Stereoscopic depth perception and vertical disparity: neural mechanisms.

The additivity assumption relates to the various stereo-disparity components in the vertical and horizontal meridians, each of which is assumed to be independent of the other, with the total disparity in each dimension being the linear sum of the separate components. Information about the position of the eyes provided by the corollary discharge leads to compensatory changes in the lateral geniculate nuclei whereby the angle of gaze disparity component at retinal level is offset by equal and opposite changes at geniculate level. These geniculate changes concern only eye position. Changes in the retinal images such as those produced by lenses (i.e. induced effect) are passed on to the cortex without modification at the geniculate level. Discrimination of the local depth disparity component can be achieved by subtracting the local vertical eccentricity component from the total horizontal disparity.

Can random-dot stereograms serve as a model for the perception of depth in relation to real three-dimensional objects?

The ability to perceive depth in a random-dot stereogram is a valuable test for the perception of retinal image disparities, whether they arise from the viewing of a stereogram or from the viewing of a real 3-D object. However, a stereogram cannot be regarded as a proper model for the perception of depth in the case of a real 3-D object. This conclusion comes out most clearly in relation to changes in viewing distance. Whereas the viewing of real objects and stereograms both obey the rules of size constancy, this is not the case with depth constancy. With changes in viewing distance, the viewing of real objects obeys the rules of depth constancy. By contrast, the magnitude of the depth intervals in a stereogram are not constant but appear to increase in direct proportion to the increase in viewing distance. In a stereogram these changes in the amplitude of the depth intervals are based on the same mechanisms as those responsible for size constancy.

Size constancy, depth constancy and vertical disparities: a further quantitative interpretation.

The size and depth constancies considered here operate only at near distances (< about 2 m) in a static stimulus situation with vergence as the only cue to distance. The innervation of the extraocular muscles, as evidenced by the corollary discharge, provides information about the vergence of the eyes and hence about the egocentric distance both for symmetrical and asymmetrical vergences. Size and depth constancies are regarded as the first and second stages of a linked two-stage process. In the lateral geniculate nuclei compensatory adjustments are separately applied to each retinal image as they are received from the two eyes. The modified ocular images, with their associated vertical and horizontal disparities, now provide synaptic inputs to binocularly activated cells in the visual cortex. Then, by a process akin to the induced effect, cortical cells with geniculate afferents with vertical disparities will have their outputs expressed in terms of horizontal disparities. The horizontal disparity outputs of these cortical cells are then further multiplied by the outputs from cortical cells with geniculate afferents with horizontal disparities. It is this second multiplicative process that brings about the quadratic relationship between horizontal retinal disparity and egocentric distance. The proposed mechanisms involve the known ability of the visual system to detect and respond to vertical as well as horizontal disparities and provide a definite role for the induced effect in the perceptual process. The above neural model is based on fairly simple equations that give a remarkably adequate description of the operation of the two constancies.

Vertical disparity, egocentric distance and stereoscopic depth constancy: a new interpretation.

There has long been a problem concerning the presence in the visual cortex of binocularly activated cells that are selective for vertical stimulus disparities because it is generally believed that only horizontal disparities contribute to stereoscopic depth perception. The accepted view is that stereoscopic depth estimates are only relative to the fixation point and that independent information from an extraretinal source is needed to scale for absolute or egocentric distance. Recently, however, theoretical computations have shown that egocentric distance can be estimated directly from vertical disparities without recourse to extraretinal sources. There has been little impetus to follow up these computations with experimental observations, because the vertical disparities that normally occur between the images in the two eyes have always been regarded as being too small to be of significance for visual perception and because experiments have consistently shown that our conscious appreciation of egocentric distance is rather crude and unreliable. Nevertheless, the veridicality of stereoscopic depth constancy indicates that accurate distance information is available to the visual system and that the information about egocentric distance and horizontal disparity are processed together so as to continually recalibrate the horizontal disparity values for different absolute distances. Computations show that the recalibration can be based directly on vertical disparities without the need for any intervening estimates of absolute distance. This may partly explain the relative crudity of our conscious appreciation of egocentric distance. From published data it has been possible to calculate the magnitude of the vertical disparities that the human visual system must be able to discriminate in order for depth constancy to have the observed level of veridicality. From published data on the induced effect it has also been possible to calculate the threshold values for the detection of vertical disparities by the visual system. These threshold values are smaller than those needed to provide for the recalibration of the horizontal disparities in the interests of veridical depth constancy. An outline is given of the known properties of the binocularly activated cells in the striate cortex that are able to discriminate and assess the vertical disparities. Experiments are proposed that should validate, or otherwise, the concepts put forward in this paper.

Stereoscopic mechanisms: binocular responses of the striate cells of cats to moving light and dark bars.

New knowledge concerning the internal structure and response properties of the receptive fields of striate cells calls for a fresh appraisal of their binocular interactions in the interest of a better understanding of the neural mechanisms underlying binocular depth discrimination. Binocular position-disparity response profiles were recorded from 71 simple and B-cells in response to moving light and dark bars. Predominantly excitatory (PE) cells (N = 48) had disparity response profiles that were spatially closely similar to their respective monocular responses. In addition, the centrally located excitatory subregions were flanked on one or both sides by non-specific inhibitory regions. PE cells with a preferred stimulus orientation within 30 degrees of the vertical (N = 17) showed binocular facilitations with maximal values that were always more than twice (mean 3.3) the sum of the two monocular responses to the same stimuli and generally greater than the facilitations shown by cells with orientations more than 30 degrees from the vertical (N = 29; mean 2.2 times the sum of the respective monocular responses). The strength of the binocular facilitation depended on the stimulus contrast, the facilitation decreasing with increasing contrast. The receptive-field disparity distribution of the 31 PE cells capable of making significant horizontal disparity discriminations has standard deviations of 0.37 degrees and 0.40 degrees, respectively. Predominantly inhibitory cells (PI) (N = 23) showed two basic types of disparity response profile: symmetric (N = 17) and asymmetric (N = 6). Uncertainty regarding the precise location of the binocular fixation point in the anaesthetized and paralysed preparation made it difficult to categorize PI cells adequately.

End-stopped cells and binocular depth discrimination in the striate cortex of cats.

Proposals concerning neural mechanisms for binocular depth discrimination have been criticized on the grounds that only striate cells with a preferred stimulus orientation not too far from the vertical can make significant horizontal disparity discriminations. We investigated this claim by preparing a two-dimensional array of position-disparity response profiles to moving light and dark bars from each of 18 cells in the simple family. From these arrays, it was possible to reconstruct disparity response profiles along any axis across the receptive field, irrespective of the cell's optimal stimulus orientation. This analysis showed that cells with a predominantly excitatory binocular response (N = 10) can make precise horizontal disparity discriminations, independent of their optimal stimulus orientation, provided that they are sufficiently end stopped. End-free cells, on the other hand, are effective for horizontal disparity discriminations only if their preferred orientation are near the vertical. Nearly all striate cells we examined were end-stopped to some degree and nearly half had an end inhibition sufficient to reduce the monocular response from the dominant eye to half its maximal amplitude. Cells having a predominantly inhibitory disparity response profile of the symmetric type (N = 8) have an inhibitory profile along every axis across the receptive field. An outline is given of a neural mechanism for the determination of absolute viewing distance based on the sensitivities of striate cells to vertical retinal-image disparities.

Simple and B-cells in cat striate cortex. Complementarity of responses to moving light and dark bars.

This report is based on the quantitatively recorded responses of 72 striate cells in the simple (S and SH) and B-cell (B and BH) families to narrow (0.14 degrees) moving light and dark bars. Cells were regarded as hypercomplex (SH and BH) if the end-zone inhibition reduced the response to 50% of its peak value. The contrast of the bars was relatively low and matched to be equal but opposite for the two kinds of bar. Average response histograms to the two kinds of bar were recorded separately and only subsequently combined. The response histogram from a given S- or SH-cell shows separate response peaks to the light and dark bars. The number of peaks varies from two to five in different cells. Cells with two response peaks were encountered most commonly (54%), and rather less common were cells with three (31%), four (7.5%), and five (7.5%) peaks. By defining the sequence of the response peaks according to the direction preferred by a moving light bar, the number of distinct spatial patterns of responses to the moving bars increases from four to eight since the first response in the sequence can be either to a light bar or to a dark bar. Examples of all eight responses have been recorded. For cells in the simple family with two response peaks, as well as for B-cells, the width of the light-bar peak was the same as, or closely similar to, that of the dark-bar peak. For S- and SH-cells with more than two response peaks this was also true for the two principal peaks, namely the largest and the next-largest immediately adjacent peak. In the simple family, the mean widths of the two principal response peaks remained closely similar despite the progressive decrease in their respective widths as the number of peaks in the pattern increased from two to five. The mean width of the two principal response peaks from S- and SH-cells (0.6 degrees) was significantly less than the mean width for B-cells (1.4 degrees). For simple-family cells the spatial overlap between the two principal peaks (mean 14%) was always less than 50% of the overall width of the two peaks, whereas for B-cells the overlap (mean 79%) was always greater than 50%. For cells in both the simple and B-cell families the length of the receptive field as given by a moving light bar is the same as that given by a moving dark bar.(ABSTRACT TRUNCATED AT 400 WORDS)

Simple cells in cat striate cortex: responses to stationary flashing and to moving light bars.

Cells in the simple family respond to a moving light bar with an average response histogram that is most commonly unimodal (single peak: encounter frequency, 64%) and less commonly bimodal (33%) or trimodal (3%). The mean width of the principal response peak given by hypercomplex I cells is narrower than that of simple cells and they have a lower mean optimal stimulus velocity. In a series of 74 cells (simple, 47; hypercomplex I, 27), detailed comparison of the spatial relations between the response peaks to the moving bar and the subregions to the stationary flashing bar led to the concept of a boundary response. The term "boundary response" refers to an isolated response peak occurring as a moving light bar leaves an OFF subregion that is the last in the sequence of subregions traversed by the bar. The presence of a boundary response leads to an apparent discrepancy between the number of response peaks to a moving light bar and the number of ON subregions in the static-field plot. The boundary response is necessarily completely direction selective. A detailed comparison of the properties of cells as revealed by hand and quantitative methods showed a very good agreement between the two methods in respect to the assignment of cells to the simple, B- and complex cell families. There were, however, serious discrepancies in respect to the receptive field organization of cells in the simple family.(ABSTRACT TRUNCATED AT 250 WORDS)

Properties of end-zone inhibition of hypercomplex cells in cat striate cortex.

The response properties of 96 striate cells in anaesthetized and paralyzed cats were examined by using narrow optimally-oriented light bars moved in the preferred direction at optimal velocity. The bar was lengthened systematically at both ends to plot and analyze bilateral length-response curves. We found a linear relationship between the maximum slope of the inhibitory phase of the curve and the strength of the end-zone inhibition for both cell families: simple and B-cells. This observation indicates that the length of the two end-zones as given by a bilateral length-response curve is approximately constant regardless of the strength of the end-zone inhibition for a change in the strength of the inhibition from 10 to 100%.

Spatial organization of subregions in receptive fields of simple cells in cat striate cortex as revealed by stationary flashing bars and moving edges.

For each of 74 simple striate cells a quantitative analysis was made of the width dimensions and spatial arrangements of the subregions responding either at light on (ON subregion) or at light off (OFF subregion). It was concluded that every cell has at least two and no more than four subregions. Cells with two subregions (57%) were much more commonly encountered than those with three (32%) or four (11%). For most cells adjacent subregions were significantly overlapped, the region of overlap responding both at light on and at light off. In the case of cells with two subregions, the overlap averaged 32% of the overall width of the two subregions. Despite the degree of the overlap, there was, on this basis, still a large measure of discrimination between cells in the simple family and those in the B-cell and complex families. In general the receptive field profiles of cells with three and four subregions were only marginally wider than those with only two subregions. In any given receptive field, the subregions tend to be roughly equal in width so that, in cells with four subregions, the subregions are, on the average, distinctly narrower than they are in cells with only two. Hypercomplex I cells tend to have receptive fields with three and four subregions much more commonly than simple cells and these cells are encountered much more frequently in cortical cell laminae 2, 3 and 4 than in lamina 6. In lamina 6 most of the cells in the simple family have receptive fields with only two subregions. The width dimensions and spatial sequences of the response peaks to moving light and dark edges were quantitatively analyzed in response profiles prepared from 82 cells. In general, for any given receptive field, the response peaks to moving edges have a one-to-one correspondence with the subregions to a stationary flashing bar. When this is not the case, the tendency is for the number of response peaks to edges to be less than the number of subregions rather than more.

Direction selectivity of simple cells in cat striate cortex to moving light bars. I. Relation to stationary flashing bar and moving edge responses.

Quantitative estimates of the direction selectivities of 118 simple cells in response to moving light bars were expressed as a percentage calculated from the ratio of the response peaks: (preferred minus nonpreferred)/preferred. Virtually all simple cells were direction selective to some degree (mean direction selectivity 73.6%). Static-field plots to a stationary flashing bar were prepared from 74 of the 118 cells. Particular attention was given to the 42 cells with only two subregions in their static-field plot, one subregion responding at light on and the other at light off. It was concluded that interactive effects between subregions, whether synergistic or antagonistic, have little if any influence on the direction selective mechanism when the stimulus is a narrow light bar. Eighty two of the 118 cells were also tested with moving light and dark edges and of these 53 had response profiles with only two response peaks, one to the light edge and the other to the dark edge. Forty one of the 53 cells were each not only direction selective for both a light edge and a dark edge but also had a preferred direction for both edges that was the same as that for a light bar. Only two cells had preferred directions for both light and dark edges that were opposite to the direction preferred by the light bar. With one possible exception, every cell with two response static-field plot showed a one-to-one correspondence between the ordinal sequence of the response peaks and the ordinal sequence of the subregions. Depending upon the polarity of the moving edge and the ordinal sequence of the subregions, the mean level of the direction selectivity to a moving edge was significantly below that to a narrow moving light bar. This reduction in the degree of the direction selectivity appears to be due to an interaction between the subregions leading to a reduction in the amplitude of the response in the preferred direction rather than a suppression of the direction selective mechanism that operates in the nonpreferred direction. Moving edges cause a weak interactive effect between the subregions that seems always to reduce the degree of the direction selectivity, never increasing it.

Direction selectivity of simple cells in cat striate cortex to moving light bars. II. Relation to moving dark bar responses.

The response properties of 84 simple striate cells in anaesthetized (N2O/O2 supplemented with sodium pentobarbital) and paralyzed cats were examined quantitatively using narrow optimally-oriented light and dark bars moving at optimal velocities. Different cells gave two to five spatially-offset response peaks, the light bar and the dark bar response peaks alternating with one another. With only 5 exceptions, the cells had the same preferred direction for movement of the dark bar as for the light bar. Static-field plots were prepared from 32 of the 84 cells using stationary flashing bars. The receptive fields of different cells had from two to four subregions responding either at light on (ON subregion) or at light off (OFF subregion) although one cell had only a single subregion. In the preferred direction of stimulus movement cells gave either the same number of response peaks to moving bars as there were subregions or one additional response peak. The additional response peak, termed a boundary response, always occurred at the end of the sequence of response peaks and was always completely direction selective. The direction selectivities of the individual response peaks in the responses from 49 of the 84 cells were analyzed. To ensure that each response peak and the corresponding peak in the opposite direction both came from the same subregion, the 49 cells were selected on the basis of having a response in the nonpreferred direction sufficient for analysis and of having a stimulus velocity less than 2.5 degrees/s so as to avoid significant spatial shifts of the peaks due to response latencies. For all but two of the 49 cells, the response peaks in any given profile always showed a progressively greater degree of direction selectivity as the stimulus advanced from one subregion to the next, the first subregion giving the least directionally-selective response peak and the last subregion the most directionally-selective peak. This observation was independent of the direction of stimulus motion and of the particular sequence in which the ON and the OFF subregions were traversed by the stimulus. The response patterns observed experimentally have been correlated with theoretical response patterns based on the responses of lateral geniculate neurons.

Binocular simple cells for local stereopsis: comparison of receptive field organizations for the two eyes.

If a cell is to serve as a depth detector in a local stereopsis mechanism, it could indicate the depth of a specific object feature by responding only when that feature is located at the cell's preferred depth and being silent at other depths, the preferred depth varying from cell to cell over a small range. In order to assign a depth value to a particular object feature, the two receptive fields of the cell should respond to one and the same feature in the visual field. This can be done only if the organizations of the two receptive fields are identical or nearly so. Out of 31 cells in the simple family in the cat striate cortex, 15 were selected as having a monocular response from each eye sufficient to be able to examine their receptive field organizations in quantitative detail. The two receptive fields of each cell were remarkably similar in respect to the number, spatial sequence and position disparities of the response peaks to moving light and dark bars, as well as in respect to the relative ocular dominances, peak separations and direction selectivities of the response peaks to the two kinds of bar.

Silent periodic cells in the cat striate cortex.

A class of neurons called silent periodic cells, having properties intermediate between those in the simple and complex families, has been discriminated in the cat striate cortex. Silent periodic cells have relatively small receptive fields, a low spontaneous activity (i.e. relatively silent) and a preference for relatively slow stimulus velocities (less than 3 degrees/sec). In addition they give a mixed on/off response to a stationary flashing bar over virtually the whole of the receptive field with usually somewhat stronger on responses in some locations and stronger off responses in others (partial phase sensitivity). The most characteristic properties of these cells are, however, found in their responses to gratings, namely the nonlinearity manifested by the absence of a null point to a stationary flashing grating, a spatial periodicity revealed by a clearly modulated discharge to drifting gratings of medium and high spatial frequency and, finally, a very sharp spatial frequency tuning curve with a half-sensitivity bandwidth between 0.5 and 0.95 octave, i.e. narrower than that of simple cells whose bandwidths are usually above 1 octave. Silent periodic cells resemble B-cells that have been described in other studies.

Theory of spatial position and spatial frequency relations in the receptive fields of simple cells in the visual cortex.

Striate cells showing linear spatial summation obey very general mathematical inequalities relating the size of their receptive fields to the corresponding spatial frequency and orientation tuning characteristics. The experimental data show that, in the preferred direction of stimulus motion, the spatial response profiles of cells in the simple family are well described by the mathematical form of Gabor elementary signals. The product of the uncertainties in signaling spatial position (delta x) and spatial frequency (delta f) has, therefore, a theoretical minimum value of delta x delta f = 1/2. We examine the implications that these conclusions have for the relationship between the spatial response profiles of simple cells and the characteristics of their spatial frequency tuning curves. Examples of the spatial frequency tuning curves and their associated spatial response profiles are discussed and illustrated. The advantages for the operation of the visual system of different relationships between the spatial response profiles and the characteristics of the spatial frequency tuning curves are examined. Two examples are discussed in detail, one system having a constant receptive field size and the other a constant bandwidth.

Spatial arrangements of responses by cells in the cat visual cortex to light and dark bars and edges.

Detailed examination is made of the responses of visual cortical cells (area 17, border 17-18 and adjacent area 18) in the anaesthetized cat to stationary flashing bars and to bars (lines) and edges moving at their optimal velocities. Particular attention is given to the receptive field organization of cells in the simple family. While there is good general agreement between the main receptive field subregions revealed by stationary and moving stimuli, the responses to moving light and dark bars, supplemented by the responses to moving light and dark edges, provide a much more rapid, accurate and complete guide to the spatial organization of the receptive fields than do the response profiles to a stationary flashing bar. Moving light and dark bars between them generally reveal more subregions in the receptive fields of simple cells than is evident from the response profiles to a stationary flashing bar, particularly when the receptive fields have many subregions. In addition the responses to moving edges provide a rapid guide to spatial summation across the width of a subregion and the possible antagonistic effects of the next subregion in sequence. Two subclasses of cells in the simple family have been recognized: ordinary simple and fast simple cells. Two cell classes (A-cells and silent periodic cells) having properties intermediate between simple and complex types are discriminated and their properties described.