The effects of noise on binocular rivalry waves: a stochastic neural field model

We analyse the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how multiplicative noise in the activity variables leads to a diffusive–like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. The multiplicative noise also renormalizes the mean speed of the wave. We use our analysis to calculate the first passage time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation leads to quenched disorder in the neural fields during propagation of a wave

Illusions in the Ring Model of visual orientation selectivity

The Ring Model of orientation tuning is a dynamical model of a hypercolumn of visual area V1 in the human neocortex that has been designed to account for the experimentally observed orientation tuning curves by local, i.e., cortico-cortical computations. The tuning curves are stationary, i.e. time independent, solutions of this dynamical model. One important assumption underlying the Ring Model is that the LGN input to V1 is weakly tuned to the retinal orientation and that it is the local computations in V1 that sharpen this tuning. Because the equations that describe the Ring Model have built-in equivariance properties in the synaptic weight distribution with respect to a particular group acting on the retinal orientation of the stimulus, the model in effect encodes an infinite number of tuning curves that are arbitrarily translated with respect to each other. By using the Orbit Space Reduction technique we rewrite the model equations in canonical form as functions of polynomials that are invariant with respect to the action of this group. This allows us to combine equivariant bifurcation theory with an efficient numerical continuation method in order to compute the tuning curves predicted by the Ring Model. Surprisingly some of these tuning curves are not tuned to the stimulus. We interpret them as neural illusions and show numerically how they can be induced by simple dynamical stimuli. These neural illusions are important biological predictions of the model. If they could be observed experimentally this would be a strong point in favour of the Ring Model. We also show how our theoretical analysis allows to very simply specify the ranges of the model parameters by comparing the model predictions with published experimental observations.Comment: 33 pages, 12 figure

Neural field model of binocular rivalry waves

We present a neural field model of binocular rivalry waves in visual cortex. For each eye we consider a one–dimensional network of neurons that respond maximally to a particular feature of the corresponding image such as the orientation of a grating stimulus. Recurrent connections within each one-dimensional network are assumed to be excitatory, whereas connections between the two networks are inhibitory (cross-inhibition). Slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We derive an analytical expression for the speed of a binocular rivalry wave as a function of various neurophysiological parameters, and show how properties of the wave are consistent with the wave–like propagation of perceptual dominance observed in recent psychophysical experiments. In addition to providing an analytical framework for studying binocular rivalry waves, we show how neural field methods provide insights into the mechanisms underlying the generation of the waves. In particular, we highlight the important role of slow adaptation in providing a “symmetry breaking mechanism” that allows waves to propagate

Context-Sensitive Binding by the Laminar Circuits of V1 and V2: A Unified Model of Perceptual Grouping, Attention, and Orientation Contrast

A detailed neural model is presented of how the laminar circuits of visual cortical areas V1 and V2 implement context-sensitive binding processes such as perceptual grouping and attention. The model proposes how specific laminar circuits allow the responses of visual cortical neurons to be determined not only by the stimuli within their classical receptive fields, but also to be strongly influenced by stimuli in the extra-classical surround. This context-sensitive visual processing can greatly enhance the analysis of visual scenes, especially those containing targets that are low contrast, partially occluded, or crowded by distractors. We show how interactions of feedforward, feedback and horizontal circuitry can implement several types of contextual processing simultaneously, using shared laminar circuits. In particular, we present computer simulations which suggest how top-down attention and preattentive perceptual grouping, two processes that are fundamental for visual binding, can interact, with attentional enhancement selectively propagating along groupings of both real and illusory contours, thereby showing how attention can selectively enhance object representations. These simulations also illustrate how attention may have a stronger facilitatory effect on low contrast than on high contrast stimuli, and how pop-out from orientation contrast may occur. The specific functional roles which the model proposes for the cortical layers allow several testable neurophysiological predictions to be made. The results presented here simulate only the boundary grouping system of adult cortical architecture. However we also discuss how this model contributes to a larger neural theory of vision which suggests how intracortical and intercortical feedback help to stabilize development and learning within these cortical circuits. Although feedback plays a key role, fast feedforward processing is possible in response to unambiguous information. Model circuits are capable of synchronizing quickly, but context-sensitive persistence of previous events can influence how synchrony develops. Although these results focus on how the interblob cortical processing stream controls boundary grouping and attention, related modeling of the blob cortical processing stream suggests how visible surfaces are formed, and modeling of the motion stream suggests how transient responses to scenic changes can control long-range apparent motion and also attract spatial attention.Defense Advanced Research Projects agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI 94-01659, IRI 97-20333); ONR (N00014-92-J-1309, N00014-95-1-0657