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A mathematical model of color and orientation processing in V1

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Abstract

Orientation processing in the primary visual cortex (V1) has been experimentally investigated in detail and reproduced in models, while color processing remains unclear. Thus, we have constructed a mathematical model of color and orientation processing in V1. The model is mainly based on the following experimental evidence concerning color blobs: A blob contains overlapping neuronal patches activated by different hues, so that each blob represents a full gamut of hue and might be structured with a loop (Xiao et al. in NeuroImage 35:771–786, 2007). The proposed model describes a set of orientation hypercolumns and color blobs, in which color and orientation preferences are represented by the poloidal and toroidal angles of a torus, correspondingly. The model consists of color-insensitive (CI) and color-sensitive (CS) neuronal populations, which are described by a firing-rate model. The set of CI neurons is described by the classical ring model (Ben-Yishai et al. in Proc Natl Acad Sci USA 92:3844–3848, 1995) with recurrent connections in the orientation space; similarly, the set of CS neurons is described in the color space and also receives input from CI neurons of the same orientation preference. The model predictions are as follows: (1) responses to oriented color stimuli are significantly stronger than those to non-oriented color stimuli; (2) the activity of CS neurons in total is higher than that of CI neurons; (3) a random color can be illusorily perceived in the case of gray oriented stimulus; (4) in response to two-color stimulus in the marginal phase, the network chooses either one of the colors or the intermediate color; (5) input to a blob has rather continual representation of a hue than discrete one (with two narrowly tuned opponent signals).

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References

  • Basalyga G, Montemurro MA, Wennekers T (2012) Information coding in a laminar computational model of cat primary visual cortex. J Comput Neurosci 34(2):273–283

    Article  PubMed  Google Scholar 

  • Battaglia D, Hansel D (2011) Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex. PLoS 7–10:1–24

    Google Scholar 

  • Ben-Yishai R, Lev Bar-Or R, Sompolinsky H (1995) Theory of orientation tuning in visual cortex. Proc Natl Acad Sci USA 92:3844–3848

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Bertalmío M, Cowan JD (2009) Implementing the Retinex algorithm with Wilson–Cowan equations. J Physiol 103:69–72

    Google Scholar 

  • Bressloff PC, Cowan JD (2002) A spherical model for orientation and spatial–frequency tuning in a cortical hypercolumn. Philos Trans R Soc Lond B 01tb0039.1-24

  • Carandini M, Ringach DL (1997) Predictions of a recurrent model of orientation selectivity. Vis Res 37(21):3061–3071

    Article  CAS  PubMed  Google Scholar 

  • Chizhov AV (2014) Conductance-based refractory density model of primary visual cortex. J Comput Neurosci 36:297–319

    Article  PubMed  Google Scholar 

  • Conway BR, Chatterjee S, Field GD, Horwitz GD, Johnson EN, Koida K, Mancuso K (2010) Advances in color science: from retina to behavior. J Neurosci 30(45):14955–14963

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Derrington AM, Krauskopf J, Lennie P (1984) Chromatic mechanisms in lateral geniculate nucleus of macaque. J Physiol 357:241–265

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Economides JR, Sincich LC, Adams DL, Horton JC (2011) Orientation tuning of cytochrome oxydase patches in macaque primary visual cortex. Nat Neurosci 14:1574–1580

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Foster D (2011) Color constancy. Vis Res 51:674–700

    Article  PubMed  Google Scholar 

  • Friedman HS, Zhou H, von der Heydt R (2003) The coding of uniform colour figures in monkey visual cortex. J Physiol 548(2):593–613

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Hansel D, Sompolinsky H (1998) Modeling feature selectivity in local cortical circuits, methods in neuronal modeling: from synapses to networks. MIT Press, Cambridge

    Google Scholar 

  • Hass ChA, Horwitz GD (2013) V1 mechanisms underlying chromatic contrast detection. J Neurophysiol 109:2483–2494

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Hubel DH, Wiesel TN (1962) Reception fields, binocular interaction and functional architecture in the cats visual cortex. J Physiol Lond 160:106–154

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Johnson EN, Hawken MJ, Shapley R (2001) The spatial transformation of color in the primary visual cortex of the macaque monkey. Nat Neurosci 4:409–416

    Article  CAS  PubMed  Google Scholar 

  • Johnson EN, Hawken MJ, Shapley R (2004) Cone inputs in macaque primary visual cortex. J Neurophysiol 91:2501–2514

    Article  PubMed  Google Scholar 

  • Johnson EN, Hawken MJ, Shapley R (2008) The orientation selectivity of color-responsive neurons in macaque V1. J Neurosci 28:8096–8106

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Land EH, McCann JJ (1971) Lightness and retinex theory. J Opt Soc Am 61:1–11

    Article  CAS  PubMed  Google Scholar 

  • Landisman CE, Ts’o DY (2002) Color processing in macaque striate cortex: relationships to ocular dominance, cytochrome oxidase, and orientation. J Neurophysiol 87:3126–3137

    CAS  PubMed  Google Scholar 

  • Lennie P, Krauskopf J, Sclar G (1990) Chromatic mechanisms in striate cortex of macaque. J Neurosci 10:649–669

    CAS  PubMed  Google Scholar 

  • Leventhal AG, Thompson KG, Liu D, Zhou Y, Ault SJ (1995) Concomitant sensitivity to orientation, direction, and color of cells in layers 2, 3, and 4 of monkey striate cortex. J Neurosci 15:1808–1818

    CAS  PubMed  Google Scholar 

  • Livingstone MS, Hubel DH (1984) Anatomy and physiology of a color system in the primate visual cortex. J Neurosci 4:309–356

    CAS  PubMed  Google Scholar 

  • Lu HD, Roe AW (2008) Functional organization of color domains in V1 and V2 of macaque monkey revealed by optical imaging. Cereb Cortex 18:516–533

    Article  PubMed Central  PubMed  Google Scholar 

  • Mundel T, Dimitrov A, Cowan JD (1997) Visual cortex circuitry and orientation tuning. Adv Neural Inf Process Syst 9:887–893

  • Rangan AV, Tao L, Kovacic G, Cai D (2009) Large-scale computational modeling of the primary visual cortex. In: Josic K, Matias M, Romo R, Rubin J (eds) Coherent behavior in neuronal networks. Springer series in computational neuroscience, vol 3. Springer, New York

  • Rizzi A, Gatta C, Marini D (2004) From retinex to automatic color equalization: issues in developing a new algorithm for unsupervised color equalization. J Electron Imaging 13(1):75–84

    Article  Google Scholar 

  • Schummers J, Cronin B, Wimmer K, Stimberg M, Martin R, Obermayer K, Koerding K, Sur M (2007) Dynamics of orientation tuning in cat V1 neurons depend on location within layers and orientation maps. Front Neurosci 1(1):145–159

    Article  PubMed Central  PubMed  Google Scholar 

  • Symes A, Wennekers T (2009) Spatiotemporal dynamics in the cortical microcircuit: a modelling study of primary visual cortex layer 2/3. Neural Netw 22:1079–1092

    Article  PubMed  Google Scholar 

  • Thomson AM, Lamy C (2007) Functional maps of neocortical local circuitry. Front Neurosci 1:19–42

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  • Xiao Y, Casti A, Xiao J, Kaplan E (2006) A spatially organised representation of colour in macaque primary visual cortex. Perception 35:21 (supplement)

  • Xiao Y, Casti A, Xiao J, Kaplan E (2007) Hue maps in primate striate cortex. NeuroImage 35:771–786

    Article  PubMed Central  PubMed  Google Scholar 

  • Zeki S (1983) Color coding in the cerebral cortex: the reaction of cells in monkey visual cortex to wavelengths and colors. Neuroscience 9:741–765

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

The contribution of Anton Chizhov into the reported study was supported by the Russian Foundation for Basic Research with the research projects 113-04-01835a and 15-04-06234a.

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Correspondence to Elena Y. Smirnova.

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Smirnova, E.Y., Chizhkova, E.A. & Chizhov, A.V. A mathematical model of color and orientation processing in V1. Biol Cybern 109, 537–547 (2015). https://doi.org/10.1007/s00422-015-0659-1

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  • DOI: https://doi.org/10.1007/s00422-015-0659-1

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