scholarly journals Learning receptive field properties of complex cells in V1

2020 ◽  
Author(s):  
Yanbo Lian ◽  
Ali Almasi ◽  
David B. Grayden ◽  
Tatiana Kameneva ◽  
Anthony N. Burkitt ◽  
...  
Keyword(s):  
Visual Cortex ◽  
Experimental Studies ◽  
Learning Rule ◽  
Energy Model ◽  
Learning Ability ◽  
Simple Cells ◽  
Complex Cells ◽  
Spatial Phase ◽  
Model Complex ◽  
The Brain

AbstractThere 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.Author summaryMany cortical functions originate from the learning ability of the brain. How the properties of cortical cells are learned is vital for understanding how the brain works. There are many models that explain how V1 simple cells can be learned. However, how V1 complex cells are learned still remains unclear. In this paper, we propose a model of learning in complex cells based on the Bienenstock, Cooper, and Munro (BCM) rule. We demonstrate that properties of receptive fields of complex cells can be learned using this biologically plausible learning rule. Quantitative comparisons between the model and experimental data are performed. Results show that model complex cells can account for the diversity of complex cells found in experimental studies. In summary, this study provides a plausible explanation for how complex cells can be learned using biologically plausible plasticity mechanisms. Our findings help us to better understand biological vision processing and provide us with insights into the general signal processing principles that the visual cortex employs to process visual information.

scholarly journals Learning receptive field properties of complex cells in V1

2021 ◽  
Vol 17 (3) ◽  
pp. e1007957
Author(s):  
Yanbo Lian ◽  
Ali Almasi ◽  
David B. Grayden ◽  
Tatiana Kameneva ◽  
Anthony N. Burkitt ◽  
...  
Keyword(s):  
Cell Model ◽  
Classical Model ◽  
Experimental Studies ◽  
Learning Rule ◽  
Energy Model ◽  
Diverse Range ◽  
Simple Cells ◽  
Complex Cells ◽  
Spatial Phase ◽  
Wide Range

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.

scholarly journals Spatial phase sensitivity of complex cells in primary visual cortex depends on stimulus contrast

2015 ◽  
Vol 114 (6) ◽  
pp. 3326-3338 ◽  
Author(s):  
H. Meffin ◽  
M. A. Hietanen ◽  
S. L. Cloherty ◽  
M. R. Ibbotson
Keyword(s):  
Visual Cortex ◽  
Primary Visual Cortex ◽  
Receptive Fields ◽  
Spatial Summation ◽  
Phase Sensitivity ◽  
Simple Cells ◽  
Low Contrast ◽  
Complex Cells ◽  
Spatial Phase ◽  
Phase Sensitive

Neurons in primary visual cortex are classified as simple, which are phase sensitive, or complex, which are significantly less phase sensitive. Previously, we have used drifting gratings to show that the phase sensitivity of complex cells increases at low contrast and after contrast adaptation while that of simple cells remains the same at all contrasts (Cloherty SL, Ibbotson MR. J Neurophysiol 113: 434–444, 2015; Crowder NA, van Kleef J, Dreher B, Ibbotson MR. J Neurophysiol 98: 1155–1166, 2007; van Kleef JP, Cloherty SL, Ibbotson MR. J Physiol 588: 3457–3470, 2010). However, drifting gratings confound the influence of spatial and temporal summation, so here we have stimulated complex cells with gratings that are spatially stationary but continuously reverse the polarity of the contrast over time (contrast-reversing gratings). By varying the spatial phase and contrast of the gratings we aimed to establish whether the contrast-dependent phase sensitivity of complex cells results from changes in spatial or temporal processing or both. We found that most of the increase in phase sensitivity at low contrasts could be attributed to changes in the spatial phase sensitivities of complex cells. However, at low contrasts the complex cells did not develop the spatiotemporal response characteristics of simple cells, in which paired response peaks occur 180° out of phase in time and space. Complex cells that increased their spatial phase sensitivity at low contrasts were significantly overrepresented in the supragranular layers of cortex. We conclude that complex cells in supragranular layers of cat cortex have dynamic spatial summation properties and that the mechanisms underlying complex cell receptive fields differ between cortical layers.

scholarly journals Encoding of Binocular Disparity by Complex Cells in the Cat's Visual Cortex

1997 ◽  
Vol 77 (6) ◽  
pp. 2879-2909 ◽  
Author(s):  
Izumi Ohzawa ◽  
Gregory C. Deangelis ◽  
Ralph D. Freeman
Keyword(s):  
Visual Cortex ◽  
Striate Cortex ◽  
Binocular Disparity ◽  
Substantial Reduction ◽  
Energy Model ◽  
Simple Type ◽  
Correspondence Problem ◽  
Complex Cell ◽  
Stimulus Contrast ◽  
Complex Cells

Ohzawa, Izumi, Gregory C. DeAngelis, and Ralph D. Freeman. Encoding of binocular disparity by complex cells in the cat's visual cortex. J. Neurophysiol. 77: 2879–2909, 1997. To examine the roles that complex cells play in stereopsis, we have recorded extracellularly from isolated single neurons in the striate cortex of anesthetized paralyzed cats. We measured binocular responses of complex cells using a comprehensive stimulus set that encompasses all possible combinations of positions over the receptive fields for the two eyes. For a given position combination, stimulus contrast could be the same for the two eyes (2 bright or 2 dark bars) or opposite (1 bright and 1 dark). These measurements provide a binocular receptive field (RF) profile that completely characterizes complex cell responses in a joint domain of left and right stimulus positions. Complex cells typically exhibit a strong selectivity for binocular disparity, but are only broadly selective for stimulus position. For most cells, selectivity for disparity is more than twice as narrow as that for position. These characteristics are highly desirable if we assume that a disparity sensor should exhibit position invariance while encoding small changes in stimulus depth. Complex cells have nearly identical binocular RFs for bright and dark stimuli as long as the sign of stimulus contrast is the same for the two eyes. When stimulus contrast is opposite, the binocular RF also is inverted such that excitatory subregions become suppressive. We have developed a disparity energy model that accounts for the behavior of disparity-sensitive complex cells. This is a hierarchical model that incorporates specific constraints on the selection of simple cells from which a complex cell receives input. Experimental data are used to examine quantitatively predictions of the model. Responses of complex cells generally agree well with predictions of the disparity energy model. However, various types of deviations from the predictions also are found, including a highly elongated excitatory region beyond that supported by a single energy mechanism. Complex cells in the visual cortex appear to provide a next level of abstraction in encoding information for stereopsis based on the activity of a group of simple-type subunits. In addition to exhibiting narrow disparity tuning and position invariance, these cells seem to provide a partial solution to the stereo correspondence problem that arises in complex natural scenes. Based on their binocular response properties, these cells provide a substantial reduction in the complexity of the correspondence problem.

Spatial Phase and the Temporal Structure of the Response to Gratings in V1

1998 ◽  
Vol 80 (2) ◽  
pp. 554-571 ◽  
Author(s):  
Jonathan D. Victor ◽  
Keith P. Purpura
Keyword(s):  
Spatial Frequency ◽  
Spike Train ◽  
Temporal Structure ◽  
Spike Timing ◽  
Dependent Manner ◽  
Data Set ◽  
Simple Cells ◽  
Complex Cells ◽  
Spatial Phase ◽  
Contrast Information

Victor, Jonathan D. and Keith P. Purpura. Spatial phase and the temporal structure of the response to gratings in V1. J. Neurophysiol. 80: 554–571, 1998. We recorded single-unit activity of 25 units in the parafoveal representation of macaque V1 to transient appearance of sinusoidal gratings. Gratings were systematically varied in spatial phase and in one or two of the following: contrast, spatial frequency, and orientation. Individual responses were compared based on spike counts, and also according to metrics sensitive to spike timing. For each metric, the extent of stimulus-dependent clustering of individual responses was assessed via the transmitted information, H. In nearly all data sets, stimulus-dependent clustering was maximal for metrics sensitive to the temporal pattern of spikes, typically with a precision of 25–50 ms. To focus on the interaction of spatial phase with other stimulus attributes, each data set was analyzed in two ways. In the “pooled phases” approach, the phase of the stimulus was ignored in the assessment of clustering, to yield an index H pooled. In the “individual phases” approach, clustering was calculated separately for each spatial phase and then averaged across spatial phases to yield an index H indiv. H pooled expresses the extent to which a spike train represents contrast, spatial frequency, or orientation in a manner which is not confounded by spatial phase (phase-independent representation), whereas H indiv expresses the extent to which a spike train represents one of these attributes, provided spatial phase is fixed (phase-dependent representation). Here, representation means that a stimulus attribute has a reproducible and systematic influence on individual responses, not a neural mechanism for decoding this influence. During the initial 100 ms of the response, contrast was represented in a phase-dependent manner by simple cells but primarily in a phase-independent manner by complex cells. As the response evolved, simple cell responses acquired phase-independent contrast information, whereas complex cells acquired phase-dependent contrast information. Simple cells represented orientation and spatial frequency in a primarily phase-dependent manner, but also they contained some phase-independent information in their initial response segment. Complex cells showed primarily phase-independent representation of orientation but primarily phase-dependent representation of spatial frequency. Joint representation of two attributes (contrast and spatial frequency, contrast and orientation, spatial frequency and orientation) was primarily phase dependent for simple cells, and primarily phase independent for complex cells. In simple and complex cells, the variability in the number of spikes elicited on each response was substantially greater than the expectations of a Poisson process. Although some of this variation could be attributed to the dependence of the response on the spatial phase of the grating, variability was still markedly greater than Poisson when the contribution of spatial phase to response variance was removed.

Half-squaring in responses of cat striate cells

1992 ◽  
Vol 9 (5) ◽  
pp. 427-443 ◽  
Author(s):  
David J. Heeger
Keyword(s):  
Linear Operator ◽  
Firing Rate ◽  
Striate Cortex ◽  
Energy Model ◽  
Linear Operators ◽  
Linear Stage ◽  
Simple Cells ◽  
Complex Cells ◽  
Cell Responses

AbstractSimple cells in striate cortex have been depicted as rectified linear operators, and complex cells have been depicted as energy mechanisms (constructed from the squared sums of linear operator outputs). This paper discusses two essential hypotheses of the linear/energy model: (1) that a cell's selectivity is due to an underlying (spatiotemporal and binocular) linear stage; and (2) that a cell's firing rate depends on the squared output of the underlying linear stage. This paper reviews physiological measurements of cat striate cell responses, and concludes that both of these hypotheses are supported by the data.

The binocular organization of simple cells in the cat's visual cortex

1986 ◽  
Vol 56 (1) ◽  
pp. 221-242 ◽  
Author(s):  
I. Ohzawa ◽  
R. D. Freeman
Keyword(s):  
Visual Cortex ◽  
Linear Model ◽  
Specific Interaction ◽  
Binocular Summation ◽  
Inhibitory Influence ◽  
Neural Signals ◽  
Simple Cells ◽  
Spatial Phase ◽  
Cell Responses ◽  
Binocular Interaction

We have studied the manner by which inputs from the two eyes are combined in simple cells of the cat's visual cortex. The stimuli for this study are drifting sinusoidal gratings, shown dichoptically at optimal spatial frequency and orientation. The relative spatial phase (disparity) between the gratings for left and right eyes is varied over 360 degrees. Most simple cells show phase-specific binocular interaction such that response amplitudes and phases vary depending on the relative spatial phase. At one phase, response is greater than either of the monocular responses and often greater than the sum of the two. At the phase 180 degrees away from the optimal, the cell's responses are strongly inhibited and often completely suppressed. Phase-specific binocular interaction disappears when the gratings presented to one eye are made orthogonal to the optimal orientation. The degree of binocular interaction does not depend critically on the ocular dominance of the cells. Simple cells that are nearly equally dominated by each eye always exhibit strong phase-specific interaction. The majority of cells that are strongly dominated by one eye, and even those that appear monocular, show phase-dependent changes in responses. We examined the extent of binocular interaction for cells with preferred orientations near vertical compared with those tuned to other optimal orientations. If these cells are conveying information about depth, one might expect a greater degree of binocular phase-specificity for units preferring nearly vertical orientations, which would then be processing horizontal disparities. We find no evidence for this. Predictions of simple-cell responses are derived from a linear model of binocular convergence in which light-evoked neural signals from each eye are summed linearly to determine cell responses. Data from cells generally follow the prediction of the model for both response amplitude and phase. Deviations from predictions of the linear model are found for a minority of cells. This deviation may be accounted for by a threshold mechanism that comes into play after the linear binocular summation. A small proportion of simple cells that appear monocular by alternate tests of each eye show a purely inhibitory influence from the silent eye. This inhibition is not generally dependent on the relative phase of the gratings. We conclude that most binocular interaction in striate simple cells may be accounted for by linear summation of neural signals from each eye.(ABSTRACT TRUNCATED AT 400 WORDS)

Internal Spatial Organization of Receptive Fields of Complex Cells in the Early Visual Cortex

2007 ◽  
Vol 98 (3) ◽  
pp. 1194-1212 ◽  
Author(s):  
Kota S. Sasaki ◽  
Izumi Ohzawa
Keyword(s):  
Visual Cortex ◽  
Minimal Model ◽  
Spatial Organization ◽  
Receptive Fields ◽  
Simple Cell ◽  
Complex Cell ◽  
Linear Filters ◽  
Simple Cells ◽  
Complex Cells ◽  
Early Visual Cortex

The receptive fields of complex cells in the early visual cortex are economically modeled by combining outputs of a quadrature pair of linear filters. For actual complex cells, such a minimal model may be insufficient because many more simple cells are thought to make up a complex cell receptive field. To examine the minimalist model physiologically, we analyzed spatial relationships between the internal structure (subunits) and the overall receptive fields of individual complex cells by a two-stimulus interaction technique. The receptive fields of complex cells are more circular and only slightly larger than their subunits in size. In addition, complex cell subunits occupy spatial extents similar to those of simple cell receptive fields. Therefore in these respects, the minimalist schema is a fair approximation to actual complex cells. However, there are violations against the minimal model. Simple cell receptive fields have significantly fewer subregions than complex cell subunits and, in general, simple cell receptive fields are elongated more horizontally than vertically. This bias is absent in complex cell subunits and receptive fields. Thus simple cells cannot be equated to individual complex cell subunits and spatial pooling of simple cells may occur anisotropically to constitute a complex cell subunit. Moreover, when linear filters for complex cell subunits are examined separately for bright and dark responses, there are significant imbalances and position displacements between them. This suggests that actual complex cell receptive fields are constructed by a richer combination of linear filters than proposed by the minimalist model.

scholarly journals Comparison Among Some Models of Orientation Selectivity

2006 ◽  
Vol 96 (1) ◽  
pp. 404-419 ◽  
Author(s):  
Andrew F. Teich ◽  
Ning Qian
Keyword(s):  
Peak Shift ◽  
Orientation Tuning ◽  
Complex Spectrum ◽  
Complex Cell ◽  
Phase Information ◽  
Simple Complex ◽  
Simple Cells ◽  
Complex Cells ◽  
Spatial Phase ◽  
Opposite Contrast

Several models exist for explaining primary visual cortex (V1) orientation tuning. The modified feedforward model (MFM) and the recurrent model (RM) are major examples. We have implemented these two models, at the same level of detail, alongside a few newer variations, and thoroughly compared their receptive-field structures. We found that antiphase inhibition in the MFM enhances both spatial phase information and orientation tuning, producing well-tuned simple cells. This remains true for a newer version of the MFM that incorporates untuned complex-cell inhibition. In contrast, when the recurrent connections in the RM are strong enough to produce typical V1 orientation tuning, they also eliminate spatial phase information, making the cells complex. Introducing phase specificity into the connections of the RM (as done in an original version of the RM) can make the cells phase sensitive, but the cells show an incorrect 90° peak shift of orientation tuning under opposite contrast signs. An inhibition-dominant version of the RM can generate well-tuned cells across the simple–complex spectrum, but it predicts that the net effect of cortical interactions is to suppress feedforward excitation across all orientations in simple cells. Finally, adding antiphase inhibition used in the MFM into the RM produces a most general model. We call this new model the modified recurrent model (MRM) and show that this model can also produce well-tuned cells throughout the simple–complex spectrum. Unlike the inhibition-dominant RM, the MRM is consistent with data from cat V1, suggesting that the net effect of cortical interactions is to boost simple cell responses at the preferred orientation. These results suggest that the MFM is well suited for explaining orientation tuning in simple cells, whereas the standard RM is for complex cells. The assignment of the RM to complex cells also avoids conflicts between the RM and the experiments of cortical inactivation (done on simple cells) and the spatial-frequency dependency of orientation tuning (found in simple cells). Because orientation-tuned V1 cells show a continuum of simple- to complex-cell behavior, the MRM provides the best description of V1 data.

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

2012 ◽  
Vol 24 (10) ◽  
pp. 2700-2725 ◽  
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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