Hauke Bartsch

A mean-field model for orientation tuning, contrast saturation, and contextual effects in the primary visual cortex.

Abstract. Orientation-selective cells in the primary visual cortex of monkeys and cats are often characterized by an orientation-tuning width that is invariant under stimulus contrast. At the same time their contrast response function saturates or even super-saturates for high values of contrast. When two bar stimuli are presented within their classical receptive field, the neuronal response decreases with the intersection angle. When two stimuli are presented inside and outside the classical receptive field, the response of the cell increases with the intersection angle. Both cats and monkeys show iso-orientation suppression, which has sometimes been reported to be combined with cross-orientation facilitation. This property has previously been described as sensitivity to orientation contrast. We address the emergence of these effects with a model that describes the processing of geniculocortical signals through cortical circuitry. We hypothesize that short intracortical fibers mediate the classical receptive field effects, whereas long-range collaterals evoke contextual effects such as sensitivity to orientation contrast. We model this situation by setting up a mean-field description of two neighboring cortical hypercolumns, which can process a nonoverlapping center and a (nonclassical) surround stimulus. Both hypercolumns interact via idealized long-range connections. For an isolated model hypercolumn, we find that either contrast saturation or contrast-invariant orientation tuning emerges, depending on the strength of the lateral excitation. There is no parameter regime, however, where both phenomena emerge simultaneously. In the regime where contrast saturation is found, the model also correctly reproduces suppression due to a second, cross-oriented grid within the classical receptive field. If two model hypercolumns are mutually coupled by long-range connections that are iso-orientation specific, nonclassical surround stimuli show either suppression or facilitation for all surround orientations. Sensitivity to orientation contrast is not observed. This property requires excitatory-to-excitatory long-range couplings that are less orientation specific than those targeting inhibitory neurons.

Second-order statistics of natural images

Abstract Assuming adaptation of the visual cortex to its environment, we analyze the invariance found in natural images to explain the selective response of visual cortical neurons. We argue that the invariant structure of images can be formally expressed by dot-products. Utilizing the specific structure of the proposed model we show how non-linear functions can be learned efficiently from natural images. In addition to localized edge detectors we found model neurons that respond to changes in texture and cells that detect edge curvature. The analysis suggests new types of features neurons in primary visual cortex may be selective to.

A Model for Orientation Tuning and Contextual Effects of Orientation Selective Receptive Fields

We investigate a mean-field model which has previously been used to explain the response properties of orientation selective neurons in the primary visual cortex of monkeys and cats [2]. Two mutually coupled orientation hypercolumns are setup as local amplifiers based on local recurrent excitation and inhibition. We first investigate the individual hypercolumns. The model correctly predicts contrast invariant tuning, but analytical and numerical results show that the contrast response functions of individual orientation columns do not saturate. We therefore hypothesize that the cortical saturation effects found experimentally may be a consequence of the non-linear properties of single neurons rather than being an effect of different gains for inhibitory and excitatory cells [13]. We then extend this model to cover non-classical receptive fields and contextual effects. The model correctly predicts effective iso-orientation inhibition between hypercolumns. As long as parameters are chosen to ensure contrast invariant orientation tuning, however, net cross-orientation facilitation emerges only, if cells of different orientation preference are connected across hypercolumns. These results hint at deficiencies of this simple approach and suggest that contextual effects are mediated by populations of neurons, which are not take part of the local gain control.

On the influence of threshold variability in a mean-field model of the visual cortex

Orientation-selective neurons in monkeys and cats show contrast saturation and contrast-invariant orientation tuning (Albrecht and Hamilton, 1982). Recently proposed models for orientation selectivity predict contrast invariant orientation tuning but no contrast saturation at high strength of recurrent intracortical coupling, whereas at lower coupling strengths the contrast response saturates but the tuning widths are contrast dependent (Hansel and Sompolinsky, 1997; Bartsch, Stetter and Obermayer, 1997). In the present work we address the question, if and under which conditions the incorporation of a stochastic distribution of activation thresholds of cortical neurons leads to the saturation of the contrast response curve as a network effect. We find that contrast saturation occurs naturally if two different classes of inhibitory inter-neurons are combined. Low threshold inhibition keeps the gain of the cortical amplification finite, whereas high threshold inhibition causes contrast saturation.

Contextual effects by short range connections in a mean-field model of V1

Abstract In this paper, we derive a model for analyzing the influence of local cortical connections on the activities of neurons in V1. A set of orientation columns is arranged according to a measured orientation map. Orientation columns are connected by local excitatory and slightly more distributed inhibitory fibers. Based on this geometrical model we demonstrate that (i) sharp and contrast–invariant orientation tuning curves are combined with contrast saturation, (ii) the strength of cortical amplification can be localized in orientation space and (iii) anisotropic contextual suppression by iso-oriented flanking stimuli arises as an emergent property and can be mediated by local connections.

The influence of threshold variability on the response of visual cortical neurons

Abstract Orientation–selective neurons in monkeys and cats show contrast saturation and contrast-invariant orientation tuning (Albrecht and Hamilton, J. Neurophysiol. 48 (1982) 217–237). Recently proposed models for orientation selectivity predict contrast invariant orientation tuning but no contrast saturation at high strength of intracortical recurrent couplings, whereas at lower coupling strengths the contrast response saturates but the tuning widths are contrast dependent (Hansel and Sompolinsky, Methods in Neuronal Modeling, MIT Press, Cambridge, MA, 1997, pp. 499–567; Stetter et al., Visual Neurosci., Submitted for publication). In the present work we address the question, if and under which conditions the incorporation of a stochastic distribution of activation thresholds for cortical neurons helps resolving that paradoxon. We find that both phenomena occurs naturally if two different classes of inhibitory inter-neurons are combined. Low-threshold inhibition keeps the gain of the cortical amplification finite, whereas high-threshold inhibition causes contrast saturation.

A structure preserving image transformation as the goal of visual sensory coding

Abstract Neuronal selectivity is often characterized by stimuli that evoke maximal responses. But early in the visual system neurons are known to respond to a richer class of stimuli than it can be expected by a feed-forward architecture. To explain this finding we present a more general functional framework for the exploration of neuronal responses. To quantify the structure or ‘interestingness’ of an image patch we introduce a measure of the symmetries that can be found in image patches at the size of local receptive fields of cortical neurons. We show how this transformation can explain strong responses to complex stimuli as well as responses to simple grating stimuli as found for neurons in V1 and V2.