Is sparse and distributed the coding goal of simple cells?

The question of why the receptive fields of simple cells in the primary visual cortex are Gabor-like is a crucial one in vision research. Many research efforts (Olshausen and Field 1996, 1997; van Hateren and Ruderman 1998; van Hateren and van der Schaaf 1998) that yield a set of localized, oriented, and bandpass Gabor-like receptive fields believe that sparse and distributed is the coding goal of simple cells. This paper investigates a more general coding strategy that measures equally any departure from normality in the simple cells responses. That is, we investigate the possibility that highly kurtotic response histograms may result if simple cells explicitly seek, not maximally kurtotic, but rather maximally non-Gaussian response histograms to natural images. It is found that, under this coding strategy, the simulations produce a majority of localized, oriented, bandpass (Gabor-like) receptive fields. Some receptive fields, however, are spatially distributed and show little oriented structure. Nearly all receptive fields, regardless of whether they are Gabor-like or non-Gabor-like, yield highly kurtotic response histograms to natural images. Thus, in seeking maximally non-Gaussian response histograms, receptive fields spontaneously yield highly kurtotic histograms. The presence in our ensemble of nonlocalized, nonoriented receptive fields may be due to the artificial requirement that receptive fields be orthonormal. We conclude that the high kurtoses observed in the response histograms of simple-cell receptive fields to natural images may reflect a property of natural images themselves rather than an explicit coding goal used to structure simple-cell receptive fields.Acknowledgement This work was supported by the US Office of Naval Research under agreement number N68936-00-2-0002.     

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.     

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.     

Response histogram shapes and tuning curves: The predicted responses of several cortical cell types to drifting gratings stimuli

The responses to visual stimuli of simple cortical cells show linear spatial summation within and between their receptive field subunits. Complex cortical cells do not show this linearity. We analyzed the simulated responses to drifting sinusoidal grating stimuli of simple and of several types of complex cells. The complex cells, whose responses are seen to be half-wave rectified before pooling, have receptive fields consisting of two or more DOG (difference-of-Gaussians) shaped subunits. In both cases of stimulation by contrast-reversal gratings or drifting gratings, the cells' response as a function of spatial frequency is affected by the subunit distances 2 and the stimulation frequency . Furthermore, an increased number of subunits (a larger receptive field) yields a narrower peak tuning curve with decreased modulation depth for many of the spatial frequencies. The average and the peak response tuning curves are compared for the different receptive field types.     

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.     

Simple model for encoding natural images by retinal ganglion cells with nonlinear spatial integration

A central goal in sensory neuroscience is to understand the neuronal signal processing involved in the encoding of natural stimuli. A critical step towards this goal is the development of successful computational encoding models. For ganglion cells in the vertebrate retina, the development of satisfactory models for responses to natural visual scenes is an ongoing challenge. Standard models typically apply linear integration of visual stimuli over space, yet many ganglion cells are known to show nonlinear spatial integration, in particular when stimulated with contrast-reversing gratings. We here study the influence of spatial nonlinearities in the encoding of natural images by ganglion cells, using multielectrode-array recordings from isolated salamander and mouse retinas. We assess how responses to natural images depend on first- and second-order statistics of spatial patterns inside the receptive field. This leads us to a simple extension of current standard ganglion cell models. We show that taking not only the weighted average of light intensity inside the receptive field into account but also its variance over space can partly account for nonlinear integration and substantially improve response predictions of responses to novel images. For salamander ganglion cells, we find that response predictions for cell classes with large receptive fields profit most from including spatial contrast information. Finally, we demonstrate how this model framework can be used to assess the spatial scale of nonlinear integration. Our results underscore that nonlinear spatial stimulus integration translates to stimulation with natural images. Furthermore, the introduced model framework provides a simple, yet powerful extension of standard models and may serve as a benchmark for the development of more detailed models of the nonlinear structure of receptive fields.     

Receptive field properties of neurons in the electrosensory lateral line lobe of the weakly electric fish, <Emphasis Type="Italic">Gnathonemus petersii</Emphasis>

The receptive field of a sensory neuron is known as that region in sensory space where a stimulus will alter the response of the neuron. We determined the spatial dimensions and the shape of receptive fields of electrosensitive neurons in the medial zone of the electrosensory lateral line lobe of the African weakly electric fish, Gnathonemus petersii, by using single cell recordings. The medial zone receives input from sensory cells which encode the stimulus amplitude. We analysed the receptive fields of 71 neurons. The size and shape of the receptive fields were determined as a function of spike rate and first spike latency and showed differences for the two analysis methods used. Spatial diameters ranged from 2 to 36 mm (spike rate) and from 2.45 to 14.12 mm (first spike latency). Some of the receptive fields were simple consisting only of one uniform centre, whereas most receptive fields showed a complex and antagonistic centre-surround organisation. Several units had a very complex structure with multiple centres and surrounding-areas. While receptive field size did not correlate with peripheral receptor location, the complexity of the receptive fields increased from rostral to caudal along the fish's body.     

Structure of receptive fields of cat pulvinar neurons sensitive to photic stimulation

Receptive fields of 262 pulvinar neurons were studied. Receptive fields of 142 of these neurons were studied in detail with the aid of a stationary spot of light, flashing in different parts of the receptive field. Depending on responses to presentation of the stationary stimulus the neurons were divided into six groups. The first group included neurons with on—off responses to photic stimulation (44 of 142), the second group neurons with off responses only (42 of 142). In cells of the third group (19 of 142) an on response only was recorded in all structures of the receptive field tested. Neurons of the fourth group (eight of 142) had a receptive field of similar structure to that of the simple receptive fields of neurons in cortical area 17. The fifth group (10 of 142) included neurons with a receptive field of concentric structure, the sixth (19 of 142) consisted of neurons with receptive fields with multiple discharge centers. The structure of the receptive field of these neurons was mosaic, with an irregular distribution of exciting and "silent" zones. The mean response latency of the pulvinar neurons was 40–70 msec. Responses of neurons with shorter (20 msec) and longer (130–160 msec) latent periods also were recorded.L. A. Orbeli Institute of Physiology, Academy of Sciences of the Armenian SSR, Erevan. Translated from Neirofiziologiya, Vol. 11, No. 1, pp. 3–10, January–February, 1979.     

Receptive field microstructure and dendritic geometry of retinal ganglion cells

We studied the fine spatial structure of the receptive fields of retinal ganglion cells and its relationship to the dendritic geometry of these cells. Cells from which recordings had been made were microinjected with Lucifer yellow, so that responses generated at precise locations within the receptive field center could be directly compared with that cell's dendritic structure. While many cells with small receptive fields had domeshaped sensitivity profiles, the majority of large receptive fields were composed of multiple regions of high sensitivity. The density of dendritic branches at any one location did not predict the regions of high sensitivity. Instead, the interactions between a ganglion cell's dendritic tree and the local mosaic of bipolar cell axons seem to define the fine structure of the receptive field center.     

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.     

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.     

Construction of complex receptive fields in cat primary visual cortex.

In primary visual cortex, neurons are classified into simple cells and complex cells based on their response properties. Although the role of these two cell types in vision is still unknown, an attractive hypothesis is that simple cells are necessary to construct complex receptive fields. This hierarchical model puts forward two main predictions. First, simple cells should connect monosynaptically to complex cells. Second, complex cells should become silent when simple cells are inactivated. We have recently provided evidence for the first prediction, and here we do the same for the second. In summary, our results suggest that the receptive fields of most layer 2+3 complex cells are generated by a mechanism that requires simple cell inputs.     

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.     

A Feedback Model of Attention Explains the Diverse Effects of Attention on Neural Firing Rates and Receptive Field Structure

Visual attention has many effects on neural responses, producing complex changes in firing rates, as well as modifying the structure and size of receptive fields, both in topological and feature space. Several existing models of attention suggest that these effects arise from selective modulation of neural inputs. However, anatomical and physiological observations suggest that attentional modulation targets higher levels of the visual system (such as V4 or MT) rather than input areas (such as V1). Here we propose a simple mechanism that explains how a top-down attentional modulation, falling on higher visual areas, can produce the observed effects of attention on neural responses. Our model requires only the existence of modulatory feedback connections between areas, and short-range lateral inhibition within each area. Feedback connections redistribute the top-down modulation to lower areas, which in turn alters the inputs of other higher-area cells, including those that did not receive the initial modulation. This produces firing rate modulations and receptive field shifts. Simultaneously, short-range lateral inhibition between neighboring cells produce competitive effects that are automatically scaled to receptive field size in any given area. Our model reproduces the observed attentional effects on response rates (response gain, input gain, biased competition automatically scaled to receptive field size) and receptive field structure (shifts and resizing of receptive fields both spatially and in complex feature space), without modifying model parameters. Our model also makes the novel prediction that attentional effects on response curves should shift from response gain to contrast gain as the spatial focus of attention drifts away from the studied cell.     

Predictive Feedback Can Account for Biphasic Responses in the Lateral Geniculate Nucleus

Biphasic neural response properties, where the optimal stimulus for driving a neural response changes from one stimulus pattern to the opposite stimulus pattern over short periods of time, have been described in several visual areas, including lateral geniculate nucleus (LGN), primary visual cortex (V1), and middle temporal area (MT). We describe a hierarchical model of predictive coding and simulations that capture these temporal variations in neuronal response properties. We focus on the LGN-V1 circuit and find that after training on natural images the model exhibits the brain's LGN-V1 connectivity structure, in which the structure of V1 receptive fields is linked to the spatial alignment and properties of center-surround cells in the LGN. In addition, the spatio-temporal response profile of LGN model neurons is biphasic in structure, resembling the biphasic response structure of neurons in cat LGN. Moreover, the model displays a specific pattern of influence of feedback, where LGN receptive fields that are aligned over a simple cell receptive field zone of the same polarity decrease their responses while neurons of opposite polarity increase their responses with feedback. This phase-reversed pattern of influence was recently observed in neurophysiology. These results corroborate the idea that predictive feedback is a general coding strategy in the brain.     

Invariance of visual operations at the level of receptive fields

The brain is able to maintain a stable perception although the visual stimuli vary substantially on the retina due to geometric transformations and lighting variations in the environment. This paper presents a theory for achieving basic invariance properties already at the level of receptive fields. Specifically, the presented framework comprises (i) local scaling transformations caused by objects of different size and at different distances to the observer, (ii) locally linearized image deformations caused by variations in the viewing direction in relation to the object, (iii) locally linearized relative motions between the object and the observer and (iv) local multiplicative intensity transformations caused by illumination variations. The receptive field model can be derived by necessity from symmetry properties of the environment and leads to predictions about receptive field profiles in good agreement with receptive field profiles measured by cell recordings in mammalian vision. Indeed, the receptive field profiles in the retina, LGN and V1 are close to ideal to what is motivated by the idealized requirements. By complementing receptive field measurements with selection mechanisms over the parameters in the receptive field families, it is shown how true invariance of receptive field responses can be obtained under scaling transformations, affine transformations and Galilean transformations. Thereby, the framework provides a mathematically well-founded and biologically plausible model for how basic invariance properties can be achieved already at the level of receptive fields and support invariant recognition of objects and events under variations in viewpoint, retinal size, object motion and illumination. The theory can explain the different shapes of receptive field profiles found in biological vision, which are tuned to different sizes and orientations in the image domain as well as to different image velocities in space-time, from a requirement that the visual system should be invariant to the natural types of image transformations that occur in its environment.     

Contextual modulation of V1 receptive fields depends on their spatial symmetry

The apparent receptive field characteristics of sensory neurons depend on the statistics of the stimulus ensemble—a nonlinear phenomenon often called contextual modulation. Since visual cortical receptive fields determined from simple stimuli typically do not predict responses to complex stimuli, understanding contextual modulation is crucial to understanding responses to natural scenes. To analyze contextual modulation, we examined how apparent receptive fields differ for two stimulus ensembles that are matched in first- and second-order statistics, but differ in their feature content: one ensemble is enriched in elongated contours. To identify systematic trends across the neural population, we used a multidimensional scaling method, the Procrustes transformation. We found that contextual modulation of receptive field components increases with their spatial extent. More surprisingly, we also found that odd-symmetric components change systematically, but even-symmetric components do not. This symmetry dependence suggests that contextual modulation is driven by oriented On/Off dyads, i.e., modulation of the strength of intracortically-generated signals. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.