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.     

Receptive field properties of near neighbor orientation selective neurons in the visual cortex: a modeling study

The primary visual cortex is organized into clusters of cells having similar receptive fields (RFs). A purely feedforward model has been shown to produce realistic simple cell receptive fields. The modeled cells capture a wide range of receptive field properties of orientation selective cortical cells. We have analyzed the responses of 78 nearby cell pairs to study which RF properties are clustered. Orientation preference shows strongest clustering. Orientation tuning width (hwhh) and tuning height (spikes/sec) at the preferred orientation are not as tightly clustered. Spatial frequency is also not as tightly clustered and RF phase has the least clustering. Clustering property of orientation preference, orientation tuning height and width depend on the location of cells in the orientation map. No such location dependence is observed for spatial frequency and RF phase. Our results agree well with experimental data.     

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.     

Spatial and Feature-Based Attention in a Layered Cortical Microcircuit Model

Directing attention to the spatial location or the distinguishing feature of a visual object modulates neuronal responses in the visual cortex and the stimulus discriminability of subjects. However, the spatial and feature-based modes of attention differently influence visual processing by changing the tuning properties of neurons. Intriguingly, neurons'' tuning curves are modulated similarly across different visual areas under both these modes of attention. Here, we explored the mechanism underlying the effects of these two modes of visual attention on the orientation selectivity of visual cortical neurons. To do this, we developed a layered microcircuit model. This model describes multiple orientation-specific microcircuits sharing their receptive fields and consisting of layers 2/3, 4, 5, and 6. These microcircuits represent a functional grouping of cortical neurons and mutually interact via lateral inhibition and excitatory connections between groups with similar selectivity. The individual microcircuits receive bottom-up visual stimuli and top-down attention in different layers. A crucial assumption of the model is that feature-based attention activates orientation-specific microcircuits for the relevant feature selectively, whereas spatial attention activates all microcircuits homogeneously, irrespective of their orientation selectivity. Consequently, our model simultaneously accounts for the multiplicative scaling of neuronal responses in spatial attention and the additive modulations of orientation tuning curves in feature-based attention, which have been observed widely in various visual cortical areas. Simulations of the model predict contrasting differences between excitatory and inhibitory neurons in the two modes of attentional modulations. Furthermore, the model replicates the modulation of the psychophysical discriminability of visual stimuli in the presence of external noise. Our layered model with a biologically suggested laminar structure describes the basic circuit mechanism underlying the attention-mode specific modulations of neuronal responses and visual perception.     

The radial bias: a different slant on visual orientation sensitivity in human and nonhuman primates

It is generally assumed that sensitivity to different stimulus orientations is mapped in a globally equivalent fashion across primate visual cortex, at a spatial scale larger than that of orientation columns. However, some evidence predicts instead that radial orientations should produce higher activity than other orientations, throughout visual cortex. Here, this radial orientation bias was robustly confirmed using (1) human psychophysics, plus fMRI in (2) humans and (3) behaving monkeys. In visual cortex, fMRI activity was at least 20% higher in the retinotopic representations of polar angle which corresponded to the radial stimulus orientations (relative to tangential). In a global demonstration of this, we activated complementary retinotopic quadrants of visual cortex by simply changing stimulus orientation, without changing stimulus location in the visual field. This evidence reveals a neural link between orientation sensitivity and the cortical retinotopy, which have previously been considered independent.     

综述: 初级视皮层的亮度信息加工

亮度(luminance)是最基本的视觉信息.与其他视觉特征相比,由于视神经元对亮度刺激的反应较弱,并且许多神经元对均匀亮度无反应,对亮度信息编码的神经机制知之甚少.初级视皮层部分神经元对亮度的反应要慢于对比度反应,被认为是由边界对比度诱导的亮度知觉(brightness)的神经基础.我们的研究表明,初级视皮层许多神经元的亮度反应要快于对比度反应,并且这些神经元偏好低的空间频率、高的时间频率和高的运动速度,提示皮层下具有低空间频率和高运动速度通路的信息输入对产生初级视皮层神经元的亮度反应有贡献.已经知道初级视皮层神经元对空间频率反应的时间过程是从低空间频率到高空间频率,我们发现的早期亮度反应是对极低空间频率的反应,与这一时间过程是一致的,是这一从粗到细的视觉信息加工过程的第一步,揭示了处理最早的粗的视觉信息的神经基础.另外,初级视皮层含有偏好亮度下降和高运动速度的神经元,这群神经元的活动有助于在光照差的环境中检测高速运动的低亮度物体.     

A specialized area in limbic cortex for fast analysis of peripheral vision

In primates, prostriata is a small area located between the primary visual cortex (V1) and the hippocampal formation. Prostriata sends connections to multisensory and high-order association areas in the temporal, parietal, cingulate, orbitofrontal, and frontopolar cortices. It is characterized by a relatively simple histological organization, alluding to an early origin in mammalian evolution. Here we show that prostriata neurons in marmoset monkeys exhibit a unique combination of response properties, suggesting a new pathway for rapid distribution of visual information in parallel with the traditionally recognized dorsal and ventral streams. Whereas the location and known connections of prostriata suggest a high-level association area, its response properties are unexpectedly simple, resembling those found in early stages of the visual processing: neurons have robust, nonadapting responses to simple stimuli, with latencies comparable to those found in V1, and are broadly tuned to stimulus orientation and spatiotemporal frequency. However, their receptive fields are enormous and form a unique topographic map that emphasizes the far periphery of the visual field. These results suggest a specialized circuit through which stimuli in peripheral vision can bypass the elaborate hierarchy of extrastriate visual areas and rapidly elicit coordinated motor and cognitive responses across multiple brain systems.     

Parsimony,Exhaustivity and Balanced Detection in Neocortex

The layout of sensory brain areas is thought to subtend perception. The principles shaping these architectures and their role in information processing are still poorly understood. We investigate mathematically and computationally the representation of orientation and spatial frequency in cat primary visual cortex. We prove that two natural principles, local exhaustivity and parsimony of representation, would constrain the orientation and spatial frequency maps to display a very specific pinwheel-dipole singularity. This is particularly interesting since recent experimental evidences show a dipolar structures of the spatial frequency map co-localized with pinwheels in cat. These structures have important properties on information processing capabilities. In particular, we show using a computational model of visual information processing that this architecture allows a trade-off in the local detection of orientation and spatial frequency, but this property occurs for spatial frequency selectivity sharper than reported in the literature. We validated this sharpening on high-resolution optical imaging experimental data. These results shed new light on the principles at play in the emergence of functional architecture of cortical maps, as well as their potential role in processing information.     

reflection of stimulus orientation in reactions of visual cortex neurons

A mathematical model of neuronal target structure with spatial anisotropy of lateral inhibition is discussed. The positions of the neuronal target to oriented sensory stimuli are investigated by computer simulation. It is suggested that visual stimuli orientation is coded in the late phase of dynamic responses of cortical neurons. This idea is in agreement with the data obtained in experiments on guinea pig visual cortex neurons.     

The role of the posterior parietal cortex in coordinate transformations for visual-motor integration

Lesion to the posterior parietal cortex in monkeys and humans produces spatial deficits in movement and perception. In recording experiments from area 7a, a cortical subdivision in the posterior parietal cortex in monkeys, we have found neurons whose responses are a function of both the retinal location of visual stimuli and the position of the eyes in the orbits. By combining these signals area 7 a neurons code the location of visual stimuli with respect to the head. However, these cells respond over only limited ranges of eye positions (eye-position-dependent coding). To code location in craniotopic space at all eye positions (eye-position-independent coding) an additional step in neural processing is required that uses information distributed across populations of area 7a neurons. We describe here a neural network model, based on back-propagation learning, that both demonstrates how spatial location could be derived from the population response of area 7a neurons and accurately accounts for the observed response properties of these neurons.     

A linear model for symmetric receptive fields: implications for classification tests with flashed and moving images

The purpose of this study was to explore the effects of spatial and temporal properties on the expected responses of visual neurons that have linear receptive fields (RFs), particularly those having a mirror symmetric distribution of spatial subregions. Receptive fields that are symmetric in at least one spatial dimension occur in neurons of the retina, the lateral geniculate nucleus (LGN), and the visual cortex of mammals. Responses to flashing bars, moving bars, and moving edges were studied for different configurations of an analog RF model in which spatial and temporal aspects were varied independently. Responses of the model at intermediate stimulus speeds were found to agree with responses in the literature for X and Y units of the LGN and often for simple units of the visual cortex. In particular, having separated regions of response to light and dark edges, an identifying property of simple cells, was found to be a linear consequence of RF regions responding inversely to stimuli of opposite polarity. Model differences from responses of cortical complex units show that a linear model cannot mimic their responses, and imply that complex units employ major nonlinearities in coding image polarity (light vs dark), which signifies a nonlinearity in coding intensity. Because sudden flux changes inherent in flashing bars test mainly temporal RF properties, and slowly moving edges test mainly spatial properties, these two tests form a useful minimal set with which to describe and classify RFs. The usefulness of this set derives both from its sensitivity to spatial and temporal variables, and from the correlation between the linearity of a cell's processing of stimulus intensity and its RF classification.     

A neural network model on self-organizing emergence of simple-cell receptive field with orientation selectivity in visual cortex

In order to probe into the self-organizing emergence of simple cell orientation selectivity, we tried to construct a neural network model that consists of LGN neurons and simple cells in visual cortex and obeys the Hebbian learning rule. We investigated the neural coding and representation of simple cells to a natural image by means of this model. The results show that the structures of their receptive fields are determined by the preferred orientation selectivity of simple cells. However, they are also decided by the emergence of self-organization in the unsupervision learning process. This kind of orientation selectivity results from dynamic self-organization based on the interactions between LGN and cortex.     

A neural network model on self-organizing emergence of simple-cell receptive field with orientation selectivity in visual cortex

In order to probe into the self-organizing emergence of simple cell orientation selectivity, we tried to construct a neural network model that consists of LGN neurons and simple cells in visual cortex and obeys the Hebbian learning rule. We investigated the neural coding and representation of simple cells to a natural image by means of this model. The results show that the structures of their receptive fields are determined by the preferred orientation selectivity of simple cells. However, they are also decided by the emergence of self-organization in the unsupervision learning process. This kind of orientation selectivity results from dynamic self-organization based on the interactions between LGN and cortex.     

The influence of cortical feature maps on the encoding of the orientation of a short line

The inhomogeneous distribution of the receptive fields of cortical neurons influences the cortical representation of the orientation of short lines seen in visual images. We construct a model of the response of populations of neurons in the human primary visual cortex by combining realistic response properties of individual neurons and cortical maps of orientation and location preferences. The encoding error, which characterizes the difference between the parameters of a visual stimulus and their cortical representation, is calculated using Fisher information as the square root of the variance of a statistically efficient estimator. The error of encoding orientation varies considerably with the location and orientation of the short line stimulus as modulated by the underlying orientation preference map. The average encoding error depends only weakly on the structure of the orientation preference map and is much smaller than the human error of estimating orientation measured psychophysically. From this comparison we conclude that the actual mechanism of orientation perception does not make efficient use of all the information available in the neuronal responses and that it is the decoding of visual information from neuronal responses that limits psychophysical performance. Action Editor: Terrence Sejnowski     

A Model of Temporal Encoding of Stimulus Orientation by Neuronal Responses in the Primary Visual Cortex

It has been shown experimentally that the stimulus orientation that elicits the optimal response in an orientation column in the primary visual cortex (area V1) undergoes rapid systemic changes that last 10–100 ms. These changes allow different orientation columns to encode information from multiple items in the visual space (the so-called temporal encoding). However, the mechanism of these changes is still unknown. In addition, most of the modern biophysical models are unable to reproduce these changes; the peak orientation of their responses is constant over time. In this paper, we suggest a method to improve the firing-rate ring model of the orientation hypercolumn by replacing the spatial symmetric distribution of local connections with a spatial anti-symmetric distribution. As a result, we obtained a more perfect model that is capable of reproducing such changes. Moreover, their amplitude is proportional to the extent of asymmetry in the spatial distribution of local connections.     

A Push-Pull CORF Model of a Simple Cell with Antiphase Inhibition Improves SNR and Contour Detection

We propose a computational model of a simple cell with push-pull inhibition, a property that is observed in many real simple cells. It is based on an existing model called Combination of Receptive Fields or CORF for brevity. A CORF model uses as afferent inputs the responses of model LGN cells with appropriately aligned center-surround receptive fields, and combines their output with a weighted geometric mean. The output of the proposed model simple cell with push-pull inhibition, which we call push-pull CORF, is computed as the response of a CORF model cell that is selective for a stimulus with preferred orientation and preferred contrast minus a fraction of the response of a CORF model cell that responds to the same stimulus but of opposite contrast. We demonstrate that the proposed push-pull CORF model improves signal-to-noise ratio (SNR) and achieves further properties that are observed in real simple cells, namely separability of spatial frequency and orientation as well as contrast-dependent changes in spatial frequency tuning. We also demonstrate the effectiveness of the proposed push-pull CORF model in contour detection, which is believed to be the primary biological role of simple cells. We use the RuG (40 images) and Berkeley (500 images) benchmark data sets of images with natural scenes and show that the proposed model outperforms, with very high statistical significance, the basic CORF model without inhibition, Gabor-based models with isotropic surround inhibition, and the Canny edge detector. The push-pull CORF model that we propose is a contribution to a better understanding of how visual information is processed in the brain as it provides the ability to reproduce a wider range of properties exhibited by real simple cells. As a result of push-pull inhibition a CORF model exhibits an improved SNR, which is the reason for a more effective contour detection.     

Learning receptive field properties of complex cells in V1

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally.     

Separate modulations of human V1 associated with spatial attention and task structure

Functional magnetic resonance imaging (fMRI) was used while normal human volunteers engaged in simple detection and discrimination tasks, revealing separable modulations of early visual cortex associated with spatial attention and task structure. Both modulations occur even when there is no change in sensory stimulation. The modulation due to spatial attention is present throughout the early visual areas V1, V2, V3, and VP, and varies with the attended location. The task structure activations are strongest in V1 and are greater in regions that represent more peripheral parts of the visual field. Control experiments demonstrate that the task structure activations cannot be attributed to visual, auditory, or somatosensory processing, the motor response for the detection/discrimination judgment, or oculomotor responses such as blinks or saccades. These findings demonstrate that early visual areas are modulated by at least two types of endogenous signals, each with distinct cortical distributions.     

Can Retinal Ganglion Cell Dipoles Seed Iso-Orientation Domains in the Visual Cortex?

It has been argued that the emergence of roughly periodic orientation preference maps (OPMs) in the primary visual cortex (V1) of carnivores and primates can be explained by a so-called statistical connectivity model. This model assumes that input to V1 neurons is dominated by feed-forward projections originating from a small set of retinal ganglion cells (RGCs). The typical spacing between adjacent cortical orientation columns preferring the same orientation then arises via Moiré-Interference between hexagonal ON/OFF RGC mosaics. While this Moiré-Interference critically depends on long-range hexagonal order within the RGC mosaics, a recent statistical analysis of RGC receptive field positions found no evidence for such long-range positional order. Hexagonal order may be only one of several ways to obtain spatially repetitive OPMs in the statistical connectivity model. Here, we investigate a more general requirement on the spatial structure of RGC mosaics that can seed the emergence of spatially repetitive cortical OPMs, namely that angular correlations between so-called RGC dipoles exhibit a spatial structure similar to that of OPM autocorrelation functions. Both in cat beta cell mosaics as well as primate parasol receptive field mosaics we find that RGC dipole angles are spatially uncorrelated. To help assess the level of these correlations, we introduce a novel point process that generates mosaics with realistic nearest neighbor statistics and a tunable degree of spatial correlations of dipole angles. Using this process, we show that given the size of available data sets, the presence of even weak angular correlations in the data is very unlikely. We conclude that the layout of ON/OFF ganglion cell mosaics lacks the spatial structure necessary to seed iso-orientation domains in the primary visual cortex.     

A functional model of the wiring of the simple cells of visual cortex

A computer model of the simple cells in the mammalian visual cortex was constructed. The model cells received inputs from a great number of isopolar centre/surround cells assumed to be located in the lateral geniculate nucleus (LGN). The distribution of input to the model simple cells was either inhibitory/excitatory or inhibitory/excitatory/inhibitory. Such arrangements produced receptive fields containing four or five consecutively antagonistic subfields. Responses produced by the model cells to different types of stimuli (periodical as well as nonperiodical) were obtained and compared to responses of living cells reported from various laboratories under comparable stimulus conditions. In all the situations tested, the responses of the model cells corresponded qualitatively very well to those of living cells. It was seen that the same wiring mechanism was able to account for orientation selectivity, spatial frequency filtering, various phase relationships between stimulus and response, subfield orientational selectivity, and slight end-inhibition. Furthermore, the receptive fields of the model simple cells closely resemble Gabor functions.