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).
Similar content being viewed by others
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
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
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
Bertalmío M, Cowan JD (2009) Implementing the Retinex algorithm with Wilson–Cowan equations. J Physiol 103:69–72
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
Chizhov AV (2014) Conductance-based refractory density model of primary visual cortex. J Comput Neurosci 36:297–319
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
Derrington AM, Krauskopf J, Lennie P (1984) Chromatic mechanisms in lateral geniculate nucleus of macaque. J Physiol 357:241–265
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
Foster D (2011) Color constancy. Vis Res 51:674–700
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
Hansel D, Sompolinsky H (1998) Modeling feature selectivity in local cortical circuits, methods in neuronal modeling: from synapses to networks. MIT Press, Cambridge
Hass ChA, Horwitz GD (2013) V1 mechanisms underlying chromatic contrast detection. J Neurophysiol 109:2483–2494
Hubel DH, Wiesel TN (1962) Reception fields, binocular interaction and functional architecture in the cats visual cortex. J Physiol Lond 160:106–154
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
Johnson EN, Hawken MJ, Shapley R (2004) Cone inputs in macaque primary visual cortex. J Neurophysiol 91:2501–2514
Johnson EN, Hawken MJ, Shapley R (2008) The orientation selectivity of color-responsive neurons in macaque V1. J Neurosci 28:8096–8106
Land EH, McCann JJ (1971) Lightness and retinex theory. J Opt Soc Am 61:1–11
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
Lennie P, Krauskopf J, Sclar G (1990) Chromatic mechanisms in striate cortex of macaque. J Neurosci 10:649–669
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
Livingstone MS, Hubel DH (1984) Anatomy and physiology of a color system in the primate visual cortex. J Neurosci 4:309–356
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
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
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
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
Thomson AM, Lamy C (2007) Functional maps of neocortical local circuitry. Front Neurosci 1:19–42
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
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
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.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00422-015-0659-1