Quantum-like signal-tuned approach to V1 modeling

Signal-tuned Gabor functions — Gaussian-modulated sinusoids whose parameters are determined by a spatial or spectral “tuning signal” — have previously been shown to provide a plausible model for the stimulus-dependent receptive fields and responses of the simple and complex cells of the primary visual cortex (V1). The signal-tuned responses obey Schrödinger equations, which has led to the proposal of a quantum-like model for V1 cells: by considering the squared magnitude of a particular signal-tuned wave function as a probability density, one arrives at a Poisson spiking process which appears consistent with the neurophysiological findings. Here, by incorporating Hermite-polynomial factors to the signal-tuned Gabor functions, we obtain a generalized quantum-like signal-tuned model for which further relevant properties are demonstrated, such as receptive-field coding of the stimulus and its derivatives, saturating spatial summation curves and half-wave rectification of the simple cell responses. Although only a one-dimensional approach is considered here, such properties will carry over to a two-dimensional model, in which case, as our preliminary analysis indicates, end-stopping — another important feature of cortical cells — can also be accommodated.

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Complex Cells Increase Their Phase Sensitivity at Low Contrasts and Following Adaptation

Journal of Neurophysiology ◽

10.1152/jn.00433.2007 ◽

2007 ◽

Vol 98 (3) ◽

pp. 1155-1166 ◽

Cited By ~ 31

Author(s):

N. A. Crowder ◽

J. van Kleef ◽

B. Dreher ◽

M. R. Ibbotson

Keyword(s):

Receptive Fields ◽

Phase Sensitivity ◽

Complex Cells ◽

Spike Threshold ◽

Cell Responses ◽

Layer 4 ◽

A Cell ◽

Phase Sensitive ◽

Simple And Complex Cells ◽

Mean Time

One of the best-known dichotomies in neuroscience is the division of neurons in the mammalian primary visual cortex into simple and complex cells. Simple cells have receptive fields with separate on and off subregions and give phase-sensitive responses to moving gratings, whereas complex cells have uniform receptive fields and are phase invariant. The phase sensitivity of a cell is calculated as the ratio of the first Fourier coefficient ( F1) to the mean time-average ( F0) of the response to moving sinusoidal gratings at 100% contrast. Cells are then classified as simple ( F1/ F0>1) or complex ( F1/ F0<1). We manipulated cell responses by changing the stimulus contrast or through adaptation. The F1/ F0ratios of cells defined as complex at 100% contrast increased at low contrasts and following adaptation. Conversely, the F1/ F0ratios remained constant for cells defined as simple at 100% contrast. The latter cell type was primarily located in thalamorecipient layers 4 and 6. Many cells initially classified as complex exhibit F1/ F0>1 at low contrasts and after adaptation (particularly in layer 4). The results are consistent with the spike-threshold hypothesis, which suggests that the division of cells into two types arises from the nonlinear interaction of spike threshold with membrane potential responses.

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Signal-Tuned Gabor Functions as Models for Stimulus-Dependent Cortical Receptive Fields

Neural Computation ◽

10.1162/neco_a_00581 ◽

2014 ◽

Vol 26 (5) ◽

pp. 920-952 ◽

Cited By ~ 4

Author(s):

José R. A. Torreão ◽

Silvia M. C. Victer ◽

Marcos S. Amaral

Keyword(s):

Receptive Fields ◽

Gabor Transform ◽

Spectral Tuning ◽

Complex Cells ◽

Model Based ◽

Accurate Detection ◽

Gabor Functions ◽

Neurophysiological Studies ◽

Simple And Complex Cells ◽

Cortical Receptive Fields

We propose and analyze a model, based on signal-tuned Gabor functions, for the receptive fields and responses of V1 cells. Signal-tuned Gabor functions are gaussian-modulated sinusoids whose parameters are obtained from a given, spatial, or spectral “tuning” signal. These functions can be proven to yield exact representations of their tuning signals and have recently been proposed as the kernels of a variant Gabor transform—the signal-tuned Gabor transform (STGT)—which allows the accurate detection of spatial and spectral events. Here we show that by modeling the receptive fields of simple and complex cells as signal-tuned Gabor functions and expressing their responses as STGTs, we are able to replicate the properties of these cells when tested with standard grating and slit inputs, at the same time emulating their stimulus-dependent character as revealed by recent neurophysiological studies.

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Generalized signal-tuned Gabor approach for signal representation and analysis

International Journal of Modern Physics C ◽

10.1142/s0129183117500012 ◽

2017 ◽

Vol 28 (01) ◽

pp. 1750001 ◽

Cited By ~ 1

Author(s):

José R. A. Torreão

Keyword(s):

Fourier Transform ◽

Visual Cortex ◽

Fourier Transforms ◽

Fractional Fourier Transform ◽

Receptive Fields ◽

Gabor Functions ◽

Plausible Model ◽

Spectral Signal ◽

Potential Applications ◽

Space Frequency

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given “tuning” signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal’s fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach.

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Binocular Combination of Contrast Signals by Striate Cortical Neurons in the Monkey

Journal of Neurophysiology ◽

10.1152/jn.1997.78.1.366 ◽

1997 ◽

Vol 78 (1) ◽

pp. 366-382 ◽

Cited By ~ 24

Author(s):

Earl L. Smith ◽

Yuzo Chino ◽

Jinren Ni ◽

Han Cheng

Keyword(s):

Cortical Neurons ◽

Striate Cortex ◽

Receptive Fields ◽

Spatial Summation ◽

Simple Cells ◽

Complex Cells ◽

Threshold Response ◽

Binocular Interactions ◽

Specific Complex ◽

Left And Right

Smith, Earl L., III, Yuzo Chino, Jinren Ni, and Han Cheng. Binocular combination of contrast signals by striate cortical neurons in the monkey. J. Neurophysiol. 78: 366–382, 1997. With the use of microelectrode recording techniques, we investigated how the contrast signals from the two eyes are combined in individual cortical neurons in the striate cortex of anesthetized and paralyzed macaque monkeys. For a given neuron, the optimal spatial frequency, orientation, and direction of drift for sine wave grating stimuli were determined for each eye. The cell's disparity tuning characteristics were determined by measuring responses as a function of the relative interocular spatial phase of dichoptic stimuli that consisted of the optimal monocular gratings. Binocular contrast summation was then investigated by measuring contrast response functions for optimal dichoptic grating pairs that had left- to right-eye interocular contrast ratios that varied from 0.1 to 10. The goal was to determine the left- and right-eye contrast components required to produce a criterion threshold response. For all functional classes of cortical neurons and for both cooperative and antagonistic binocular interactions, there was a linear relationship between the left- and right-eye contrast components required to produce a threshold response. Thus, for example for cooperative binocular interactions, a reduction in contrast to one eye was counterbalanced by an equivalent increase in contrast to the other eye. These results showed that in simple cells and phase-specific complex cells, the contrast signals from the two eyes were linearly combined at the subunit level before nonlinear rectification. In non-phase-specific complex cells, the linear binocular convergence of contrast signals could have taken place either before or after the rectification process, but before spike generation. In addition, for simple cells, vector analysis of spatial summation showed that the inputs from the two eyes were also combined in a linear manner before nonlinear spike-generating mechanisms. Thus simple cells showed linear spatial summation not only within and between subregions in a given receptive field, but also between the left- and right-eye receptive fields. Overall, the results show that the effectiveness of a stimulus in producing a response reflects interocular differences in the relative balance of inputs to a given cell, however, the eye of origin of a light-evoked signal has no specific consequence.

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Spatial and Temporal Features of Synaptic to Discharge Receptive Field Transformation in Cat Area 17

Journal of Neurophysiology ◽

10.1152/jn.90946.2008 ◽

2010 ◽

Vol 103 (2) ◽

pp. 677-697 ◽

Cited By ~ 7

Author(s):

Lionel G. Nowak ◽

Maria V. Sanchez-Vives ◽

David A. McCormick

Keyword(s):

Spatial Frequency ◽

Response Latency ◽

Frequency Tuning ◽

Receptive Fields ◽

Width Ratio ◽

Area 17 ◽

Simple Cells ◽

Complex Cells ◽

Temporal Features ◽

Simple And Complex Cells

The aim of the present study was to characterize the spatial and temporal features of synaptic and discharge receptive fields (RFs), and to quantify their relationships, in cat area 17. For this purpose, neurons were recorded intracellularly while high-frequency flashing bars were used to generate RFs maps for synaptic and spiking responses. Comparison of the maps shows that some features of the discharge RFs depended strongly on those of the synaptic RFs, whereas others were less dependent. Spiking RF duration depended poorly and spiking RF amplitude depended moderately on those of the underlying synaptic RFs. At the other extreme, the optimal spatial frequency and phase of the discharge RFs in simple cells were almost entirely inherited from those of the synaptic RFs. Subfield width, in both simple and complex cells, was less for spiking responses compared with synaptic responses, but synaptic to discharge width ratio was relatively variable from cell to cell. When considering the whole RF of simple cells, additional variability in width ratio resulted from the presence of additional synaptic subfields that remained subthreshold. Due to these additional, subthreshold subfields, spatial frequency tuning predicted from synaptic RFs appears sharper than that predicted from spiking RFs. Excitatory subfield overlap in spiking RFs was well predicted by subfield overlap at the synaptic level. When examined in different regions of the RF, latencies appeared to be quite variable, but this variability showed negligible dependence on distance from the RF center. Nevertheless, spiking response latency faithfully reflected synaptic response latency.

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Substructure of Direction-Selective Receptive Fields in Macaque V1

Journal of Neurophysiology ◽

10.1152/jn.00822.2002 ◽

2003 ◽

Vol 89 (5) ◽

pp. 2743-2759 ◽

Cited By ~ 33

Author(s):

Margaret S. Livingstone ◽

Bevil R. Conway

Keyword(s):

Receptive Fields ◽

Direction Selectivity ◽

Positive Interactions ◽

Null Direction ◽

Simple Cells ◽

Complex Cells ◽

Preferred Direction ◽

Orientation Axis ◽

Interaction Regions ◽

Simple And Complex Cells

We used two-dimensional (2-D) sparse noise to map simultaneous and sequential two-spot interactions in simple and complex direction-selective cells in macaque V1. Sequential-interaction maps for both simple and complex cells showed preferred-direction facilitation and null-direction suppression for same-contrast stimulus sequences and the reverse for inverting-contrast sequences, although the magnitudes of the interactions were weaker for the simple cells. Contrast-sign selectivity in complex cells indicates that direction-selective interactions in these cells must occur in antecedent simple cells or in simple-cell-like dendritic compartments. Our maps suggest that direction selectivity, and on andoff segregation perpendicular to the orientation axis, can occur prior to receptive-field elongation along the orientation axis. 2-D interaction maps for some complex cells showed elongated alternating facilitatory and suppressive interactions as predicted if their inputs were orientation-selective simple cells. The negative interactions, however, were less elongated than the positive interactions, and there was an inflection at the origin in the positive interactions, so the interactions were chevron-shaped rather than band-like. Other complex cells showed only two round interaction regions, one negative and one positive. Several explanations for the map shapes are considered, including the possibility that directional interactions are generated directly from unoriented inputs.

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Image statistics at the point of gaze during human navigation

Visual Neuroscience ◽

10.1017/s0952523808080978 ◽

2009 ◽

Vol 26 (1) ◽

pp. 81-92 ◽

Cited By ~ 16

Author(s):

CONSTANTIN A. ROTHKOPF ◽

DANA H. BALLARD

Keyword(s):

Visual System ◽

Selection Process ◽

Human Subjects ◽

Image Features ◽

Complex Cells ◽

Cell Responses ◽

Active Selection ◽

Active Nature ◽

Simple And Complex Cells ◽

Distinct Features

AbstractTheories of efficient sensory processing have considered the regularities of image properties due to the structure of the environment in order to explain properties of neuronal representations of the visual world. The regularities imposed on the input to the visual system due to the regularities of the active selection process mediated by the voluntary movements of the eyes have been considered to a much lesser degree. This is surprising, given that the active nature of vision is well established. The present article investigates statistics of image features at the center of gaze of human subjects navigating through a virtual environment and avoiding and approaching different objects. The analysis shows that contrast can be significantly higher or lower at fixation location compared to random locations, depending on whether subjects avoid or approach targets. Similarly, significant differences in the distribution of responses of model simple and complex cells between horizontal and vertical orientations are found over timescales of tens of seconds. By clustering the model simple cell responses, it is established that gaze was directed toward three distinct features of intermediate complexity the vast majority of time. Thus, this study demonstrates and quantifies how the visuomotor tasks of approaching and avoiding objects during navigation determine feature statistics of the input to the visual system through the combined influence on body and eye movements.

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Cone Inputs to Simple and Complex Cells in V1 of Awake Macaque

Journal of Neurophysiology ◽

10.1152/jn.00965.2006 ◽

2007 ◽

Vol 97 (4) ◽

pp. 3070-3081 ◽

Cited By ~ 35

Author(s):

Gregory D. Horwitz ◽

E. J. Chichilnisky ◽

Thomas D. Albright

Keyword(s):

Linear Models ◽

Noise Analysis ◽

Receptive Fields ◽

Light Responses ◽

Simple Cells ◽

Complex Cells ◽

V1 Neurons ◽

Spike Triggered Averaging ◽

Simple And Complex Cells ◽

Simple And Complex Cell

Rules by which V1 neurons combine signals originating in the cone photoreceptors are poorly understood. We measured cone inputs to V1 neurons in awake, fixating monkeys with white-noise analysis techniques that reveal properties of light responses not revealed by purely linear models used in previous studies. Simple cells were studied by spike-triggered averaging that is robust to static nonlinearities in spike generation. This analysis revealed, among heterogeneously tuned neurons, two relatively discrete categories: one with opponent L- and M-cone weights and another with nonopponent cone weights. Complex cells were studied by spike-triggered covariance, which identifies features in the stimulus sequence that trigger spikes in neurons with receptive fields containing multiple linear subunits that combine nonlinearly. All complex cells responded to nonopponent stimulus modulations. Although some complex cells responded to cone-opponent stimulus modulations too, none exhibited the pure opponent sensitivity observed in many simple cells. These results extend the findings on distinctions between simple and complex cell chromatic tuning observed in previous studies in anesthetized monkeys.

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Replicating Receptive Fields of Simple and Complex Cells in Primary Visual Cortex in a Neuronal Network Model with Temporal and Population Sparseness and Reliability

Neural Computation ◽

10.1162/neco_a_00341 ◽

2012 ◽

Vol 24 (10) ◽

pp. 2700-2725 ◽

Cited By ~ 6

Author(s):

Takuma Tanaka ◽

Toshio Aoyagi ◽

Takeshi Kaneko

Keyword(s):

Visual Cortex ◽

Receptive Field ◽

Primary Visual Cortex ◽

Receptive Fields ◽

Learning Rule ◽

Simple Cell ◽

Complex Cells ◽

Receptive Field Properties ◽

Output Neurons ◽

Simple And Complex Cells

We propose a new principle for replicating receptive field properties of neurons in the primary visual cortex. We derive a learning rule for a feedforward network, which maintains a low firing rate for the output neurons (resulting in temporal sparseness) and allows only a small subset of the neurons in the network to fire at any given time (resulting in population sparseness). Our learning rule also sets the firing rates of the output neurons at each time step to near-maximum or near-minimum levels, resulting in neuronal reliability. The learning rule is simple enough to be written in spatially and temporally local forms. After the learning stage is performed using input image patches of natural scenes, output neurons in the model network are found to exhibit simple-cell-like receptive field properties. When the output of these simple-cell-like neurons are input to another model layer using the same learning rule, the second-layer output neurons after learning become less sensitive to the phase of gratings than the simple-cell-like input neurons. In particular, some of the second-layer output neurons become completely phase invariant, owing to the convergence of the connections from first-layer neurons with similar orientation selectivity to second-layer neurons in the model network. We examine the parameter dependencies of the receptive field properties of the model neurons after learning and discuss their biological implications. We also show that the localized learning rule is consistent with experimental results concerning neuronal plasticity and can replicate the receptive fields of simple and complex cells.

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