cottaris, R. L. De Valois, “Temporal dynamics of chromatic tuning in macaque primary visual cortex,” Nature 395, 896–900 (1998).
[CrossRef] [PubMed]

Neural Networks (1)

This is a highly modified version of the Lotka–Volterra population dynamics model; for review see S. Grossberg, “Nonlinear neural networks,” Neural Networks 1, 17–61 (1988).
[CrossRef]

Neuroscience (N.Y.) (1)

S. Zeki, “Color coding in the cerebral cortex,” Neuroscience (N.Y.) 9, 741–756 (1983).
[CrossRef]

Optom. Vision Sci. (1)

The transparency effects are reminiscent of superimposition effects sometimes seen in binocular color mixtures (two subjects report luster effects similar to binocular luster). J. Hovis, “Review of dichoptic color mixing,” Optom. Vision Sci. 66, 181–190 (1989).
[CrossRef]

Science (5)

H. D. Crane, T. P. Piantanida, “On seeing reddish green and yellowish blue,” Science 221, 1078–1080 (1983).
[CrossRef] [PubMed]

D. H. Kelly, “Disappearance of stabilized chromatic gratings,” Science 214, 1257–1258 (1981).
[CrossRef] [PubMed]

V. A. Billock, “Consequences of retinal color coding for cortical color decoding,” Science 274, 2118–2119 (1996).
[CrossRef] [PubMed]

T. Poggio, E. B. Gamble, L. T. Little, “Parallel integration of visual modules,” Science 242, 436–440 (1988).
[CrossRef] [PubMed]

M. Barinaga, “Listening in on the brain,” Science 280, 376–378 (1998).
[CrossRef] [PubMed]

Vision Res. (8)

U. T. Keesey, D. J. Nichols, “Fluctuations in target visibility as related to the alpha component of the electroencephalogram,” Vision Res. 7, 859–879 (1967).
[CrossRef]

One rationale for low-pass filtering (pooling) and rectification can be found in demultiplexing theory: V. A. Billock, “Cortical simple cells can extract achromatic information from the multiplexed chromatic and achromatic signals in the parvocellular pathway,” Vision Res. 35, 2359–2369 (1995). Other evidence is found in psychophysical data of subjects with low ganglion cell densities (Ref. 6). See Ref. 3 for a different but related approach.
[CrossRef] [PubMed]

J. Larimer, D. H. Krantz, C. M. Cicerone, “Opponent process additivity. I. Red/green equilibria,” Vision Res. 14, 1127–1140 (1974).
[CrossRef] [PubMed]

A. A. Baloch, S. Grossberg, “A neural model of high level motion processing,” Vision Res. 37, 3037–3059 (1997).
[CrossRef]

We can however speculate. Niebur et al.’s model of competition interactions uses frequency-gated inhibition; e.g., there is no inhibition unless the neural activity into the inhibitory mechanism falls within a particular spike rate (centered around gamma-band spike rates in the Niebur et al. model). E. Niebur, C. Koch, C. Rosin, “An oscillation-based model for the neuronal basis of attention,” Vision Res. 33, 2789–2802 (1993). It is an interesting coincidence that during image stabilization, when stabilized images fade or fragment, the power ratio of alpha rhythm to higher-frequency components in the electroencephalogram (EEG) drastically increases just before and during image fading or fragmentation and wanes when images reappear (see Refs. 34 and 35). Why this happens is unclear, but if stabilization somehow eliminates higher-frequency neural activity, then it should also be expected to eliminate frequency-gated cortical competition. Such an analysis depends on drawing a tighter relationship between EEG spectra and the neural activity in specific cortical units [like those modeled in Eq. (4)–(6)] than we currently can.
[CrossRef] [PubMed]

R. T. Eskew, “The gap effect revisited: Slow changes in chromatic sensitivity as affected by luminance and chromatic borders,” Vision Res. 29, 717–729 (1989).
[CrossRef] [PubMed]

R. L. De Valois, K. K. De Valois, “A multistage vision model,” Vision Res. 33, 1053–1065 (1993).
[CrossRef] [PubMed]

R. L. De Valois, K. K. De Valois, E. Switkes, L. Mahon, “Hue scaling of isoluminant and cone specific lights,” Vision Res. 37, 885–897 (1997).
[CrossRef] [PubMed]

Visual Neurosci. (1)

V. A. Billock, A. J. Vingrys, P. E. King-Smith, “Opponent color detection threshold asymmetries may result from reduction of ganglion cell subpopulations,” Visual Neurosci. 11, 99–109 (1994).
[CrossRef]

Other (10)

Although image stabilization often induces gradual fading, most of our subjects (6 out of 7) reported simultaneously binocular abrupt transitions to pitch blackness or to complete loss of any visual sense; one psychophysicist characterized it as like the optic nerve being cut; another compared it with the visual blackout that accompanies manual carotid strangulation in the martial arts. This strikingly unnatural phenomenon is believed to be mediated by central mechanisms. R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, UK, 1973).

D. Hume, Treatise on Human Nature (Oxford U. Press, Oxford, UK, 1739/1955).

O. W. Sacks, An Anthropologist on Mars: Seven Paradoxical Tales (Vintage, New York, 1995).

For a review see P. Cavanagh, “Vision at equiluminance,” in Limits of Vision, Vol. 5 of Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, I. J. Murray, eds. (CRC Press, Boca Raton, Fla., 1991), pp. 234–250.

We used a Generation 5 dual Purkinje image eye tracker (Fourward Technologies, El Cajon, Calif.), which transduces moving infrared reflections from cornea and lens. This signal is fed back to a servo-driven mirror to stabilize the image of a stimulus reflected therein (see Ref. 1). The primary subjects were two of the authors, but five additional observers, including outside color researchers, also participated. Because Ref. 1 reported difficulty characterizing non-Hering colors, we used only extremely experienced observers (all but one—a doctoral candidate in color vision—are professional psychophysicists). All subjects had normal color vision (gauged by anomaloscope and F2 tritan test plates). Experiments were in accord with U.S. Air Force human-use protocols. Subjects were fixed by forehead and chin rests, with their left eyes patched and their right pupils dilated by 1 drop of 1% Tropicamide to facilitate tracking of the 4th Purkinje image. Red/green and blue/yellow bipartite fields were presented on a photometrically and colorimetrically calibrated VisionWorks (VRG, Inc., Durham, NH) display system. The two sides of the field could be equated for luminance by flicker photometry. The standard red field had CIE chromaticity coordinates of (0.631, 0.338) and a CIE luminance of 13.8 cd/m2. The green field flicker matched to it had coordinates (0.287, 0.604). The blue field was (0.151, 0.061) and had a luminance of 8 cd/m2(the maximum available). The yellow field flicker matched to it consisted of equal mixtures of the red and green guns. Its CIE coordinates were (0.393, 0.525), which is considered a greenish-yellow location in CIE space but which appeared golden under experimental conditions. Refractive error and monitor distance were optically compensated. To achieve stabilization, subjects controlled mirror deflection circuit gain. Stabilization was checked by observations of eye movement effects on the position of colored borders relative to the unstabilized aperture. As in Ref. 1, the stabilized bipartite fields were viewed through unstabilized vertical occluders to reduce the incidence of image fading (which is otherwise severe). The visible stimulus subtended 14° horizontal×24° vertical.

For a review of related models of drug- and migraine-induced geometric hallucinations see O. W. Sacks, R. M. Siegal, “Migraine aura and hallucinatory constants,” in Migraine, O. W. Sacks, ed. (Picador, London, 1992), pp. 273–297.

A good physical analogy is two separated reservoirs respectively filled with infinite supplies of red and green ink (at fixed concentrations). If connected by a long clear pipe, Eqs. (9) and (10) give the concentrations of red and green ink along the length of the pipe (at steady state). At steady state, the values of the diffusion rate constants are irrelevant. For a brief discussion of related issues see J. M. Smith, Mathematical Ideas in Biology (Cambridge U. Press, Cambridge, UK, 1971).

For example Eq. 4 could be modified to  ∂ωR/∂t=ωR[LC*(λ)-(aωR+bωG+cωv)]+DR(∂2ωR/∂x2+∂2ωR/∂y2), a Lotka–Volterra (LV) version of a reaction–diffusion (RD) equation. We take diffusion to be the prototypical filling-in mechanism (see Refs. 29 and 30). Both RD and diffusive LV systems are capable of spatiotemporal pattern formation (morphogenesis) for some parameterizations (in general, ωR,ωG,ωV would need different diffusion rates or asymmetrical coupling, or cross diffusion). Such models give rise to transient or stable stationary spatial structures.A. Okubo, Diffusion and Ecological Problems: Mathematical Models (Springer, Berlin, 1980).

H. R. Wilson, Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience (Oxford U. Press, Oxford, UK, 1999).

P. E. Lennie, P. W. Haake, D. R. Williams, “The design of chromatically opponent receptive fields,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 71–82.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Early mechanisms in multistage color processing. (a) L-, M- and S-cone spectral sensitivities.27 (b) Chromatic sensitivities of retino-geniculate mechanisms from Eqs. (1)–(3), with receptive field centers driven by L, M, and S cones and surrounds driven by a mixture of cones (a plausible, but not crucial, assumption). Computed from the unrectified portions of Eqs. (1)–(3) with k=0.95, PL=0.625, PM=0.3125, PS=0.0625. (c) Cortical wavelength-selective mechanisms produced by filtering and rectifying the outputs of units like those of Fig. 1(b). Normalized for comparison with Fig. 1(a).

Fig. 2
Fig. 2

A winner-take-all competition model of classic red–green color opponency. Nonlinear dynamic interactions between units driven by the mechanisms in Fig.1(c) give rise to Hering-like color opponency. Points are Jameson and Hurvich’s25 two-observer measurements of the red–green color-opponent response. The plotted line is the least-squares fit (to the average of the observers) of competitive mechanisms labeled for hue [Eqs. (4)–(6)], with each lobe being the output of one equation (integrated numerically25) and graphed with conventional polarity (which is arbitrary). Under some conditions this kind of opponency can be deactivated, permitting violations of color opponency.

Fig. 3
Fig. 3

If competition between units in the winner-take-all network is blocked, then red- and green-labeled units are free to signal red and green on each side of the bipartite field. This figure shows red- and green-labeled activity gradients [Eqs. (9) and (10)] that result from diffusion-like filling-in processes occurring from each side of a red/green bipartite field of 14 deg horizontal extent.

Tables (1)

Tables Icon

Table 1 Parameters Used for Calculation in Fig. 2a

Equations (11)

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

LC*=Rect[LC]=Rect[(1-kPL)L-kPMM],
MC*=Rect[MC]=Rect[(1-kPM)M-kPLL],
SC*=Rect[SC]=Rect[(1-kPS)S-k(PMM+PLL)]
dωR/dt=ωR[LC*(λ)-(aωR+bωG+cωV)],
dωG/dt=ωG[MC*(λ)-(dωG+eωR+fωV)],
dωV/dt=ωV[SC*(λ)-(hωV+iωR+jωG)].
ωR/t=ωR[LC*(λ)-aωR-bωG]+DR2ωR/x2,
ωG/t=ωG[MC*(λ)-dωG-eωR]+DG2ωG/x2,
ωR(x)=LC*(610)/a-x[LC*(610)-LC*(545)]/14a.
ωG(x)=MC*(545)/d-(14-x)[MC*(545)]/14d.
ωR/t=ωR[LC*(λ)-(aωR+bωG+cωv)]+DR(2ωR/x2+2ωR/y2),

Metrics