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 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.

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

1986 ◽  
Vol 56 (1) ◽  
pp. 243-259 ◽  
Author(s):  
I. Ohzawa ◽  
R. D. Freeman
Keyword(s):  
Visual Cortex ◽  
Relative Phase ◽  
Specific Interaction ◽  
Linear Convergence ◽  
Inhibitory Influence ◽  
Complex Cell ◽  
Neural Signals ◽  
Simple Cells ◽  
Complex Cells ◽  
Binocular Interaction

We have studied the manner by which inputs from the two eyes are combined in complex cells of the cat's visual cortex. The stimuli are drifting sinusoidal gratings presented dichoptically at optimal spatial frequency and orientation. The relative phase between the gratings for left and right eyes is varied over 360 degrees. Approximately 40% of complex cells show phase-specific binocular interaction where response amplitudes vary depending on the relative phase of the gratings shown to the two eyes. This interaction is similar to that observed for most simple cells. We devised a test to examine whether the phase-specific interaction in complex cells results from linear convergence of neural signals at subunits of the receptive fields. The data from this test are consistent with a linear combination model. The phase-specific binocular interaction data from complex cells imply that the optimal relative phase of the receptive field subunits is closely matched. Another type of complex cell, approximately 40% of the total, could be driven through either eye, but exhibited non-phase-specific responses to dichoptically presented gratings. This type of interaction is found only in complex cells. Binocularly non-phase-specific complex cells may have subunits whose optimal relative phases are random or monocular. The division of complex cells into these two major groups (binocularly phase specific and non-phase specific) is independent of whether they are standard or special complex-cell types. A small proportion (8%) of complex 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. Unlike simple cells, complex cells are not a homogeneous group. However, nearly half of complex cells show phase-specific binocular interaction that is probably the result of linear convergence. Combined with the results from simple cells, the majority of binocular interaction in the striate cortex may be accounted for by linear summation of neural signals from each eye. This provides a simplified view of the nature of binocular interaction in the visual cortex.

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.

Spatial Organization of Receptive Fields of V1 Neurons of Alert Monkeys: Comparison With Responses to Gratings

2002 ◽  
Vol 88 (5) ◽  
pp. 2557-2574 ◽  
Author(s):  
Igor Kagan ◽  
Moshe Gur ◽  
D. Max Snodderly
Keyword(s):  
Eye Movements ◽  
Spatial Organization ◽  
Receptive Fields ◽  
Window Size ◽  
Group 14 ◽  
Simple Cells ◽  
Complex Cells ◽  
V1 Neurons ◽  
Fixational Eye Movements ◽  
Spatial Frequencies

We studied the spatial organization of receptive fields and the responses to gratings of neurons in parafoveal V1 of alert monkeys. Activating regions (ARs) of 228 cells were mapped with increment and decrement bars while compensating for fixational eye movements. For cells with two or more ARs, the overlap between ARs responsive to increments (INC) and ARs responsive to decrements (DEC) was characterized by a quantitative overlap index (OI). The distribution of overlap indices was bimodal. The larger group (78% of cells) was composed of complex cells with strongly overlapping ARs (OI ≥ 0.5). The smaller group (14%) was composed of simple cells with minimal spatial overlap of ARs (OI ≤ 0.3). Simple cells were preferentially located in layers dominated by the magnocellular pathway. A third group of neurons, the monocontrast cells (8%), responded only to one sign of contrast and had more sustained responses to flashed stimuli than other cells. One hundred fourteen neurons were also studied with drifting sinusoidal gratings of various spatial frequencies and window widths. For complex cells, the relative modulation (RM, the ratio of the 1st harmonic to the mean firing rate), ranged from 0.6 ± 0.4 to 1.1 ± 0.5 (mean ± SD), depending on the stimulus conditions and the mode of correction for eye movements. RM was not correlated with the degree of overlap of ARs, indicating that the spatial organization of receptive fields cannot reliably be predicted from RM values. In fact, a subset of complex cells had RM > 1, the traditional criterion for identifying simple cells. However, unlike simple cells, even those complex cells with high RM could exhibit diverse nonlinear responses when the spatial frequency or window size was changed. Furthermore, the responses of complex cells to counterphase gratings were predominantly nonlinear even harmonics. These results show that RM is not a robust test of linearity. Our results indicate that complex cells are the most frequently encountered neurons in primate V1, and their behavior needs to receive more emphasis in models of visual function.

Contrast-dependent phase sensitivity in V1 but not V2 of macaque visual cortex

2015 ◽  
Vol 113 (2) ◽  
pp. 434-444 ◽  
Author(s):  
Shaun L. Cloherty ◽  
Michael R. Ibbotson
Keyword(s):  
Visual Cortex ◽  
Receptive Fields ◽  
Brain Regions ◽  
Sine Wave ◽  
Phase Sensitivity ◽  
Simple Cells ◽  
Low Contrast ◽  
Cortical Input ◽  
Hierarchical Processing ◽  
Complex Cells

Some neurons in early visual cortex are highly selective for the position of oriented edges in their receptive fields (simple cells), whereas others are largely position insensitive (complex cells). These characteristics are reflected in their sensitivity to the spatial phase of moving sine-wave gratings: simple cell responses oscillate at the fundamental frequency of the stimulus, whereas this is less so for complex cells. In primates, when assessed at high stimulus contrast, simple cells and complex cells are roughly equally represented in the first visual cortical area, V1, whereas in the second visual area, V2, the majority of cells are complex. Recent evidence has shown that phase sensitivity of complex cells is contrast dependent. This has led to speculation that reduced contrast may lead to changes in the spatial structure of receptive fields, perhaps due to changes in how feedforward and recurrent signals interact. Given the substantial interconnections between V1 and V2 and recent evidence for the emergence of unique functional capacity in V2, we assess the relationship between contrast and phase sensitivity in the two brain regions. We show that a substantial proportion of complex cells in macaque V1 exhibit significant increases in phase sensitivity at low contrast, whereas this is rarely observed in V2. Our results support a degree of hierarchical processing from V1 to V2 with the differences possibly relating to the fact that V1 combines both subcortical and cortical input, whereas V2 receives input purely from cortical circuits.

Direction selectivity of cells in the cat's striate cortex: Differences between bar and grating stimuli

1992 ◽  
Vol 9 (5) ◽  
pp. 505-513 ◽  
Author(s):  
C. Casanova ◽  
J. P. Nordmann ◽  
I. Ohzawa ◽  
R. D. Freeman
Keyword(s):  
Visual Cortex ◽  
Striate Cortex ◽  
Direction Selectivity ◽  
Simple Cell ◽  
Simple Cells ◽  
Complex Cells ◽  
Sinusoidal Gratings ◽  
Standard Techniques ◽  
Selective Behavior

AbstractWe have investigated the notion that directional responses of cells in the visual cortex depend on the type of stimulus used to drive the cell. Specifically, we have asked if sinusoidal gratings provide a different estimate of direction selectivity than bars that are brighter or darker than the background.Using standard techniques, we recorded from 176 cells in the visual cortex of nine cats. For each cell, bright bars, dark bars, and sinusoidal gratings were presented in a randomly interleaved fashion. Complex cells exhibited around twice as many direction-selective as nondirection-selective responses. Estimates of direction selectivity were nearly identical for bright and dark bars and for gratings. For simple cells, a similar ratio of direction-selective to nondirection-selective responses was observed for gratings. However, a larger proportion of simple cells were classified as direction selective when bars were used for stimulation.A simple cell that exhibited direction selectivity to a grating behaved in a similar manner when stimulated with bright or dark bars. However, in contrast to complex cells, some simple cells classed as directionally nonselective on the basis of their responses to gratings, displayed directionally selective behavior to bars. In addition, the preferred directions for dark and bright bars sometimes differed. These results demonstrate that the classification of a simple cell as directionally selective or nonselective can depend critically on the visual stimulus used.

scholarly journals Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces

2000 ◽  
Vol 12 (7) ◽  
pp. 1705-1720 ◽  
Author(s):  
Aapo Hyvärinen ◽  
Patrik Hoyer
Keyword(s):  
Sparse Coding ◽  
Receptive Fields ◽  
Natural Images ◽  
Simple Cell ◽  
Linear Filter ◽  
Linear Filters ◽  
Complex Cells ◽  
Linear Subspaces ◽  
Invariant Features ◽  
Gabor Functions

Olshausen and Field (1996) applied the principle of independence maximization by sparse coding to extract features from natural images. This leads to the emergence of oriented linear filters that have simultaneous localization in space and in frequency, thus resembling Gabor functions and simple cell receptive fields. In this article, we show that the same principle of independence maximization can explain the emergence of phase- and shift-invariant features, similar to those found in complex cells. This new kind of emergence is obtained by maximizing the independence between norms of projections on linear subspaces (instead of the independence of simple linear filter outputs). The norms of the projections on such “independent feature subspaces” then indicate the values of invariant features.

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.

Direction selectivity of complex cells in a comparison with simple cells

1975 ◽  
Vol 38 (6) ◽  
pp. 1524-1540 ◽  
Author(s):  
A. W. Goodwin ◽  
G. H. Henry
Keyword(s):  
Spontaneous Activity ◽  
Visual Information ◽  
Striate Cortex ◽  
Cell Types ◽  
Direction Selectivity ◽  
Complex Cell ◽  
Simple Cells ◽  
Complex Cells ◽  
Sequential Processing

Following our earlier study on direction selectivity in simple cells (5), the present findings on complex cells made it possible to compare the direction selectivity in the two types of striate cell. Common properties were found in the dimension of the smallest stimulus displacement giving a direction-selective response and in the role of inhibition in suppressing the response as the stimulus moved in the nonpreferred direction. However, the effectiveness of this inhibition varied in the two cell types since it suppressed both driven and spontaneous activity in the simple cell, but only driven firing in the complex cell. It is argued that direction selectivity must enter the response before the complex cell if the inhibition responsible for it's generation fails to influence the spontaneous activity of the cell. The consequences of this finding are considered in the terms of parallel or sequential processing of visual information in striate cortex.

Receptive-field characteristics of neurons in cat striate cortex: Changes with visual field eccentricity

1976 ◽  
Vol 39 (3) ◽  
pp. 512-533 ◽  
Author(s):  
J. R. Wilson ◽  
S. M. Sherman
Keyword(s):  
Visual Field ◽  
Receptive Field ◽  
Striate Cortex ◽  
Ocular Dominance ◽  
Receptive Fields ◽  
Direction Selectivity ◽  
Orientation Selectivity ◽  
Simple Cells ◽  
Complex Cells ◽  
Cat Striate Cortex

1. Receptive-field properties of 214 neurons from cat striate cortex were studied with particular emphasis on: a) classification, b) field size, c) orientation selectivity, d) direction selectivity, e) speed selectivity, and f) ocular dominance. We studied receptive fields located throughtout the visual field, including the monocular segment, to determine how receptivefield properties changed with eccentricity in the visual field.2. We classified 98 cells as "simple," 80 as "complex," 21 as "hypercomplex," and 15 in other categories. The proportion of complex cells relative to simple cells increased monotonically with receptive-field eccenticity.3. Direction selectivity and preferred orientation did not measurably change with eccentricity. Through most of the binocular segment, this was also true for ocular dominance; however, at the edge of the binocular segment, there were more fields dominated by the contralateral eye.4. Cells had larger receptive fields, less orientation selectivity, and higher preferred speeds with increasing eccentricity. However, these changes were considerably more pronounced for complex than for simple cells.5. These data suggest that simple and complex cells analyze different aspects of a visual stimulus, and we provide a hypothesis which suggests that simple cells analyze input typically from one (or a few) geniculate neurons, while complex cells receive input from a larger region of geniculate neurons. On average, this region is invariant with eccentricity and, due to a changing magnification factor, complex fields increase in size with eccentricity much more than do simple cells. For complex cells, computations of this geniculate region transformed to cortical space provide a cortical extent equal to the spread of pyramidal cell basal dendrites.

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