Elsevier

Biosystems

Volume 89, Issues 1–3, May–June 2007, Pages 264-272
Biosystems

Inhomogeneous retino-cortical mapping is supported and stabilized with correlation-learning during self-motion

https://doi.org/10.1016/j.biosystems.2006.04.024Get rights and content

Abstract

In primates, the area of primary visual cortex representing a fixed area of visual space decreases with increasing eccentricity. We identify visual situations to which this inhomogeneous retino-cortical mapping is well adapted and study their relevance during natural vision and development. We assume that cortical activations caused by stationary objects during self-motion along the direction of gaze travel on average with constant speed across the cortical surface, independent of retinal eccentricity. This is the case if the distribution of objects corresponds to an ellipsoid with the observer in its center. We apply the resulting flow field to train a simple network of pulse coding neurons with Hebbian learning and demonstrate that the density of learned receptive field centers is in close agreement with primate retino-cortical magnification. In addition, the model reproduces the increase of receptive field size and the decrease of its peak sensitivity with increasing eccentricity. Our results suggest that self-motion may have played an important role in the evolution of the visual system and that cortical magnification can be refined and stabilized by Hebbian learning mechanisms in ontogenesis under natural viewing conditions.

Introduction

The spatial resolution of the representation of the visual field in primate primary visual cortex decreases strongly with increasing eccentricity (e.g., Daniel and Whitteridge, 1961) in parallel with the increase of receptive field (RF) sizes of retinal, thalamic and cortical neurons Hubel and Wiesel, 1974, Dow et al., 1981, Croner and Kaplan, 1995, Xu et al., 2002. A large number of cortical neurons process stimuli near the fovea, while relatively few represent the periphery. This inhomogeneous mapping keeps the number of retino-cortical connections relatively low, but requires eye movements over larger areas of the visual field for perception at high spatial resolution. The inhomogeneous retino-cortical mapping is to a large part determined genetically, but development of theories on its underlying principles and its shaping during ontogeny may help to understand fundamental coding mechanisms in the visual system. We investigate whether visual situations exist to which the inhomogeneous retino-cortical mapping is well adapted and ask how relevant these situations are during natural vision and development. Because vision plays an important role during navigation, visual processing should be well adapted to self-motion. Thus, it is reasonable to hypothesize that self-motion plays a role in determining retino-cortical mapping and magnification. Virsu and Hari ( 1996) showed that cortical magnification can be estimated by linear self-motion in a world, idealized as a sphere, under the assumption that cortical activations, caused by stationary objects, travel at constant cortical speed, independent of eccentricity. We take the complementary approach and investigate which average geometrical arrangement of static objects in the environment is best suited to predict cortical magnification from flow fields arising during self-motion along the direction of gaze. Furthermore, we demonstrate that a RF distribution, whose density is consistent with cortical magnification, can be learned in a basic network model of spiking neurons by training with flow fields similar to those experienced during self-motion.

Section snippets

Relating cortical magnification to self-motion

The dependence of RF density of neurons in primary visual cortex on retinal eccentricity can be quantitatively described by the linear cortical magnification factor M Daniel and Whitteridge, 1961, Van Essen et al., 1984, which is defined as the cortical distance corresponding to one degree of visual angle. M depends strongly on the retinal eccentricity α and can be approximated asM(α)=C2C1+α,where C2 is a scaling factor and the quotient C2/C1 is the cortical magnification in the fovea (α=0).

We

Model simulations

Here we demonstrate that a minimal network model with spiking neurons and other biologically plausible properties can learn an RF distribution whose density is consistent with the experimental cortical magnification factor, if trained with flow fields similar to those present during self-motion.

Summary of results

Our results demonstrate that cortical magnification is well adapted to represent flow fields generated during linear self-motion of an observer walking in the direction of gaze, if the distribution of stationary objects in the environment corresponds to an ellipsoid with the observer in its center. Additionally, we show that a distribution of RF centers whose density is in qualitative agreement with primate cortical magnification Dow et al., 1981, Van Essen et al., 1984, Adams and Horton, 2003

Acknowledgements

This work was supported by funding of the Friedrich-Ebert-Foundation to BA, and DFG Research group Ec 53/11 to RE and TW.

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