Visual receptive field organization

Increasingly systematic approaches to quantifying receptive fields in primary visual cortex, combined with inspired ideas about functional circuitry, non-linearities, and visual stimuli, are bringing new interest to classical problems. This includes the distinction and hierarchy between simple and complex cells, the mechanisms underlying the receptive field surround, and debates about optimal stimuli for mapping receptive fields. An important new problem arises from recent observations of stimulus-dependent spatial and temporal summation in primary visual cortex. It appears that the receptive field can no longer be considered unique, and we might have to relinquish this cherished notion as the embodiment of neuronal function in primary visual cortex.     

Visual field maps in human cortex

Much of the visual cortex is organized into visual field maps: nearby neurons have receptive fields at nearby locations in the image. Mammalian species generally have multiple visual field maps with each species having similar, but not identical, maps. The introduction of functional magnetic resonance imaging made it possible to identify visual field maps in human cortex, including several near (1) medial occipital (V1,V2,V3), (2) lateral occipital (LO-1,LO-2, hMT+), (3) ventral occipital (hV4, VO-1, VO-2), (4) dorsal occipital (V3A, V3B), and (5) posterior parietal cortex (IPS-0 to IPS-4). Evidence is accumulating for additional maps, including some in the frontal lobe. Cortical maps are arranged into clusters in which several maps have parallel eccentricity representations, while the angular representations within a cluster alternate in visual field sign. Visual field maps have been linked to functional and perceptual properties of the visual system at various spatial scales, ranging from the level of individual maps to map clusters to dorsal-ventral streams. We survey recent measurements of human visual field maps, describe hypotheses about the function and relationships between maps, and consider methods to improve map measurements and characterize the response properties of neurons comprising these maps.     

Predicting functional properties of visual cortex from an evolutionary scaling law

The number of neurons in the primary visual cortex (V1) is, across primate species, related to the number of neurons in the visual thalamus (the lateral geniculate nucleus [LGN]) by a power law with an exponent of 3/2. This evolutionary scaling law is explained by a simple relation according to which the fineness of resolution in cortex is related to the number of neurons in the area of cortex used to process the information from a single point of light (the point-spread area). The same theory provides a link between two functional properties of the visual cortex, the areal cortical magnification factor (ACMF) and the receptive field (RF) area.     

Selective disruption of one Cartesian axis of cortical maps and receptive fields by deficiency in ephrin-As and structured activity

The topographic representation of visual space is preserved from retina to thalamus to cortex. We have previously shown that precise mapping of thalamocortical projections requires both molecular cues and structured retinal activity. To probe the interaction between these two mechanisms, we studied mice deficient in both ephrin-As and retinal waves. Functional and anatomical cortical maps in these mice were nearly abolished along the nasotemporal (azimuth) axis of the visual space. Both the structure of single-cell receptive fields and large-scale topography were severely distorted. These results demonstrate that ephrin-As and structured neuronal activity are two distinct pathways that mediate map formation in the visual cortex and together account almost completely for the formation of the azimuth map. Despite the dramatic disruption of azimuthal topography, the dorsoventral (elevation) map was relatively normal, indicating that the two axes of the cortical map are organized by separate mechanisms.     

Plasticity and stability of the visual system in human achiasma

The absence of the optic chiasm is an extraordinary and extreme abnormality in the nervous system. The abnormality produces highly atypical functional responses in the cortex, including overlapping hemifield representations and bilateral population receptive fields in both striate and extrastriate visual cortex. Even in the presence of these large functional abnormalities, the effect on visual perception and daily life is not easily detected. Here, we demonstrate that in two achiasmic humans the gross topography of the geniculostriate and occipital callosal connections remains largely unaltered. We conclude that visual function is preserved by reorganization of intracortical connections instead of large-scale reorganizations of the visual cortex. Thus, developmental mechanisms of local wiring within cortical maps compensate for the improper gross wiring to preserve function in human achiasma.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist 'What' and 'Where' pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives 'where', for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The compu- tational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

Computational model for perception of objects and motions

Perception of objects and motions in the visual scene is one of the basic problems in the visual system. There exist ‘What’ and ‘Where’ pathways in the superior visual cortex, starting from the simple cells in the primary visual cortex. The former is able to perceive objects such as forms, color, and texture, and the latter perceives ‘where’, for example, velocity and direction of spatial movement of objects. This paper explores brain-like computational architectures of visual information processing. We propose a visual perceptual model and computational mechanism for training the perceptual model. The computational model is a three-layer network. The first layer is the input layer which is used to receive the stimuli from natural environments. The second layer is designed for representing the internal neural information. The connections between the first layer and the second layer, called the receptive fields of neurons, are self-adaptively learned based on principle of sparse neural representation. To this end, we introduce Kullback-Leibler divergence as the measure of independence between neural responses and derive the learning algorithm based on minimizing the cost function. The proposed algorithm is applied to train the basis functions, namely receptive fields, which are localized, oriented, and bandpassed. The resultant receptive fields of neurons in the second layer have the characteristics resembling that of simple cells in the primary visual cortex. Based on these basis functions, we further construct the third layer for perception of what and where in the superior visual cortex. The proposed model is able to perceive objects and their motions with a high accuracy and strong robustness against additive noise. Computer simulation results in the final section show the feasibility of the proposed perceptual model and high efficiency of the learning algorithm.     

Cortical modulation of the transient visual response at thalamic level: a TMS study

The transient visual response of feline dorsal lateral geniculate nucleus (dLGN) cells was studied under control conditions and during the application of repetitive transcranial magnetic stimulation at 1 Hz (rTMS@1Hz) on the primary visual cortex (V1). The results show that rTMS@1Hz modulates the firing mode of Y cells, inducing an increase in burst spikes and a decrease in tonic firing. On the other hand, rTMS@1Hz modifies the spatiotemporal characteristics of receptive fields of X cells, inducing a delay and a decrease of the peak response, and a change of the surround/center amplitude ratio of RF profiles. These results indicate that V1 controls the activity of the visual thalamus in a different way in the X and Y pathways, and that this feedback control is consistent with functional roles associated with each cell type.     

Inhibitory zones of receptive fields of the lateral geniculate body and visual cortex of the cat

Unit responses to moving strips were investigated. The organization of the inhibitory zones in the receptive fields of the lateral geniculate body and visual cortex of the cat was compared. The response in the receptive field of the lateral geniculate body was inhibited only during simultaneous stimulation of the excitatory and inhibitory zones of the field. Stimulation of the inhibitory zone in the receptive field of the visual cortex was effective for a long time (several hundreds of milliseconds) after stimulation of the excitatory zone. The inhibitory zones of the simple and complex receptive fields of the visual cortex differed significantly. An increase in the width of the strip above the optimal size reduced the inhibitory effect in the complex fields. This was not observed in the simple receptive fields. The functional and structural models of the receptive field of the visual cortex are discussed.I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 5, No. 2, pp. 201–209, March–April, 1973.     

Shaping of Receptive Fields in the Visual Cortex During Retinal Maturation

We present a computational study of the formation of simple-cell receptive field patterns in the primary visual cortex. Based on the observation that the spatial frequency of the retinal filter increases postnatally, our results explain differences in the time course of the development of orientation selectivity in binocularly deprived and normally reared kittens. Development after eye-opening in normal animals is modelled by training with natural images, whereas in the case of binocular deprivation noise-like stimulation continues. Further, it is shown that different orientation selectivities are obtained for network models trained with natural images in contrast to random phase images of identical second order statistics. The latter finding suggests that higher-order statistics of the inputs influences development of primary visual cortex. Finally, we search for quantities that identify possible signatures of natural image statistics in order to specify the amount of constructiveness that visual experience has on the formation of receptive fields.     

A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields

Computational models of primary visual cortex have demonstrated that principles of efficient coding and neuronal sparseness can explain the emergence of neurones with localised oriented receptive fields. Yet, existing models have failed to predict the diverse shapes of receptive fields that occur in nature. The existing models used a particular "soft" form of sparseness that limits average neuronal activity. Here we study models of efficient coding in a broader context by comparing soft and "bard" forms of neuronal sparseness. As a result of our analyses, we propose a novel network model for visual cortex. The model forms efficient visual representations in which the number of active neurones, rather than mean neuronal activity, is limited. This form of hard sparseness also economises cortical resources like synaptic memory and metabolic energy. Furthermore, our model accurately predicts the distribution of receptive field shapes found in the primary visual cortex of cat and monkey.     

用脑光学成像精确测定猫初级视皮层视野拓扑投射关系

利用基于脑内源信号的光学成像和二维互相关分析的方法,对猫初级视皮层17区的视野拓扑离心度(即视网膜-皮层拓扑关系)进行了精确测量。当采用在同一屏幕内处于上下视野的、方位互相垂直的两个相邻光栅刺激时,皮层中一部分区域的绝大部分细胞因同时兴奋而导致方位功能图模糊不清。将这种方位功能图和用单一方位(水平或垂直)全屏光栅刺激所得到的功能图进行比较,通过计算每一像素的互相关系数,从而获得皮层的精确视野拓扑离心度。同时用电生理的方法测量了同一视皮层内的单细胞的感受野位置,证明这种方法得到的视野离心度和光学记录方法得到的相同。因此,本研究为大面积地确定视皮层细胞感受野在视野中的位置提供了一种快速和较准确的方法。     

Recursive features of circular receptive fields

The distribution of excitability in retinal receptive fields may be well approximated by functions with recursive features. Physiological data do not exclude an implementation of recursive structures in the visual system. It is the most remarkable advantage of a recursive visual system, that cortical receptive fields tuned to different spatial frequencies will have an identical neuronal circuitry. Structural consequences for retina, LGN and visual cortex are discussed.     

A strategy for mapping biophysical to abstract neuronal network models applied to primary visual cortex

A fundamental challenge for the theoretical study of neuronal networks is to make the link between complex biophysical models based directly on experimental data, to progressively simpler mathematical models that allow the derivation of general operating principles. We present a strategy that successively maps a relatively detailed biophysical population model, comprising conductance-based Hodgkin-Huxley type neuron models with connectivity rules derived from anatomical data, to various representations with fewer parameters, finishing with a firing rate network model that permits analysis. We apply this methodology to primary visual cortex of higher mammals, focusing on the functional property of stimulus orientation selectivity of receptive fields of individual neurons. The mapping produces compact expressions for the parameters of the abstract model that clearly identify the impact of specific electrophysiological and anatomical parameters on the analytical results, in particular as manifested by specific functional signatures of visual cortex, including input-output sharpening, conductance invariance, virtual rotation and the tilt after effect. Importantly, qualitative differences between model behaviours point out consequences of various simplifications. The strategy may be applied to other neuronal systems with appropriate modifications.     

The Gaussian derivative model for spatial-temporal vision: I. Cortical model

How do we see the motion of objects as well as their shapes? The Gaussian Derivative (GD) spatial model is extended to time to help answer this question. The GD spatio-temporal model requires only two numbers to describe the complete three-dimensional space-time shapes of individual receptive fields in primate visual cortex. These two numbers are the derivative numbers along the respective spatial and temporal principal axes of a given receptive field. Nine transformation parameters allow for a standard geometric association of these intrinsic axes with the extrinsic environment. The GD spatio-temporal model describes in one framework the following properties of primate simple cell fields: motion properties, number of lobes in space-time, spatial orientation. location, and size. A discrete difference-of-offset-Gaussians (DOOG) model provides a plausible physiological mechanism to form GD-like model fields in both space and time. The GD model hypothesizes that receptive fields at the first stage of processing in the visual cortex approximate 'derivative analyzers' that estimate local spatial and temporal derivatives of the intensity profile in the visual environment. The receptive fields as modeled provide operators that can allow later stages of processing in either a biological or machine vision system to estimate the motion as well as the shapes of objects in the environment.     

Clustered organization of neurons with similar extra-receptive field properties in the primary visual cortex

The primary visual cortex is organized into clusters of cells having similar classical receptive field (CRF) properties. Nonclassical, extra-receptive fields (ERFs) can either inhibit or facilitate the response elicited by stimulation within the CRF. Here, we report that in the primary visual cortex of cat, neurons with similar inhibitory or facilitatory ERF properties are also grouped into clusters. These clusters are randomly distributed in all cortical layers, with no detectable relationship with orientation and ocular dominance columns. This functional organization of neurons with respect to ERF properties may allow an efficient processing of global visual information.     

Recurrent inhibition and clustered connectivity as a basis for Gabor-like receptive fields in the visual cortex

A continuous-space model of visual cortex interactions which, starting from elongate Gaussian functions, leads to high-selective Gabor-like receptive fields, is proposed. The model is based on intracortical inhibition mechanisms occurring through medium-range clustered connections. The analysis, carried out under the assumption of a linear superposition of geniculate and intracortical contributions, shows how inhibition enhances both spatial and spatial-frequency selectivity. The effects of inhibition strength and of its spatial organization on the properties of the resulting receptive field are investigated. Specifically, the relationships between receptive fields and inhibition schemes are investigated by deriving analytical expressions for their dependence and through a systematic numerical parametric study. The emergence of periodic receptive fields, like the ones observed in neurophysiological measurements, is also pointed out in relation to the clustered nature of the inhibitory scheme.     

Receptive fields of disparity-tuned simple cells in macaque V1

Binocular simple cells in primary visual cortex (V1) are the first cells along the mammalian visual pathway to receive input from both eyes. Two models of how binocular simple cells could extract disparity information have been put forward. The phase-shift model proposes that the receptive fields in the two eyes have different subunit organizations, while the position-shift model proposes that they have different overall locations. In five fixating macaque monkeys, we recorded from 30 disparity-tuned simple cells that showed selectivity to the disparity in a random dot stereogram. High-resolution maps of the left and right eye receptive fields indicated that both phase and position shifts were common. Single cells usually showed a combination of the two, and the optimum disparity was best correlated with the sum of receptive field phase and position shift.     

Initial processing of visual information within the retina and the LGN

The initial stage of information processing by the visual system reduces the information contained in the continuous image on the retina into a discrete set of responses which are carried from the lateral geniculate nucleus (LGN) to the visual cortex.-1. The optimal sampling of the light intensity distribution in the visual environment is achieved only if each channel in the visual pathways carries undistorted information corresponding to an image element. The visual system approaches as closely as possible the scheme of optimal spatial sampling, retaining the full information on the low spatial frequency content of the object light intensity. The ideal receptive field of a sustained LGN cell is then of the form J ₁ (Kr)/Kr.-2. The experimentally determined receptive fields of sustained LGN cells (and to some extent retinal ganglion cells as well) in cat closely resemble the functional form J ₁ (Kr)/Kr. The centre-surround organization of the receptive fields is therefore understood as a scheme which leads to a maximal information flow through the visual pathways.-3. The optimal sampling scheme cannot be realized by the retina alone, because of restrictions on the size of neural networks. It is therefore constructed in two stages, ending at the LGN level. A recombination of ganglion cell signals into optimal receptive fields is a major role of the LGN.     

Prediction of orientation selectivity from receptive field architecture in simple cells of cat visual cortex

From the intracellularly recorded responses to small, rapidly flashed spots, we have quantitatively mapped the receptive fields of simple cells in the cat visual cortex. We then applied these maps to a feedforward model of orientation selectivity. Both the preferred orientation and the width of orientation tuning of the responses to oriented stimuli were well predicted by the model. Where tested, the tuning curve was well predicted at different spatial frequencies. The model was also successful in predicting certain features of the spatial frequency selectivity of the cells. It did not successfully predict the amplitude of the responses to drifting gratings. Our results show that the spatial organization of the receptive field can account for a large fraction of the orientation selectivity of simple cells.