Interneurons exhibiting centre--surround antagonism within their receptive fields are commonly found in peripheral visual pathways. We propose that this organization enables the visual system to encode spatial detail in a manner that minimizes the deleterious effects of intrinsic noise, by exploiting the spatial correlation that exists within natural scenes. The antagonistic surround takes a weighted mean of the signals in neighbouring receptors to generate a statistical prediction of the signal at the centre. The predicted value is subtracted from the actual centre signal, thus minimizing the range of outputs transmitted by the centre. In this way the entire dynamic range of the interneuron can be devoted to encoding a small range of intensities, thus rendering fine detail detectable against intrinsic noise injected at later stages in processing. This predictive encoding scheme also reduces spatial redundancy, thereby enabling the array of interneurons to transmit a larger number of distinguishable images, taking into account the expected structure of the visual world. The profile of the required inhibitory field is derived from statistical estimation theory. This profile depends strongly upon the signal: noise ratio and weakly upon the extent of lateral spatial correlation. The receptive fields that are quantitatively predicted by the theory resemble those of X-type retinal ganglion cells and show that the inhibitory surround should become weaker and more diffuse at low intensities. The latter property is unequivocally demonstrated in the first-order interneurons of the fly's compound eye. The theory is extended to the time domain to account for the phasic responses of fly interneurons. These comparisons suggest that, in the early stages of processing, the visual system is concerned primarily with coding the visual image to protect against subsequent intrinsic noise, rather than with reconstructing the scene or extracting specific features from it. The treatment emphasizes that a neuron's dynamic range should be matched to both its receptive field and the statistical properties of the visual pattern expected within this field. Finally, the analysis is synthetic because it is an extension of the background suppression hypothesis (Barlow & Levick 1976), satisfies the redundancy reduction hypothesis (Barlow 1961 a, b) and is equivalent to deblurring under certain conditions (Ratliff 1965).

Predictive Coding: A Fresh View of Inhibition in the Retina

Quantitative analysis of cat retinal ganglion cell response to visual stimuli

The construction of directionally selective units, and their use in the processing of visual motion, are considered. The zero crossings of $\nabla ^{2}$G(x, y) * I(x,y) are located, as in Marr & Hildreth (1980). That is, the image is filtered through centre-surround receptive fields, and the zero values in the output are found. In addition, the time derivative $\delta $[$\nabla ^{2}$G(x, y) * I(x, y)]/$\partial $t is measured at the zero crossings, and serves to constrain the local direction of motion to within 180 degrees. The direction of motion can be determined in a second stage, for example by combining the local constraints. The second part of the paper suggests a specific model of the information processing by the X and Y cells of the retina and lateral geniculate nucleus, and certain classes of cortical simple cells. A number of psychophysical and neurophysiological predictions are derived from the theory.

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Directional Selectivity and its Use in Early Visual Processing

The Topography of Vision in Mammals of Contrasting Life Style: Comparative Optics and Retinal Organisation

Assessing the reliability of neuronal spike trains is fundamental to an understanding of the neural code. We measured the reproducibility of retinal responses to repeated visual stimuli. In both tiger salamander and rabbit, the retinal ganglion cells responded to random flicker with discrete, brief periods of firing. For any given cell, these firing events covered only a small fraction of the total stimulus time, often less than 5%. Firing events were very reproducible from trial to trial: the timing jitter of individual spikes was as low as 1 msec, and the standard deviation in spike count was often less than 0.5 spikes. Comparing the precision of spike timing to that of the spike count showed that the timing of a firing event conveyed several times more visual information than its spike count. This sparseness and precision were general characteristics of ganglion cell responses, maintained over the broad ensemble of stimulus waveforms produced by random flicker, and over a range of contrasts. Thus, the responses of retinal ganglion cells are not properly described by a firing probability that varies continuously with the stimulus. Instead, these neurons elicit discrete firing events that may be the fundamental coding symbols in retinal spike trains.

https://www.pnas.org/content/pnas/94/10/5411.full.pdf

R. W. Rodieck

Papers

Response of cat retinal ganglion cells to moving visual patterns