Comparison of contrast-normalization and threshold models of the responses of simple cells in cat striate cortex

1997 ◽  
Vol 14 (2) ◽  
pp. 293-309 ◽  
Author(s):  
D. J. Tolhurst ◽  
D. J. Heeger
Keyword(s):  
Receptive Field ◽  
Striate Cortex ◽  
Frequency Tuning ◽  
Tuning Curve ◽  
Threshold Model ◽  
Output Stage ◽  
Simple Cells ◽  
Neurophysiological Data ◽  
Contrast Normalization ◽  
The Relationship

AbstractIn almost every study of the linearity of spatiotemporal summation in simple cells of the cat's visual cortex, there have been systematic mismatches between the experimental observations and the predictions of the linear theory. These mismatches have generally been explained by supposing that the initial spatiotemporal summation stage is strictly linear, but that the following output stage of the simple cell is subject to some contrast-dependent nonlinearity. Two main models of the output nonlinearity have been proposed: the threshold model (e.g. Tolhurst & Dean, 1987) and the contrast-normalization model (e.g. Heeger, 1992a, b). In this paper, the two models are fitted rigorously to a variety of previously published neurophysiological data, in order to determine whether one model is a better explanation of the data. We reexamine data on the interaction between two bar stimuli presented in different parts of the receptive field; on the relationship between the receptive-field map and the inverse Fourier transform of the spatial-frequency tuning curve; on the dependence of response amplitude and phase on the spatial phase of stationary gratings; on the relationships between the responses to moving and modulated gratings; and on the suppressive action of gratings moving in a neuron's nonpreferred direction. In many situations, the predictions of the two models are similar, but the contrast-normalization model usually fits the data slightly better than the threshold model, and it is easier to apply the equations of the normalization model. More importantly, the normalization model is naturally able to account very well for the details and subtlety of the results in experiments where the total contrast energy of the stimuli changes; some of these phenomena are completely beyond the scope of the threshold model. Rigorous application of the models' equations has revealed some situations where neither model fits quite well enough, and we must suppose, therefore, that there are some subtle nonlinearities still to be characterized.

Spatiotemporal organization of simple-cell receptive fields in the cat's striate cortex. II. Linearity of temporal and spatial summation

1993 ◽  
Vol 69 (4) ◽  
pp. 1118-1135 ◽  
Author(s):  
G. C. DeAngelis ◽  
I. Ohzawa ◽  
R. D. Freeman
Keyword(s):  
Receptive Field ◽  
Striate Cortex ◽  
Frequency Tuning ◽  
Temporal Frequency ◽  
Spatial Summation ◽  
Direction Selectivity ◽  
Simple Cells ◽  
Tuning Curves ◽  
Spatiotemporal Receptive Field ◽  
Temporal And Spatial

1. We have tested the hypothesis that simple cells in the cat's visual cortex perform a linear spatiotemporal filtering of the visual image. To conduct this study we note that a visual neuron behaves linearly if the responses to small, brief flashes of light are mathematically related, via the Fourier transform, to the responses elicited by sinusoidal grating stimuli. 2. We have evaluated the linearity of temporal and spatial summation for 118 simple cells recorded from the striate cortex (area 17) of adult cats and kittens at ages 4 and 8 wk postnatal. These neurons represent a subset of the population of cells for which we have described the postnatal development of spatiotemporal receptive-field structure in the preceding paper. Spatiotemporal receptive-field profiles are constructed, with the use of a reverse correlation technique, from the responses to random sequences of small bar stimuli that are brighter or darker than the background. Fourier analysis of spatiotemporal receptive-field profiles yields linear predictions of the cells' spatial and temporal frequency tuning. These predicted responses are compared with spatial and temporal frequency tuning curves measured by the use of drifting, sinusoidal-luminance grating stimuli. 3. For most simple cells, there is good agreement between spatial and temporal frequency tuning curves predicted from the receptive-field profile and those measured by the use of sinusoidal gratings. These results suggest that both spatial and temporal summation within simple cells are approximately linear. There is a tendency for predicted tuning curves to be slightly broader than measured tuning curves, a finding that is consistent with the effects of a threshold nonlinearity at the output of these neurons. In some cases, however, predicted tuning curves deviate from measured responses only at low spatial and temporal frequencies. This cannot be explained by a simple threshold nonlinearity. 4. If linearity is assumed, it should be possible to predict the direction selectivity of simple cells from the structure of their spatiotemporal receptive-field profiles. For virtually all cells, linear predictions correctly determine the preferred direction of motion of a visual stimulus. However, the strength of the directional bias is typically underestimated by a factor of about two on the basis of linear predictions. Consideration of the expansive exponential nonlinearity revealed in the contrast-response function permits a reconciliation of the discrepancy between measured and predicted direction selectivity indexes. 5. Overall, these findings show that spatiotemporal receptive-field profiles obtained with the use of reverse correlation may be used to predict a variety of response properties for simple cells.(ABSTRACT TRUNCATED AT 400 WORDS)

Spatial and temporal frequency tuning in striate cortex: functional uniformity and specializations related to receptive field eccentricity

2010 ◽  
Vol 31 (6) ◽  
pp. 1043-1062 ◽  
Author(s):  
Hsin-Hao Yu ◽  
Richa Verma ◽  
Yin Yang ◽  
Heath A. Tibballs ◽  
Leo L. Lui ◽  
...  
Keyword(s):  
Receptive Field ◽  
Striate Cortex ◽  
Frequency Tuning ◽  
Temporal Frequency

The Study of Spatial Frequency Channels for Human Visual System

2019 ◽  
Vol 33 (06) ◽  
pp. 1955007
Author(s):  
Xiangyang Xu ◽  
Qiao Chen ◽  
Ruixin Xu
Keyword(s):  
Receptive Field ◽  
Spatial Frequency ◽  
Visual System ◽  
Human Visual System ◽  
Frequency Tuning ◽  
Tuning Curve ◽  
Vision System ◽  
Human Vision ◽  
Psychophysical Experiment ◽  
Human Vision System

Similar to auditory perception of sound system, color perception of the human visual system also presents a multi-frequency channel property. In order to study the multi-frequency channel mechanism of how the human visual system processes color information, the paper proposed a psychophysical experiment to measure the contrast sensitivities based on 17 color samples of 16 spatial frequencies on CIELAB opponent color space. Correlation analysis was carried out on the psychophysical experiment data, and the results show obvious linear correlations of observations for different spatial frequencies of different observers, which indicates that a linear model can be used to model how human visual system processes spatial frequency information. The results of solving the model based on the experiment data of color samples show that 9 spatial frequency tuning curves can exist in human visual system with each lightness, R–G and Y–B color channel and each channel can be represented by 3 tuning curves, which reflect the “center-around” form of the human visual receptive field. It is concluded that there are 9 spatial frequency channels in human vision system. The low frequency tuning curve of a narrow-frequency bandwidth shows the characteristics of lower level receptive field for human vision system, the medium frequency tuning curve shows a low pass property of the change of medium frequent colors and the high frequency tuning curve of a width-frequency bandwidth, which has a feedback effect on the low and medium frequency channels and shows the characteristics of higher level receptive field for human vision system, which represents the discrimination of details.

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.

Spatial properties of neurons in the monkey striate cortex

1987 ◽  
Vol 231 (1263) ◽  
pp. 251-288 ◽  
Keyword(s):  
Receptive Field ◽  
Contrast Sensitivity ◽  
Visual Processing ◽  
Striate Cortex ◽  
Receptive Fields ◽  
Spatial Filter ◽  
Cortical Cells ◽  
Simple Cells ◽  
Gabor Function ◽  
Difference Of Gaussians

Contrast sensitivity as a function of spatial frequency was determined for 138 neurons in the foveal region of primate striate cortex. The accuracy of three models in describing these functions was assessed by the method of least squares. Models based on difference-of-Gaussians (DOG) functions were shown to be superior to those based on the Gabor function or the second differential of a Gaussian. In the most general case of the DOG models, each subregion of a simple cell’s receptive field was constructed from a single DOG function. All the models are compatible with the classical observation that the receptive fields of simple cells are made up of spatially discrete ‘on’ and ‘off’ regions. Although the DOG-based models have more free parameters, they can account better for the variety of shapes of spatial contrast sensitivity functions observed in cortical cells and, unlike other models, they provide a detailed description of the organization of subregions of the receptive field that is consistent with the physiological constraints imposed by earlier stages in the visual pathway. Despite the fact that the DOG-based models have spatially discrete components, the resulting amplitude spectra in the frequency domain describe complex cells just as well as simple cells. The superiority of the DOG-based models as a primary spatial filter is discussed in relation to popular models of visual processing that use the Gabor function or the second differential of a Gaussian.

The effect of threshold on the relationship between the receptive-field profile and the spatial-frequency tuning cure in simple cells of the cat's striate cortex

1989 ◽  
Vol 3 (5) ◽  
pp. 445-454 ◽  
Author(s):  
Y. Tadmor ◽  
D. J. Tolhurst
Keyword(s):  
Fourier Transform ◽  
Spatial Frequency ◽  
Fourier Transforms ◽  
Frequency Tuning ◽  
Weighting Function ◽  
Tuning Curve ◽  
Spatial Summation ◽  
Response Threshold ◽  
Simple Cells ◽  
Spatial Frequency Tuning

AbstractIt is believed that spatial summation in most simple cells is a linear process. If this were so, then the Fourier transform of a simple cell's line weighting function should predict the cell's spatial frequency tuning curve. We have compared such predictions with experimental measurements and have found a consistent discrepancy: the predicted tuning curve is much too broad. We show qualitatively that this kind of discrepancy is consistent with the well-known threshold nonlinearity shown by most cortical cells. We have tested quantitatively whether a response threshold could explain the observed disagreements between predictions and measurements: a least-squares minimization routine was used to fit the inverse Fourier Transform of the measured frequency tuning curve to the measured line weighting function. The fitting procedure permitted us to introduce a threshold to the reconstructed line weighting function. The results of the analysis show that, for all of the cells tested, the Fourier transforms produced better predictions when a response threshold was included in the model. For some cells, the actual magnitude of the response threshold was measured independently and found to be compatible with that suggested by the model. The effects of nonlinearities of spatial summation are considered.

scholarly journals Strobe Rearing Reduces Direction Selectivity in Area 17 by Altering Spatiotemporal Receptive-Field Structure

1998 ◽  
Vol 80 (6) ◽  
pp. 2991-3004 ◽  
Author(s):  
Allen L. Humphrey ◽  
Alan B. Saul
Keyword(s):  
Receptive Field ◽  
Frequency Tuning ◽  
Temporal Frequency ◽  
Receptive Fields ◽  
Direction Selectivity ◽  
Field Structure ◽  
Area 17 ◽  
Directional Tuning ◽  
Simple Cells ◽  
Spatiotemporal Receptive Field

Humphrey, Allen L. and Alan B. Saul. Strobe rearing reduces direction selectivity in area 17 by altering spatiotemporal receptive-field structure. J. Neurophysiol. 80: 2991–3004, 1998. Direction selectivity in simple cells of cat area 17 is linked to spatiotemporal (S-T) receptive-field structure. S-T inseparable receptive fields display gradients of response timing across the receptive field that confer a preferred direction of motion. Receptive fields that are not direction selective lack gradients; they are S-T separable, displaying uniform timing across the field. Here we further examine this link using a developmental paradigm that disrupts direction selectivity. Cats were reared from birth to 8 mo of age in 8-Hz stroboscopic illumination. Direction selectivity in simple cells was then measured using gratings drifting at different temporal frequencies (0.25–16 Hz). S-T structure was assessed using stationary bars presented at different receptive-field positions, with bar luminance being modulated sinusoidally at different temporal frequencies. For each cell, plots of response phase versus bar position were fit by lines to characterize S-T inseparability at each temporal frequency. Strobe rearing produced a profound loss of direction selectivity at all temporal frequencies; only 10% of cells were selective compared with 80% in normal cats. The few remaining directional cells were selective over a narrower than normal range of temporal frequencies and exhibited weaker than normal direction selectivity. Importantly, the directional loss was accompanied by a virtual elimination of S-T inseparability. Nearly all cells were S-T separable, like nondirectional cells in normal cats. The loss was clearest in layer 4. Normally, inseparability is greatest there, and it correlates well ( r = 0.77) with direction selectivity; strobe rearing reduced inseparability and direction selectivity to very low values. The few remaining directional cells were inseparable. In layer 6 of normal cats, most direction-selective cells are only weakly inseparable, and there is no consistent relationship between the two measures. However, after strobe rearing, even the weak inseparability was eliminated along with direction selectivity. The correlated changes in S-T structure and direction selectivity were confirmed using conventional linear predictions of directional tuning based on responses to counterphasing bars and white noise stimuli. The developmental changes were permanent, being observed up to 12 yr after strobe rearing. The deficits were remarkably specific; strobe rearing did not affect spatial receptive-field structure, orientation selectivity, spatial or temporal frequency tuning, or general responsiveness to visual stimuli. These results provide further support for a critical role of S-T structure in determining direction selectivity in simple cells. Strobe rearing eliminates directional tuning by altering the timing of responses within the receptive field.

Length and width tuning of neurons in the cat's primary visual cortex

1994 ◽  
Vol 71 (1) ◽  
pp. 347-374 ◽  
Author(s):  
G. C. DeAngelis ◽  
R. D. Freeman ◽  
I. Ohzawa
Keyword(s):  
Receptive Field ◽  
Spatial Frequency ◽  
Spatial Organization ◽  
Striate Cortex ◽  
Frequency Tuning ◽  
Variable Parameter ◽  
Visual Space ◽  
Similar Degree ◽  
Tuning Curves ◽  
Number Of Cycles

1. The classically defined receptive field of a visual neuron is the area of visual space over which the cell responds to visual stimuli. It is well established, however, that the discharge produced by an optimal stimulus can be modulated by the presence of additional stimuli that by themselves do not produce any response. This study examines inhibitory influences that originate from areas located outside of the classical (i.e., excitatory) receptive field. Previous work has shown that for some cells the response to a properly oriented bar of light becomes attenuated when the bar extends beyond the receptive field, a phenomenon known as end-inhibition (or length tuning). Analogously, it has been shown that increasing the number of cycles of a drifting grating stimulus may also inhibit the firing of some cells, an effect known as side-inhibition (or width tuning). Very little information is available, however, about the relationship between end- and side-inhibition. We have examined the spatial organization and tuning characteristics of these inhibitory effects by recording extracellularly from single neurons in the cat's striate cortex (Area 17). 2. For each cortical neuron, length and width tuning curves were obtained with the use of rectangular patches of drifting sinusoidal gratings that have variable length and width. Results from 82 cells show that the strengths of end- and side-inhibition tend to be correlated. Most cells that exhibit clear end-inhibition also show a similar degree of side-inhibition. For these cells, the excitatory receptive field is surrounded on all sides by inhibitory zones. Some cells exhibit only end- or side-inhibition, but not both. Data for 28 binocular cells show that length and width tuning curves for the dominant and nondominant eyes tend to be closely matched. 3. We also measured tuning characteristics of end- and side-inhibition. To obtain these data, the excitatory receptive field was stimulated with a grating patch having optimal orientation, spatial frequency, and size, whereas the end- or side-inhibitory regions were stimulated with patches of gratings that had a variable parameter (such as orientation). Results show that end- and side-inhibition tend to be strongest at the orientation and spatial frequency that yield maximal excitation. However, orientation and spatial frequency tuning curves for inhibition are considerably broader than those for excitation, suggesting that inhibition is mediated by a pool of neurons.(ABSTRACT TRUNCATED AT 400 WORDS)

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