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Optimal design of photoreceptor mosaics: Why we do not see color at night

Published online by Cambridge University Press:  01 January 2009

JEREMY R. MANNING  and
DAVID H. BRAINARD
JEREMY R. MANNING*
Affiliation:
Neuroscience Graduate Group and Department of Psychology, University of Pennsylvania, Philadelphia, Pennsylvania
DAVID H. BRAINARD*
Affiliation:
Neuroscience Graduate Group and Department of Psychology, University of Pennsylvania, Philadelphia, Pennsylvania
*
*Address correspondence and reprint requests to: David H. Brainard, 3401 Walnut Street, Philadelphia, PA 19104. E-mail: brainard@psych.upenn.edu
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Abstract

While color vision mediated by rod photoreceptors in dim light is possible (Kelber & Roth, 2006), most animals, including humans, do not see in color at night. This is because their retinas contain only a single class of rod photoreceptors. Many of these same animals have daylight color vision, mediated by multiple classes of cone photoreceptors. We develop a general formulation, based on Bayesian decision theory, to evaluate the efficacy of various retinal photoreceptor mosaics. The formulation evaluates each mosaic under the assumption that its output is processed to optimally estimate the image. It also explicitly takes into account the statistics of the environmental image ensemble. Using the general formulation, we consider the trade-off between monochromatic and dichromatic retinal designs as a function of overall illuminant intensity. We are able to demonstrate a set of assumptions under which the prevalent biological pattern represents optimal processing. These assumptions include an image ensemble characterized by high correlations between image intensities at nearby locations, as well as high correlations between intensities in different wavelength bands. They also include a constraint on receptor photopigment biophysics and/or the information carried by different wavelengths that produces an asymmetry in the signal-to-noise ratio of the output of different receptor classes. Our results thus provide an optimality explanation for the evolution of color vision for daylight conditions and monochromatic vision for nighttime conditions. An additional result from our calculations is that regular spatial interleaving of two receptor classes in a dichromatic retina yields performance superior to that of a retina where receptors of the same class are clumped together.

Keywords

Photoreceptor mosaicColor visionNocturnal visionBayesian decision theoryRetina
Type
Natural Scene Statistics and Efficient Coding
Information
Visual Neuroscience , Volume 26 , Issue 1 , January 2009 , pp. 5 - 19
Copyright
Copyright © Cambridge University Press 2009

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References

Aguilar, M. & Stiles, W.S. (1954). Saturation of the rod mechanism of the retina at high light levels. Journal of Modern Optics 1, 59–65.Google Scholar
Ala-Laurila, P., Donner, K., Crouch, R.K. & Cornwall, M.C. (2007). Chromophore switch from 11-cis-dehydroretinal (A2) to 11-cis-retinal (A1) decreases dark noise in salamander red rods. Journal of Physiology 585, 57–74.CrossRefGoogle ScholarPubMed
Ala-Laurila, P., Pahlberg, J., Koskelainen, A. & Donner, K. (2004). On the relation between the photoactivation energy and the absorbance spectrum of visual pigments. Vision Research 44, 2153–2158.CrossRefGoogle ScholarPubMed
Atick, J.J. (1992). Could information theory provide an ecological theory of sensory processing. Network: Computation in Neural Systems 3, 213–251.CrossRefGoogle Scholar
Atick, J.J., Li, Z.P. & Redlich, A.N. (1992). Understanding retinal color coding from first principles. Neural Computation 4, 559–572.CrossRefGoogle Scholar
Balasubramanian, V. & Berry, M.J. (2002). A test of metabolically efficient coding in the retina. Network, 13, 531–552.CrossRefGoogle ScholarPubMed
Balasubramanian, V., Kimber, D. & Berry, M.J. (2001). Metabolically efficient information processing. Neural Computation 13, 799–815.CrossRefGoogle ScholarPubMed
Barlow, H.B. (1956). Retinal noise and absolute threshold. Journal of the Optical Society of America 46, 634–639.CrossRefGoogle ScholarPubMed
Barlow, H.B. (1957). Purkinje shift and retinal noise. Nature 179, 255–256.CrossRefGoogle ScholarPubMed
Baylor, D.A., Lamb, T.D. & Yau, K.W. (1979). Responses of retinal rods to single photons. Journal of Physiology (London) 288, 613–634.CrossRefGoogle ScholarPubMed
Baylor, D.A., Nunn, B.J. & Schnapf, J.L. (1984). The photocurrent, noise, and spectral sensitivity of rods of the monkey macaca fascicularis. Journal of Physiology (London) 357, 575–607.CrossRefGoogle ScholarPubMed
Berger, T.O. (1985). Statistical Decision Theory and Bayesian Analysis. New York: Springer-Verlag.CrossRefGoogle Scholar
Blackwell, D. & Girschick, M.A. (1954). Theory of Games and Statistical Decisions. New York: Wiley.Google Scholar
Bossomaier, T.R.J., Snyder, A.W. & Hughes, A. (1985). Irregularity and aliasing: Solution? Vision Research 25, 145–147.CrossRefGoogle ScholarPubMed
Bowmaker, J.K. (1991). The evolution of vertebrate visual pigments and photoreceptors. In Vision and Visual disfunction, vol.2, ed. Cronly-Dillon, J.R. & Gregory, R.L., pp. 63–81. London: Macmillan.Google Scholar
Bowmaker, J.K. & Kunz, Y.W. (1987). Ultraviolet receptors, tetrachromatic colour vision and retinal mosaics in the brown trout (salmo trutta): Age-dependent changes. Vision Research 27, 2101–2108.CrossRefGoogle ScholarPubMed
Brainard, D.H. (1993). Perceptual variability as a fundamental axiom of perceptual science: Comments on Ashby and Lee. In Foundations of Perceptual Theory, ed. Masin, S.C., pp. 385–388. Amsterdam: Elsevier Science Publishers.Google Scholar
Brainard, D.H., Williams, D.R. & Hofer, H. (2008). Trichromatic reconstruction from the interleaved cone mosaic: Bayesian model and the color appearance of small spots. Journal of Vision 8, 15, 1–23.CrossRefGoogle ScholarPubMed
Brenner, N., Bialek, W. & de Ruyter van Steveninck, R. (2000). Adaptive rescaling maximizes information transmission. Neuron 26, 695–702.CrossRefGoogle ScholarPubMed
Buchsbaum, G. & Gottschalk, A. (1983). Trichromacy, opponent colour coding and optimum colour information transmission in the retina. Proceedings of the Royal Society of London B 220, 89–113.Google ScholarPubMed
Burns, M. & Arshavsky, V. (2005). Beyond counting photons: Trials and trends in vertebrate visual transduction. Neuron 48, 387–401.CrossRefGoogle ScholarPubMed
Burton, G.J. & Moorehead, I.R. (1987). Color and spatial structure in natural images. Applied Optics 26, 157–170.CrossRefGoogle Scholar
Chittka, L. & Menzel, R. (1992). The evolutionary adaptation of flower colours and the insect pollinators’ colour vision. Journal of Comparative Physiology A: Neuroethology, Sensory, Neural, and Behavioral Physiology 171, 171–181.CrossRefGoogle Scholar
Cover, T.M. & Thomas, J.A. (1991). Elements of Information Theory. New York: John Wiley & Sons.Google Scholar
Cummings, M.E. (2004). Modelling divergence in luminance and chromatic detection performance across measured divergence in surfperch (embiotocidae) habitats. Vision Research 44, 1127–1145.CrossRefGoogle ScholarPubMed
Curcio, C.A., Allen, K., Sloan, K., Lerea, C., Klock, I. & Milam, A. (1991). Distribution and morphology of human cone photoreceptors stained with anti-blue opsin. Journal of Comparative Neurology, 312, 610–624.CrossRefGoogle ScholarPubMed
Demontis, G.C., Bisti, S. & Cervetto, L. (1993). Light sensitivity, adaptation and saturation in mammalian rods. Progress in Brain Research 95, 15–24.CrossRefGoogle ScholarPubMed
DeVries, S., Qi, X., Smith, R.G., Makous, W. & Sterling, P. (2002). Electrical coupling between mammalian cones. Current Biology 12, 1900–1907.CrossRefGoogle ScholarPubMed
Field, D.J. (1987). Relations between the statistics of natural images and the response properties of cortical cells. Journal of the Optical Society of America A 4, 2379–2394.CrossRefGoogle ScholarPubMed
Fu, Y., Kefalov, V., Luo, D.G., Xue, T. & Yau, K.W. (2008). Quantal noise from human red cone pigment. Nature Neuroscience 11, 565–571.CrossRefGoogle ScholarPubMed
Garrigan, P., Ratliff, C., Klein, J.M., Sterling, P., Brainnard, D.H. & Balasubramanian, V. (2006, March). Structure of the primate cone mosaic and the statistics of color in nocturnal images. Chromatic scene statistics and primate cone mosaic structure. Salt Lake City, UT.Google Scholar
Garrigan, P., Ratliff, C.P., Klein, J.M., Sterling, P., Brainard, D.H. & Balasubramanian, V. (2008). Design of a trichromatic cone array (manuscript in preparation).Google Scholar
Geisler, W.S. (1987). The ideal observer concept as a modeling tool. In Frontiers of Visual Science, pp. 17–31. Washington, DC: National Academy Press.Google Scholar
Gelman, A., Carlin, J.B., Stern, H.S. & Rubin, D.B. (2004). Bayesian Data Analysis, 2nd edition. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Graham, C.H. & Hsia, Y. (1969). Saturation and the foveal achromatic interval. Journal of the Optical Society of America 59, 993.CrossRefGoogle ScholarPubMed
Hofer, H., Carroll, J., Neitz, J., Neitz, M. & Williams, D.R. (2005). Organization of the human trichromatic cone mosaic. Journal of Neuroscience 42, 9669–9679.CrossRefGoogle Scholar
Hsu, A., Smith, R.G., Buchsbaum, G. & Sterling, P. (2000). Cost of cone coupling to trichromacy in primate fovea. Journal of the Optical Society of America 17, 635–640.CrossRefGoogle ScholarPubMed
Jacobs, G.H. (1981). Comparative Color Vision. New York: Academic Press.Google Scholar
Jacobs, G.H. (1996). Primate photopigments and primate color vision. Proceedings of the National Academy of Sciences of the United States of America 93, 577–581.CrossRefGoogle ScholarPubMed
Jacobs, G.H., Neitz, M. & Neitz, J. (1996). Mutations in S-cone pigment genes and the absence of colour vision in two species of nocturnal primate. Proceeding of the Royal Society of London B, 263, 705–710.Google ScholarPubMed
Jacobs, G.H. & Rowe, M.P. (2004). Evolution of vertebrate colour vision. Clinical and Experimental Optometry 87, 206–216.CrossRefGoogle ScholarPubMed
Kelber, A. & Roth, L.S. (2006). Nocturnal colour vision—Not as rare as we might think. Journal of Experimental Biology 209, 281–288.CrossRefGoogle ScholarPubMed
Koch, K., McLean, J., Berry, M., Sterling, P., Balasubramanian, V. & Freed, M. (2004). Efficiency of information transmission by retinal ganglion cells. Current Biology 14, 1523–1530.CrossRefGoogle ScholarPubMed
Koch, K., McLean, J., Segev, R., Freed, M.A., Berry, M.J., Balasubramanian, V. & Sterling, P. (2006). How much the eye tells the brain. Current Biology, 16, 1428–1434.CrossRefGoogle ScholarPubMed
Land, M. & Osorio, D. (2003). Colour vision: Colouring the dark. Current Biology 13, R83–R85.CrossRefGoogle ScholarPubMed
Laughlin, S.B. (2001). Energy as a constraint on the coding and processing of sensory information. Current Opinion in Neurobiology 11, 475–480.CrossRefGoogle ScholarPubMed
Laughlin, S.B. & Hardie, R.C. (1978). Common strategies for light adaptation in the peripheral visual systems of fly and dragonfly. Journal of Comparative Physiology A: Neuroethology, Sensory, Neural, and Behavioral Physiology 128, 319–340.CrossRefGoogle Scholar
Laughlin, S.B. & Sejnowski, T.J. (2003). Communication in neuronal networks. Science 301, 1879–1874.CrossRefGoogle ScholarPubMed
Levin, A., Durand, F. & Freeman, W.T. (2008). Understanding Camera Trade-Offs Through a Bayesian Analysis of Light Field Projections. Cambridge, MA: MIT.CrossRefGoogle Scholar
Lewis, A. & Zhaoping, L. (2006). Are cone sensitivities determined by natural color statistics? Journal of Vision 6, 285–302.CrossRefGoogle ScholarPubMed
Luce, R.D. (2003). Whatever happened to information theory in psychology? Review of General Psychology 7, 183–188.CrossRefGoogle Scholar
Lythgoe, J.N. & Partridge, J.C. (1989). Visual pigments and the acquisition of visual information. Journal of Experimental Biology 146, 1–20.CrossRefGoogle ScholarPubMed
Massof, R.W. (1977). A quantum fluctuation model for foveal color thresholds. Vision Research 17, 565–570.CrossRefGoogle ScholarPubMed
Mollon, J.D. & Bowmaker, J.K. (1992). The spatial arrangement of cones in the primate fovea. Nature 360, 677–679.CrossRefGoogle ScholarPubMed
Osorio, D. & Vorobyev, M. (1996). Colour vision as an adaptation to frugivory in primates. Proceedings of the Royal Society of London B 263, 593–599.Google ScholarPubMed
Platt, J.R. (1956). Wavelength dependence of radiation-noise limits on sensitivity of infrared photodetectors. Journal of the Optical Society of America 46, 609–610.CrossRefGoogle Scholar
Pratt, W.K. (1978). Digital Image Processing. New York: John Wiley & Sons.Google Scholar
Regan, B.C., Julliot, C., Simmen, B., Vienot, F., Charles-Dominique, P. & Mollon, J.D. (2001). Fruits, foliage and the evolution of primate color vision. Philosophical Transactions: Biological Sciences 356, 229–283.CrossRefGoogle Scholar
Rieke, F. & Baylor, D.A. (2000). Origin and functional impact of dark noise in retinal cones. Neuron 26, 181–186.CrossRefGoogle ScholarPubMed
Ruderman, D.L., Cronin, T.W. & Chiao, C.C. (1998). Statistics of cone responses to natural images: Implications for visual coding. Journal of the Optical Society of America A 15, 2036–2045.CrossRefGoogle Scholar
Rushton, W.A.H. (1962). Visual pigments in man. Scientific American 207, 120–132.CrossRefGoogle ScholarPubMed
Schnapf, J.L., Nunn, B.J., Meister, M. & Baylor, D.A. (1990). Visual transduction in cones of the monkey macaca fascicularis. Journal of Physiology (London) 427, 681–713.CrossRefGoogle ScholarPubMed
Schneeweis, D.M. & Schnapf, J.L. (1999). The photovoltage of macaque cone photoreceptors: Adaptation, noise, and kinetics. Journal of Neuroscience 19, 1203–1216.CrossRefGoogle ScholarPubMed
Schneeweis, D.M. & Schnapf, J.L. (2000). Noise and light adaptation in rods of the macaque monkey. Visual Neuroscience 17, 659–666.CrossRefGoogle ScholarPubMed
Schneider, D. (1969). Insect olfaction: Deciphering system for chemical messages. Science 163, 1031–1037.CrossRefGoogle ScholarPubMed
Scholes, J.H. (1975). Colour receptors and their synaptic connexions in the retina of a cyprinid fish. Philosophical Transactions of the Royal Society of London B 270, 61–118.Google ScholarPubMed
Sellick, P.M., Patuzzi, R. & Johnstone, B.M. (1982). Measurement of basilar membrane motion in the guinea pig using the Mössbauer technique. Journal of the Acoustical Society of America 72, 131–141.CrossRefGoogle ScholarPubMed
Simonceli, E.P. (2005). Statistical modeling of photographic images. In Handbook of Image and Video Processing, ed. Bovik, A., pp. 431–441. New York, NY: Academic Press.CrossRefGoogle Scholar
Skorupski, P. & Chittka, L. (2008). Towards a cognitive definition of colour vision. Available from Nature Precedings 4 April 2008, http://hdl.handle.net/10101/npre.2008.1766.1.Google Scholar
Snyder, A.W., Stavenga, D.G. & Laughlin, S.B. (1977). Spatial information capacity of compound eyes. Journal of Comparative Physiology A: Neuroethology, Sensory, Neural, and Behavioral Physiology 116, 183–207.CrossRefGoogle Scholar
Srinivasan, M.V., Laughlin, S.B. & Dubs, A. (1982). Predictive coding: A fresh view of inhibition in the retina. Proceedings of the Royal Society of London B 216, 427–459.Google ScholarPubMed
Tamura, T., Nakatani, K. & Yau, K.W. (1989). Light adaptation in cat retinal rods. Science 245, 755–757.CrossRefGoogle ScholarPubMed
Thomson, E.E. & Kristan, W.B. (2005). Quantifying stimulus discriminability: A comparison of information theory and ideal observer analysis. Neural Computation 17, 741–778.CrossRefGoogle ScholarPubMed
van Hateren, J.H. (1992). A theory of maximizing sensory information. Biological Cybernetics 68, 23–29.CrossRefGoogle ScholarPubMed
van Hateren, J.H. (1993). Spatial, temporal and spectral pre-processing for colour vision. Proceedings of the Royal Society of London Series B: Biological Sciences 251, 61–68.Google ScholarPubMed
von der Twer, T. & MacLeod, D.I.A. (2001). Optimal nonlinear codes for the perception of natural colors. Network: Computation in Neural Systems 12, 395–407.CrossRefGoogle Scholar
Walls, G.L. (1942). The Vertebrate Eye and its Adaptive Radiation. New York: Cranbrook Institute of Science.Google Scholar
Walraven, J., Enroth-Cugell, C., Hood, D.C., MacLeod, D.I.A. & Schnapf, J.L. (1990). The control of visual sensitivity. receptoral and postreceptoral processes. In Visual Perception: The Neurophysiological Foundations, ed. Spillman, L. & Werner, J.S., pp. 53–101. San Diego, CA: Academic Press.CrossRefGoogle Scholar
Walraven, P.L. (1962). On the Mechanisms of Colour Vision. Soesterberg, The Netherlands: TNO.Google Scholar
Wassle, H. & Riemann, H.J. (1978). The mosaic of nerve cells in the mammalian retina. Proceedings of the Royal Society of London Series B 200, 441–461.Google ScholarPubMed
Watson, A.B. (1987). The ideal observer concept as a modeling tool. In Frontiers of Visual Science, ed. The Committee on Vision, pp. 32–37. Washington, DC: National Academy Press.Google Scholar
Weymouth, F.W. (1958). Visual sensory units and the minimal angle of resolution. American Journal of Ophthalmology 46, 102–112.CrossRefGoogle ScholarPubMed
Yellott, J. (1982). Spectral analysis of spatial sampling by photoreceptors: Topological disorder prevents aliasing. Vision Research 22, 1205–1210.CrossRefGoogle ScholarPubMed
Yellott, J. (1983). Spectral consequences of photoreceptor sampling in the rhesus monkey. Science 221, 383–385.CrossRefGoogle Scholar
Yin, L., Smith, R.G., Sterling, P. & Brainard, D.H. (2006). Chromatic properties of horizontal and ganglion cell responses follow a dual gradient in cone opsin expression. Journal of Neuroscience 26, 12351–12361.CrossRefGoogle ScholarPubMed