Size-disparity correlation in human binocular depth perception.

To use the small horizontal disparities between images projected to the eyes for the recovery of three-dimensional information, our visual system must first identify which feature in one eye's image corresponds with which in the other. The earliest level of disparity processing in primates (V1) contains cells that are spatial-frequency tuned. If such cells have a disparity range that covers only a single period of their mean tuning frequency, there will always be exactly one potential match within this range. Here, this 'size-disparity' hypothesis was tested by measuring the contrast sensitivity of stereopsis as a function of disparity for single bandpass-filtered items. It was found that thresholds were low and relatively constant up to disparities an order of magnitude larger than is predicted by this constraint. Furthermore, peak sensitivity was relatively independent of spatial frequency. A control experiment showed that binocular correlation of the carrier is necessary for this task. In a third experiment, the maximum disparity that supports threshold performance was compared for an isolated bandpass item and bandpass-filtered noise. This limit was found to be five times larger for the isolated stimuli. In summary, these findings show that the initial stage of disparity detection is not limited by the size-disparity constraint. For stimuli with multiple false targets, however, processes subsequent to this stage reduce the disparity range over which the correspondence problem can be solved.     

Evidence for implication of primate area V1 in neural 3-D spatial localization processing.

We investigated the neural mechanisms underlying visual localization in 3-D space in area V1 of behaving monkeys. Three different sources of information, retinal disparity, viewing distance and gaze direction, that participate in these neural mechanisms are being reviewed. The way they interact with each other is studied by combining retinal and extraretinal signals. Interactions between retinal disparity and viewing distance have been shown in foveal V1; we have observed a strong modulation of the spontaneous activity and of the visual response of most V1 cells that was highly correlated with the vergence angle. As a consequence of these gain effects, neural horizontal disparity coding is favoured or refined for particular distances of fixation. Changing the gaze direction in the fronto-parallel plane also produces strong gains in the visual response of half of the cells in foveal V1. Cells tested for horizontal disparity and orientation selectivities show gain effects that occur coherently for the same spatial coordinates of the eyes. Shifts in preferred disparity also occurred in several neurons. Cells tested in calcarine V1 at retinal eccentricities larger than 10 degrees , show that horizontal disparity is encoded at least up to 20 degrees around both the horizontal and vertical meridians. At these large retinal eccentricities we found that vertical disparity is also encoded with tuning profiles similar to those of horizontal disparity coding. Combinations of horizontal and vertical disparity signals show that most cells encode both properties. In fact the expression of horizontal disparity coding depends on the vertical disparity signals that produce strong gain effects and frequent changes in peak selectivities. We conclude that the vertical disparity signal and the eye position signal serve to disambiguate the horizontal disparity signal to provide information on 3-D spatial coordinates in terms of distance, gaze direction and retinal eccentricity. We suggest that the relative weight among these different signals is the determining factor involved in the neural processing that gives information on 3-D spatial localization.     

Linear and nonlinear transparencies in binocular vision.

When the product of a vertical square-wave grating (contrast envelope) and a horizontal sinusoidal grating (carrier) are viewed binocularly with different disparity cues they can be perceived transparently at different depths. We found, however, that the transparency was asymmetric; it only occurred when the envelope was perceived to be the overlaying surface. When the same two signals were added, the percept of transparency was symmetrical; either signal could be seen in front of or behind the other at different depths. Differences between these multiplicative and additive signal combinations were examined in two experiments. In one, we measured disparity thresholds for transparency as a function of the spatial frequency of the envelope. In the other, we measured disparity discrimination thresholds. In both experiments the thresholds for the multiplicative condition, unlike the additive condition, showed distinct minima at low envelope frequencies. The different sensitivity curves found for multiplicative and additive signal combinations suggest that different processes mediated the disparity signal. The data are consistent with a two-channel model of binocular matching, with multiple depth cues represented at single retinal locations.     

The stereoscopic anisotropy affects manual pointing

Although binocular disparity can in principle provide absolute depth information, perceived stereoscopic depth depends on the relative disparities between points and their spatial arrangement. An example of this is the stereoscopic anisotropy--observers typically perceive less depth for stereoscopic surfaces when depth varies in the horizontal direction than in the vertical direction. We investigated whether this anisotropy also affects manual pointing. Participants were presented with stereograms depicting surfaces that were slanted in depth about either a horizontal axis (inclination) or a vertical axis (slant), and were asked either to point to the edge of a surface, or to estimate its inclination or slant. For both tasks, a clear anisotropy was observed, with participants perceiving greater depth, and also pointing out steeper surfaces, for inclined surfaces than for slanted surfaces. We conclude that both perception and the control of action are subject to a similar stereoscopic anisotropy, and that performance on the two tasks relies on similar depth processing mechanisms.     

Spatial and temporal properties of luminosity horizontal cells in the turtle retina

Luminosity horizontal cells in the turtle retina respond approximately linearly to visual stimuli with contrast levels spanning a large part of the physiological range. We characterized the response properties of these cells under conditions of low photopic background illumination by measuring their spatial and temporal frequency transfer functions. Our experimental results indicate in two ways that, under these conditions, feedback from luminosity horizontal cells to cones does not play a major role in the mechanisms underlying the spatial and temporal tuning of horizontal cell responses. First, the shape of the spatial transfer function depended only weakly on the temporal frequency with which it was measured. Second, the shape of the temporal transfer function depended only weakly on the spatial frequency with which it was measured.     

Stereoscopic acuity and observation distance

The amount of depth perceived from a fixed pattern of horizontal disparities varies with viewing distance. We investigated whether thresholds for discriminating stereoscopic corrugations at a range of spatial frequencies were also affected by viewing distance or whether they were determined solely by the angular disparity in the stimulus prior to scaling. Although thresholds were found to be determined primarily by disparity over a broad range of viewing distances, they were on average a factor of two higher at the shortest viewing distance (28.5 cm) than at larger viewing distances (57 to 450 cm). We found the same pattern of results when subjects' accommodation was arranged to be the same at all viewing distances. The change in thresholds at close distances is in the direction expected if subjects' performance is limited by a minimum perceived depth.     

Isotropic integration of binocular disparity and relative motion in the perception of three-dimensional shape

Richards (1985) showed that veridical three-dimensional shape may be recovered from the integration of binocular disparity and retinal motion information, but proposed that this integration may only occur for horizontal retinal motion. Psychophysical evidence supporting the combination of stereo and motion information is limited to the case of horizontal motion (Johnston et al., 1994), and has been criticised on the grounds of potential object boundary cues to shape present in the stimuli. We investigated whether veridical shape can be recovered under more general conditions. Observers viewed cylinders that were defined by binocular disparity, two-frame motion or a combination of disparity and motion, presented at simulated distances of 30 cm, 90 cm or 150 cm. Horizontally and vertically oriented cylinders were rotated about vertical and horizontal axes. When rotation was about the cylinder's own axis, no boundary cues to shape were introduced. Settings were biased for the disparity and two-frame motion stimuli, while more veridical shape judgements were made under all conditions for combined cue stimuli. These results demonstrate that the improved perception of three-dimensional shape in these stimuli is not a consequence of the presence of object boundary cues, and that the combination of disparity and motion is not restricted to horizontal image motion.     

Stereoscopic depth constancy

Depth constancy is the ability to perceive a fixed depth interval in the world as constant despite changes in viewing distance and the spatial scale of depth variation. It is well known that the spatial frequency of depth variation has a large effect on threshold. In the first experiment, we determined that the visual system compensates for this differential sensitivity when the change in disparity is suprathreshold, thereby attaining constancy similar to contrast constancy in the luminance domain. In a second experiment, we examined the ability to perceive constant depth when the spatial frequency and viewing distance both changed. To attain constancy in this situation, the visual system has to estimate distance. We investigated this ability when vergence, accommodation and vertical disparity are all presented accurately and therefore provided veridical information about viewing distance. We found that constancy is nearly complete across changes in viewing distance. Depth constancy is most complete when the scale of the depth relief is constant in the world rather than when it is constant in angular units at the retina. These results bear on the efficacy of algorithms for creating stereo content.This article is part of the themed issue ‘Vision in our three-dimensional world’.     

Anisotropy in the chromatic channel: a horizontal-vertical effect

We compared the chromatic contrast thresholds of drifting (2Hz) red-green sine-wave gratings of horizontal, vertical, and two oblique orientations at three spatial frequencies (2, 4, 8 cpd). Luminance contrast thresholds for yellow-black gratings were also obtained. The classic oblique effect was found for high spatial frequency luminance and chromatic stimuli. For chromatic thresholds, a significant difference was found between the horizontal and vertical thresholds of all observers. One observer was retested with her head tilted 45 deg and demonstrated that the anisotropy was specific to retinal coordinates. These results give evidence for orientation selectivity in the chromatic channel which is at least partially independent of that in the luminance channel. We estimated the degree of lateral chromatic aberration in our observers' eyes and discuss the possible contribution of this aberration to the horizontal-vertical difference in the chromatic channel.     

Spatial summation in taste: NaCl thresholds and stimulated area on the anterior human tongue

Spatial summation has been demonstrated in several sensory modalities.In this study, spatial summation of sensitivity to NaCl wasinvestigated as a function of stimulated area. In a two-alternativeforced choice procedure, a filter paper stimulation method wasused to determine the sensitivity to, and the detection probabilitiesof, five low-intensity NaCl stimuli. Each of the stimuli waspresented 32 times in two conditions, a circular area (ø9 mm) and half that circle in four counterbalanced orientations.Only one side of the tongue was used. The results showed that(a) the summation found was partial; (b) the observed relationshipbetween threshold intensity and area obeyed Piper's Law, and(c) detection probabilities increased according to chance. Adhoc analysis of orientation yielded sensitivity differencesalong the vertical but not the horizontal axis.     

Small-field, binocular neurons in the superficial layers of the frog optic tectum

Binocular neurons with receptive fields about 5 degrees across were recorded just beneath the pia. Most of them responded to dark stimuli in the lower half of their receptive field and to light stimuli above. There was almost no vertical disparity between the left and right fields and the modal value of the horizontal disparity of the population of cells was 1.7 degrees. Because frogs do not verge their eyes it is possible to calculate at what distance the receptive fields through the two eyes are superimposed. This calculation suggests that the neurons are tuned to detect features in the external world about 50 cm away. This is too far for the neurons to be involved in the frog's everyday distance vision. It is more likely that they are concerned with assessing the vertical position of a horizontal surface.     

A computational model of stereoscopic prey capture in praying mantises

We present a simple model which can account for the stereoscopic sensitivity of praying mantis predatory strikes. The model consists of a single “disparity sensor”: a binocular neuron sensitive to stereoscopic disparity and thus to distance from the animal. The model is based closely on the known behavioural and neurophysiological properties of mantis stereopsis. The monocular inputs to the neuron reflect temporal change and are insensitive to contrast sign, making the sensor insensitive to interocular correlation. The monocular receptive fields have a excitatory centre and inhibitory surround, making them tuned to size. The disparity sensor combines inputs from the two eyes linearly, applies a threshold and then an exponent output nonlinearity. The activity of the sensor represents the model mantis’s instantaneous probability of striking. We integrate this over the stimulus duration to obtain the expected number of strikes in response to moving targets with different stereoscopic disparity, size and vertical disparity. We optimised the parameters of the model so as to bring its predictions into agreement with our empirical data on mean strike rate as a function of stimulus size and disparity. The model proves capable of reproducing the relatively broad tuning to size and narrow tuning to stereoscopic disparity seen in mantis striking behaviour. Although the model has only a single centre-surround receptive field in each eye, it displays qualitatively the same interaction between size and disparity as we observed in real mantids: the preferred size increases as simulated prey distance increases beyond the preferred distance. We show that this occurs because of a stereoscopic “false match” between the leading edge of the stimulus in one eye and its trailing edge in the other; further work will be required to find whether such false matches occur in real mantises. Importantly, the model also displays realistic responses to stimuli with vertical disparity and to pairs of identical stimuli offering a “ghost match”, despite not being fitted to these data. This is the first image-computable model of insect stereopsis, and reproduces key features of both neurophysiology and striking behaviour.     

Spatial stereoresolution for depth corrugations may be set in primary visual cortex

Stereo "3D" depth perception requires the visual system to extract binocular disparities between the two eyes' images. Several current models of this process, based on the known physiology of primary visual cortex (V1), do this by computing a piecewise-frontoparallel local cross-correlation between the left and right eye's images. The size of the "window" within which detectors examine the local cross-correlation corresponds to the receptive field size of V1 neurons. This basic model has successfully captured many aspects of human depth perception. In particular, it accounts for the low human stereoresolution for sinusoidal depth corrugations, suggesting that the limit on stereoresolution may be set in primary visual cortex. An important feature of the model, reflecting a key property of V1 neurons, is that the initial disparity encoding is performed by detectors tuned to locally uniform patches of disparity. Such detectors respond better to square-wave depth corrugations, since these are locally flat, than to sinusoidal corrugations which are slanted almost everywhere. Consequently, for any given window size, current models predict better performance for square-wave disparity corrugations than for sine-wave corrugations at high amplitudes. We have recently shown that this prediction is not borne out: humans perform no better with square-wave than with sine-wave corrugations, even at high amplitudes. The failure of this prediction raised the question of whether stereoresolution may actually be set at later stages of cortical processing, perhaps involving neurons tuned to disparity slant or curvature. Here we extend the local cross-correlation model to include existing physiological and psychophysical evidence indicating that larger disparities are detected by neurons with larger receptive fields (a size/disparity correlation). We show that this simple modification succeeds in reconciling the model with human results, confirming that stereoresolution for disparity gratings may indeed be limited by the size of receptive fields in primary visual cortex.     

Lateral feedback from monophasic horizontal cells to cones in carp retina. I. Experiments

The spatial and color coding of the monophasic horizontal cells were studied in light- and dark-adapted retinae. Slit displacement experiments revealed differences in integration area for the different cone inputs of the monophasic horizontal cells. The integration area measured with a 670-nm stimulus was larger than that measured with a 570-nm stimulus. Experiments in which the diameter of the test spot was varied, however, revealed at high stimulus intensities a larger summation area for 520-nm stimuli than for 670-nm stimuli. The reverse was found for low stimulus intensities. To investigate whether these differences were due to interaction between the various cone inputs to the monophasic horizontal cell, adaptation experiments were performed. It was found that the various cone inputs were not independent. Finally, some mechanisms for the spatial and color coding will be discussed.     

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.     

Collinear effects on 3-Gabor alignment as a function of spacing, orientation and detectability.

Our ability to align three Gabor patches depends upon their internal carrier orientation; we are better at aligning vertical or horizontal patches than oblique patches (Keeble and Hess, 1998). However, the tuning of alignment to patch orientation has not studied in detail. We measured the alignment of a vertical target with reference patches varying in orientation and found it tuned to vertical (collinear) patches at centre-to-centre separation of three carrier periods, with a steep increase for oblique references and slight downturn for horizontal (orthogonal) references. Next, we increased separation between the patches, testing collinear, side-by-side, orthogonal and oblique configurations. Surprisingly, we found that the tuning for collinear patches was preserved. All ten observers tested had lower alignment thresholds for collinear patches. This effect extended to an inter-patch separation of 10 carrier periods (20 envelope standard deviations). Additionally, we measured contrast detection thresholds for the reference patches using the same stimuli. The collinear facilitation of alignment was even greater than the collinear facilitation of detection.     

Screening for carriers of Tay-Sachs disease: a community project

Heterozygotes for Tay-Sachs disease can be distinguished by measuring the serum hexosaminidase activity and calculating the percentage of the heat-labile (A) form. We tested 7565 Ashkenazi Jews in Metropolitan Toronto and found a carrier frequency of 0.071. This figure was similar to the predicted frequency on the basis of caseload over a five-year period. We also found that 15% of women taking oral contraceptives were false-positive carriers. As with pregnant women, these false-positive carriers could be distinguished from true carriers by assaying leukocyte hexosaminidases.     

Motion adaptation distorts perceived visual position

After an observer adapts to a moving stimulus, texture within a stationary stimulus is perceived to drift in the opposite direction-the traditional motion aftereffect (MAE). It has recently been shown that the perceived position of objects can be markedly influenced by motion adaptation. In the present study, we examine the selectivity of positional shifts resulting from motion adaptation to stimulus attributes such as velocity, relative contrast, and relative spatial frequency. In addition, we ask whether spatial position can be modified in the absence of perceived motion. Results show that when adapting and test stimuli have collinear carrier gratings, the global position of the object shows a substantial shift in the direction of the illusory motion. When the carrier gratings of the adapting and test stimuli are orthogonal (a configuration in which no MAE is experienced), a global positional shift of similar magnitude is found. The illusory positional shift was found to be immune to changes in spatial frequency and to contrast between adapting and test stimuli-manipulations that dramatically reduce the magnitude of the traditional MAE. The lack of sensitivity for stimulus characteristics other than direction of motion suggests that a specialized population of cortical neurones, which are insensitive to changes in a number of rudimentary visual attributes, may modulate positional representation in lower cortical areas.     

Effects of stimulus size and spatial organization on pigeons’ conditional same-different discrimination

In two experiments, we explored the effects of varying the size and the spatial organization of the stimuli in multi-item arrays on pigeons’ same-different discrimination behavior. The birds had previously learned to discriminate a simultaneously presented array of 16 identical (Same) visual items from an array of 16 nonidentical (Different) visual items, when the correct choice was conditional on the presence of another cue: the color of the background (Castro et al., in press). In Experiment 1, we trained pigeons with 7-item arrays and then tested them with arrays containing the same item, but in a variety of sizes. In Experiment 2, we tested the birds with the items grouped in novel locations: the top, the bottom, the left, or the right portions of the display area, which generated different vertical and horizontal alignments. Accuracy scores revealed virtually perfect stimulus generalization across various item sizes and spatial organizations. Reaction times revealed that the birds perceived different sizes of a single icon as the same stimulus (Experiment 1) and that the birds processed vertical arrangements faster than horizontal arrangements (Experiment 2). These results suggest that the pigeons noticed both physical and spatial changes in the stimuli (as shown by their reaction times), but that these changes did not disrupt the birds’ discriminating the sameness or differentness of the multi-item arrays (as shown by their accuracy scores).     

A comparison of vernier acuity for narrowband and broadband stimuli

This study investigates the influence of contrast and exposure duration on vernier acuity thresholds for abutting and separated narrowband stimuli, and asks whether these data can predict broadband vernier performance. Vernier thresholds were determined for sinusoidal grating stimuli at two spatial frequencies (1 and 8 c/deg) across a range of contrasts (0.05-0.8) and exposure durations (35-2100 ms). Performance was assessed for the abutting configuration, and when a gap equivalent to 0.5 to 1.5 times the spatial period of the grating was introduced between the upper and lower halves of the grating. Vernier thresholds were also determined for a square-wave stimulus as a function of contrast (0.06 to 0.78). Exposure duration was fixed at 2100 ms. In addition, thresholds were determined at the appropriate contrast levels for the fundamental frequency (1.8 c/deg) of the square-wave, and for a number of the harmonics (3F, 5F, 7F, 9F). Our results provide support for filter models of vernier acuity by showing that vernier performance for abutting and closely-separated broadband stimuli represents the envelope of vernier sensitivity of those spatial frequency mechanisms that are activated by the broadband stimulus. In the case of high frequency grating stimuli presented for long exposure durations, vernier performance can be invariant across much of the contrast range. Despite this, however, contrast independence is not exhibited for abutting broadband stimuli because, within the broadband stimuli, the contrast of the higher harmonic components never reaches a level to reveal this plateau.