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How are binocular disparities encoded and represented in the human visual system? We introduce an "encoding cube" diagram to visualise differences between competing models. To distinguish the models experimentally, we measured the depth increment detectio n function (discriminating disparity d from dądelta d) as a function of standing disparity (d) with spatially-filtered random dot stereograms of different centre spatial frequencies. Stereothresholds degraded quicker as standing disparity was increased w ith stimuli defined by high- rather than low centre spatial frequency. This is consistent with a close correlation between the spatial scale of detection mechanisms and the disparities they process. We show that a simple model, where discrimination is l imited by the noisy ratio of outputs of three disparity-selective mechanisms at each spatial scale, can account for the data. It is not necessary to invoke a population code for disparity to model the depth increment detection function.
This type of encoding scheme implies insensitivity to large interocular phase differences. Might the system have developed a strategy to disambiguate or shift the matches made at fine scales with those made at the coarse scales at large standing dispariti es? In agreement with Rohaly and Wilson (1993a), we found no evidence that this is so. Such a scheme would predict that stereothresholds determined with targets composed of compounds of high and low frequency should be superior to those of either compon ent alone. Although a small stereoacuity benefit was found at small disparities, the more striking result was that stereothresholds for compound frequency targets were actually degraded at large standing disparities. The results argue against neural shift ing of the matching range of fine scales by coarse scale matches posited by certain stereo models.
It has been suggested that breaking camouflage is one of the major functions of stereopsis (Julesz, 1971). In this study, we found that stereopsis is less effective in breaking camouflage for moving targets than for static ones. Observers were asked to de tect a single dot moving on a straight trajectory amidst identical noise dots in random motion. In the 3D condition, the noise dots filled a cylindical volume 5.7 cm in height and diameter; the trajectory signal dot moved on an oblique 3D trajectory throu gh the center of the cylinder. In the 2D control condition, observers viewed one half-image of the 3D cylinder binocularly. Surprisingly, trajectory detection in the 3D condition was only slightly better than in the 2D condition. Stereoscopic tuning for m otion detection was also measured with a novel target configuration in which random motion noise was presented in two depth planes that straddled the fixation plane where the trajectory target was presented. As the disparity between the noise planes and t he fixation plane was increased, trajectory detection imporved, reaching a peak between 6 and 12 arcmin, and then declining to the 2D level at larger disparities, where the noise became diplopic. Similar tuning measurements were made for detecting a stati c pattern, a string of five aligned dots presented in the fixation plane between two planes of static noise dots. Adding disparity to the noise planes produced a far greater improvment in static detection than in motion detection, for a comparable range o f disparities (1.5-12 arcmin). We speculate that the temporal characteristics of the stereo system are not well suited for responding to moving targets, with the result that stereo does not greatly enhance motion detection in noise.
In his 1963 Nature paper, Richard Gregory defined size constancy as "the tendency for objects to appear much the same over a wide range of distances in spite of changes of the retinal images associated with the distance of the object." As this defi nition makes clear, size constancy is about the appearance of objects, about what things look like. Strictly speaking, size constancy denotes only the apparent size of an object is nearly invariant with changes in distance, not that the observer perceives the true physical size of an object. This invariance implies, however, that some process corrects the angle subtended on the retina by some measure of relative distance, and thus that observers have good information about the relative physical siz e of objects surrounding them. If the body is used to provide a "metric" for both size and distance, e.g. hand viewed at arm's length, then, in principle, true physical size could be estimated with some degree of accuracy (Morgan, 1989). In this chapter, we will examine how well observers estimate objective size. Because speed constancy is often treated as an extension of size constancy, we will also look at the human ability to estimate objective speed.
It is widely held that in human spatial vision the visual scene is initially processed through visual filters each responsive to narrow ranges of image spatial frequencies. The physiological basis of these filters are thought to be cortical neurons with r eceptive fields of different sizes. The grain of the neural representation of spatial vision is much finer than had been supposed. Using laser interferometry, which effectively bypasses the demodulation of the eye's optics, we measured discrimination of , and adaptation to, high spatial frequency laser interference fringe patterns. Spatial frequency discrimination was good right up to the visual resolution limit (average Weber fractions of 0.13 at 50 c/deg). Both contrast and spatial frequency matches made after adapting to extremely fine interference fringes strongly suggested that there existed even finer, relatively unadapted, filters (mechanisms with small receptive fields). The smallest cortical receptive fields processing spatial information in human vision are so small that they can possess receptive field centers hardly wider than single cone photoreceptors.
Stereopsis employs differences in the location of features in the two eyes to reconstruct their relative depths. Computational models largely ignore the contrast of these features; they simply require them to be visible in each eye and to possess the same contrast polarity. With a competitive matching paradigm we show that only f eatures with a certain ratio of contrasts in the two eyes match. Increasing the contrast in one eye requires proportionally more contrast in the other eye for matching. This contrast relationship exactly parallels the relationship found for dichoptic ma sking, which behaves unlike any other form of contrast masking. A strange consequence of this contrast ratio constraint is that a feature may be monocularly visible yet unmatched because the contrast ratio has not been satisfied. In this case features a re seen as faint unmatched "ghosts" near the plane of fixation. In a competitive matching situation then, stereopsis acts as if it imposes a contrast threshold on matches; features failing to exceed the threshold remain unmatched. This is a simple and b iologically-plausible way for the system to eliminate false matches and reduce matching ambiguity.
In stereo-matching algorithms, the 'uniqueness constraint' requires that a feature in one stereo half-image be matched to, at most, one similar feature in the other half-image. Experiments are reported in which binocular contrast thresholds and depth-discrimination judgements have been used to determine whether the human stereo system makes unique matches. A single high-spatial-frequency target in the left eye was paired stereoscopically with two identical targets, presented near retinal correspondence (+/-3.5 arc min of disparity), in the right eye. Contrast-increment threshold s were measured for each of the targets in the right eye, and it was found that the target in the left eye masked both. Indeed, the amount of binocular masking for each member of the double targets nearly equalled the masking observed when only a single t arget was presented to the right eye. Depth judgements confirmed that the target in the left eye had been matched to both targets in the right eye. It is concluded that uniqueness is not an absolute constraint on human stereo matching.
Spatial frequency-selectivity has been incorporated into various theories of stereo matching, along with spatial scale interactions operating from coarse to fine spatial scales. We concentrate here on the role of fine scale information in the stereo matching process and show that fine scale information is capable of disambiguatin g matches made at coarser scales.
An ambiguous coarse scale stimulus was created by presenting a low frequency (2 cpd) sine wave in anti-phase to the two eyes, whose endpoints betrayed no information about which way the sine wave should be matched. It could be seen with crossed or uncrossed disparity equally validly and at chance from trial to trial. To this was added a fine scale (8 cpd) filtered random dot stimulus specifying unambiguously a certain disparity. Observers judged the apparent depth of the two stimuli as the disparity of the fine scale stimulus was varied. The sine wave was usually perceived to have the same sign disparity as the fine scale stimulus. Depth matching with the two superimposed stimuli confirmed that the coarse scale stimulus was actually disambiguated, and seen with disparities equal to half its spatial period. The results suggest the operation of a cross-spatial scale matching-disambiguation process, which can operate in a fine-to-coarse fashion.
Contrast thresholds for 75% correct depth identification in narrow-band filtered random dot stereograms were determined for different center spatial frequencies and binocular disparities. Rigorous control over vergence was maintained during testing and a forced choice procedure was used. The resulting contrast sensitivity function for stereopsis revealed sensitivity over a greater range of disparities at low spatial frequencies than high. Sensitivity peaked for large disparities at low spatial frequencies and for small disparities at high spatial frequencies. When disparities were converted to effective binocular phase differences, the variation of contrast sensitivity with phase followed a consistent pattern across spatial frequencies, with peak sensitiv ity mainly occurring for binocular phases of between 90[[ring]] and 180[[ring]]. These results have implications for the extent of spatial integration at the input to the disparity sensing mechanism. A model postulating a spread of positional disparities independent of the spatial frequency selectivity of disparity sensitive units cannot account for the results. But the "size-disparity correlation" strongly evident in our data is predicted by certain models of stereopsis, such as phase disparity encoding. An ideal observer analysis is developed which demonstrates that our results were not forced by the nature of the stimulus employed; rather, the quantum efficiency for stereopsis at contrast threshold follows the size-disparity correlation.
Basic colours segregate well in displays - but no better than nonbasic ones equally well separated in colour space. We asked whether basic colour coding would afford an advantage over an individuals preferred code made up of a personal choice of colours. These codes yielded equally good segregation when assessed in a visual search task. However, when tested on another person's codes, with which they had had no previous experience, there was a suggestion that subjects were quicker to learn the basic than t he idiosyncratic code. When coding qualitative data in a crowded display we advocate a code made up of users' internally-generated set of basic colours. This code is easy to generate and obviates the need for complicated colour calibration procedures.
Previous studies of the role of color in visual search have shown that efficient coding for as many as six colors in a high-density display. In an effort to increase this limit, we established an optimal basic color code from extensive surface-color-namin g data. This code yielded excellent segregation in a visual search task: the time required to find a critical target of the cued color increased only marginally as up to nine groups of different colors were added to the display. It made no difference whet her the cue was provided by name or example. Significant color differences in this task triggered a second experiment, which examined the detectability of the critical target feature in the periphery. A close correlation was found to exist in the order of color performance between the two experiments. Color segregation was tested again in a third experiment, in which subjects were required to count the number of targets of the cued color. The colors again segregated well. A final experiment tested the pro position that it was the basic nature of the colors that was responsible for good segregation. When seven basic colors were pitted against seven equally discriminable nonbasic ones in a modified version of the visual search task, no significant difference was found between the two groups. it is concluded that basic colors segregate well not because they are universally named but because they are well separated in color space.
Categorical color perception has previously been tested using a naming method, and the data from 27 subjects so examined in several experiments have been combined to yield a "categorical color difference index" (CCDI) that can be computed for any pair of colors in the OSA set of 424 samples. A new experiment is performed in which categorical color perception is encouraged without the explicit use of names by allowing 10 seconds to elapse between the presentation of two stimuli before they are judged same or different. All of the colors being compared are either identical or nearest neighbors in the orange region of the OSA space. Nearest neighbors, which are separated by 2 OSA units, clearly differ when presented simultaneously; with the delay, errors ("s ame" responses) sometimes occur. These errors decrease as CCDI increases, suggesting that categorization occurs when colors must be remembered. Response time, on the other hand, is independent of CCDI and therefore may reflect color differences based upon discrimination, rather than identification.
Purpose Masking experiments with mixtures of spatial frequencies provide a challenge to the notion that there are independent mechanisms tuned to spatial frequency and orientation. Here, masks made of two high similar spatial frequencies produce unexpectedly large threshold elevations at the low difference, or beat, frequency. One explanation for the paradoxical masking is that an early nonlinear stimulus transformation has injected a real grating at the beat frequency (a distortion product) and this is responsible. Is this correct? If so, what is the nature of the early nonlinearity and how does it come about? Methods We measured masking of a 1cpd test grating of random phase by a mask composed of two, 20% contrast, 8 and 9 cpd gratings (this beats at 1 cpd). Masking was measured as a function of the contrast of another real grating which was added so as to cancel or reinforce the putative distortion product at 1cpd. Results Adding a 1 cpd grating, of 2% contrast, at a phase of 270 degrees (with respect to the 8 and 9 cpd carriers), reduces the amount of masking - adding it in at 90 degrees increased the amount of masking. Conclusions The phase of the 1cpd grating that results in minimal masking implies that the distortion product is generated by an expansive nonlinearity. An expansive receptoral luminance transformation is incompatible with the phenomenon of light adaptation. However, a simple asymmetry in the treatment of light increments and decrements can account for the results. For example, if both ON's and OFF's were nonlinearly compressed, but ON's were compressed less than OFF's an 'effective expansion' would result. It can be shown that this simple model accounts for physiological and psychophysical data on nonlinearity that was thought to be due to an early compressive nonlinearity - including the observation that the bright bars of sine wave gratings appear wider than the dark bars (Pelli, ARVO, 1986).
When a high spatial frequency sine wave is contrast-modulated (CM) at a low envelope (or beat) spatial frequency, it can severely mask detection of a test grating at the beat frequency (Henning, G.B., Hertz, B.G. & Broadbent, D.E. (1975)Vision Rese arch 15, 887-899). This is surprising because signals are thought to be processed by independent linear spatial frequency channels. Thus, high frequency gratings should not mask low frequency gratings. Henning et al. suggested that a retinal nonline arity might inject a distortion product at the beat frequency and that this could account for the unexpected masking.
We have re-examined CM masking in detail. We reasoned that if the nonlinearity is early, the distortion product should mask low frequ encies in the same way as a real grating of the appropriate contrast at the beat frequency. We measured threshold elevations for different test frequencies for 2 types of maskers: (i) an 8 plus a 9 cpd CM grating (beats at 1 cpd), both of 20% cont rast; (ii) an 8 cpd grating of 20% contrast plus a real 1 cpd grating of 3% contrast. The two conditions yielded the same pattern of threshold elevations around the beat frequency, suggesting that an early nonlinearity precedes spatial filtering.
Contrast-modulated (CM) gratings, made by adding two high spatial frequency carriers of similar frequency, produce unexpectedly large masking at the modulation, or beat, frequency (Henning, G.B., Hertz, B.G. & Broadbent, D.E. (1975)Vision Research 15, 887-899). One explanation is that a nonlinear stimulus transformation generates a grating at the beat frequency (a distortion product), which is responsible for the paradoxical masking. This hypothesis predicts that adding a real grating to the CM masker, should physically cancel, or null, the distortion product and reduce the observed masking; if the real grating is added so as to reinforce the distortion product, masking should increase.
We measured masking of a 1cpd test grating of random phase, by a CM masker composed of two, 20% contrast, 8 and 9 cpd gratings (beats at 1 cpd). Adding a 1 cpd grating, of 2% contrast, at a phase of 270 degrees (with respect to the 8 and 9 cpd carriers), reduces the amount of masking by the CM grati ng. When the 1cpd grating phase is 90 degrees, the amount of masking is increased. Surprisingly, the phase of the 1cpd grating that results in minimal masking implies that the distortion product is generated by an expansive nonlinearity.
Purpose, Computational models of the stereo matching process largely ignore the contrast of the features that are matched - they simply require them to be visible monocularly and to possess the same contrast polarity. However, unequal intero cular contrast severely degrades stereoacuity. The relative contrast of features clearly matters but can it influence the assignment of matches? Methods, Subjects matched the depth of a test line of variable contrast, CT, in a simple stereog ram containing 2 lines in each eye. The other 3 lines had equal contrast C. When the test line had the same contrast as the other lines (CT=C), subjects saw two lines in the front-parallel plane. When CT=0 they saw Panum's limiting case. We asked what val ue of CT was required to shift the depth from one configuration to the other, for different values of C. Results, Depth configuration did not shift when CT exceeded monocular detection threshold. Over a range of contrasts it was seen as an unmatched ghostly feature near the plane of fixation. At a critical CT, the depth configuration shifted; this value depended on C. When CT>>C then the test line was again unmatched and was seen as a bright ghost. Thus features only matched ove r a limited range of contrast ratios (this varied with subject from 2.5:1 to 7:1). The CT required for depth to shift was directly proportional to C (slope 1.03 averaged across 3 Ss). This contrast relationship exactly parallels the slope found for dichop tic masking, which behaves unlike any other contrast masking. Conclusions There is a contrast ratio constraint on stereo matching, which may be implemented as a contrast increment threshold. In a competitive matching situation, features fail ing to satisfy the contrast ratio are not matched. This matching constraint is a simple and biologically-plausible way for the system to eliminate false matches and reduce matching ambiguity.
To investigate neural constraints on the visual resolution of fine detail, we measured contrast-sensitivity functions (CSFs) and spatial-frequency discrimination functions using interference patterns to bypass optical losses.
(1) Forced-choice orientation discrimination for orientation differences less than about 20 degrees yielded a CSF in agreement with subjects' self-adjusted thresholds. These CSFs fall steeply, varying inversely as the fourth or fifth power of frequency ne ar the resolution limit (45-55 cpd for near-horizontal fringes, lower for oblique). Orthogonal orientation discrimination can be made at higher spatial frequencies, but these may be based on cues created by aliasing and nonlinear distortion. (2) Pattern a daptation at 35 cpd produced a sharply tuned frequency-specific sensitivity-loss, preserving sensitivity for higher frequencies but shifting apparent spatial frequency away from the adapting frequency; this implies the existence of neural channels centere d at spatial frequencies higher than 35 cpd. The Weber fraction for frequency discrimination, df/f, remained almost constant up to the resolution limit. (3) Exposure to unresolvable adapting stimuli not far above the subjective resolution limit led to ori entation-specific sensitivity losses. Evidently these stimuli do activate the orientation-selective cells in primary visual cortex, and are then subjectively-obliterated by subsequent spatial filtering within the cortex.
Purpose, Binocular disparity processing is thought to involve some form of correlation of the two eyes' views. Evidence favoring this idea come from the human ability to discriminate between partially-correlated and uncorrelated noise. Human correlation discrimination improves steadily with increasing area (> 1sq. deg.).But this observation does not constrain the size of the detectors responsible for this correlation. We estimated the size of the smallest correlation window that permits c orrect identification of disparity sign. Methods, The stimulus was a single row of randomly-spaced dots, 3 deg. wide. The central region of the row was perfectly correlated (zero disparity), except for one dot in the middle which was presen ted with a crossed or uncrossed disparity of varying magnitude. The regions flanking this central region consisted of uncorrelated noise (random disparities). Subjects judged the sign of the central disparate dot as a function of the width of the correlat ed region. Results, Human performance was hardly affected by the encroaching noise until the central correlated region was less than 6 arc min. Observers could easily judge the sign of the small disparities (1-5 arc min), despite the large f lanking regions (1.45 deg wide) of disparity noise. Larger disparities were not so well discriminated. Computer simulations showed that the test dot disparity could not be identified by cross-correlation if the correlation window was large, or if the rang e of disparities for a small window was extensive. Only a small correlation window constrained to a narrow range of disparities could successfully discriminate the disparity of the test dot. Conclusions Human disparity detectors can be model led as local correlators that estimate the disparity of a limited region of visual space. Our results suggest that some of these detectors are surprisingly small, and responsive to only a narrow range of disparities.
Purpose. How are binocular disparities represented neurally? Following adaptation to a given disparity, nearby test disparities are perceived shifted away from the adapting stimulus in depth. A population code model accounts for this by the centroid of activity in an array of disparity-tuned channels shifting away from the adapting disparity. However, inspection of an extreme crossed disparity should adapt the near-most neurons, say, and make all subsequently presented test disparitie s appear smaller, including test disparities even larger than the adapting disparity. The size-disparity correlation predicts that this extreme preferred disparity will be smaller as stimulus spatial frequency is increased. Methods. Subjects adapted to disparities in Julesz stereograms which were isotropically bandpass-filtered to contain a narrow range of spatial frequencies (1.6 octave bandwidth). They then matched the perceived depth of various adapted test disparities with an unadapted c omparison in a staircase procedure. Vergence was controlled by short stimulus presentation times and nonius lines. Results. Adaptation shifted the p.s.e.. For stimuli of center spatial frequency 1 cpd, test disparities greater than 20 min a rc shifted towards adapting disparities of 20 min arc, by up to 2 mins. This paradoxical shift was also found for adapting disparities of 15 min arc at 4 cpd and 5 min arc at 16 cpd, in accordance with the size-disparity correlation. Also, adaptati on tended to steepen the psychometric function and hence improve depth discrimination. Conclusions. Our data support a population code model in which arrays of disparity-tuned channels cover ranges of disparities which inversely scale with c enter spatial frequency. Our data do not support W. Richard's coarse ("trichromatic-like") code for disparity. To highlight differences between competing neural encoding schemes we present our new 'encoding cube'. Finally, the same analysis might be appli ed to other sensory dimensions that possess 'last units', including spatial frequency but not stimulus orientation.
We recently presented evidence for a strong correlation between spatial frequency and the range of disparities processed (the so-called "size-disparity correlation") in stereopsis at contrast threshold in narrow-band filtered random-dot stereograms. A determination of stereothreshold with standing disparity with these targets also demonstrates this correlation. Stereothresholds increased away from the fixation plane faster for stimuli of high- than of low center spatial frequency. Stereothresholds could be measured over a greater range of standing disparities with low- than w ith high frequency targets.
Might the visual system have developed a strategy to disambiguate or shift the matches made at fine scales with those made at the coarse scales at large standing disparities? This would predict stereothresholds for compound frequency targets be be superio r to either component's alone. A small effect existed at small disparities, but a more striking observation was that stereothresholds for compound frequency targets were degraded at large standing disparities, when stereothresholds of the high frequency c omponent were at chance. This disruption of stereo depth by high frequency content is analogous to the shrinking of the Braddick limit in broad-band kinematograms, accounts for the Kulikowski stereogram and argues against coarse-on-fine range shifting.
Contrast thresholds for detection of patches of narrow-band isotropically-filtered two-dimensional noise of various center spatial frequencies were determined when the patches were surrounded by a field of the same space-average luminance or surrounds of high contrast made of filtered 2D noise of the same or different center frequencies. In addition, the surrounds could be given binocular disparities to set them in different planes than the test patches, and the test patches themselves could be offset in depth. Contrast thresholds for low spatial frequencies (1-2 cpd) were elevated by up to 0.5 Log units when set in surrounds of similar frequency; however, thresholds for higher center frequencies were sometimes facilitated by the coarse context. Surprisin gly, setting the test patches and context in different planes affected thresholds - when the test patch was presented with a crossed disparity of 15 min while the context had an uncrossed disparity of 15 min the threshold elevation was reduced from 0.5 to 0.2 Log units, and there was a monotonic reduction of threshold elevation for intermediate disparities. A similar effect of disparity on threshold elevation was found when the context was presented in the fixation plane. The frequency- and disparity-sele ctivity of the threshold changes suggest a neural locus for much of the threshold elevation at a level of binocular combination, unlike the Chubb et al. (PNAS '89) effect. The results suggest that contrast compression (Brown & MacLeod, ARVO '91) or normalization may operate in a frequency-selective fashion and the effect of disparity on thresholds suggests that contrast normalization may proceed separately in different coarsely-tuned disparity-selective neural pools.
Purpose, Many computational models of stereo matching assume a "uniqueness constraint" -- a feature in one eye can be matched with only one feature in the other eye. Panum's limiting case, in which two adjacent vertical bars are apparen tly matched to a single vertical bar in the other eye, would seem to contradict this premise. However, there is considerable dispute over whether both bars are matched binocularly, or one bar is an unpaired monocular feature that is assigned a depth signa l. Rather than relying on judgements of depth appearance, we used contrast discrimination thresholds to demonstrate that both bars are matched binocularly. Methods, A pair of identical test bars, separated by 7 min, was presented to one ey e and a single identical masking bar was presented to the other eye at a retinal locus half way between the two test bars. Nonius lines and a brief duration (200 msec) were used to control convergence. The test and masking bars were 5.6 arc min wide and w ere composed of a bright central region flanked by two narrow dark regions, so that their space-averaged luminance equalled the background. During different blocks of trials, observers discriminated changes in the contrast of one or the other bar. R esults, The respective increment thresholds for both test bars were elevated by the single masking bar in the other eye. Indeed, the threshold elevation was nearly equal to that observed when a single test bar was matched to single masking bar in the other eye. A single masking bar also elevated the monocular increment threshold for each of three test bars presented to the other eye. Since the bars had a high spatial frequency bandwidth, the contrast increment threshold was determined by a local filter selective for each test bar, rather than by a low frequency filter that summed test bars. Conclusions The human stereo system makes multiple matches, at least at the neural level that limits contrast discrimination. We speculat e that the brain always makes possible matches between similar features falling within a narrow disparity range, a range that scales with spatial frequency.
Interest has recently centered on interactions across spatial scales in the processing of stereo disparity, e.g. the demonstration of coarse-to-fine scale constraints on fusion by Wilson, Blake & Halpern (JOSA '91). Many computational models of the matching process operate in a coarse-to-fine way to circumvent the correspondence problem. We concentrate here on the role of fine scale information in the matching process and show that fine scale information is unexpectedly effective in disambiguating matching at coarser scales. Narrow band-filtered fine texture (8-10 cpd) random dot stereograms were created to which were added N cycles of low spatial frequency (coarse) sinusoidal luminance modulation (3 cpd) to one eye and N+1 cycles to the other eye in counter-phase. This yield ed an ambiguous coarse scale stimulus that could be matched with disparities equal to half its period in the crossed or uncrossed direction. The texture and the sine wave had equal contrast. Observers judged the apparent depth of the sine wave as the disparity of the texture was varied. Stimuli were presented for 150 msec to prevent vergence eye movements. It was found that the sine wave was usually perceived to have the same sign disparity a s that given to the texture. That is, the fine scale disparity signal disambiguated that of the coarser scale signal consistently. This occurred both when the texture disparity was small (2 mins arc) and when it was equal to a candidate sine wave disparit y match. The results suggest a more active role for fine scale information in the matching process than has generally been supposed. And the potency of large disparities at fine scales argues against the hypothesis that large disparities can be processed only by n eurones with large monocular receptive fields.
We have investigated disparity averaging using a novel stimulus which yields two spatially coextensive disparity signals carried by different spatial scales at each point in a random dot stereogram. This was accomplished by sinusoidally modulating the lu minance of dots carrying various disparities with phase differences between the two eyes' views that were equal or different to the dot disparity. In a 2AFC task Observers judged the relative depths of two panels in a random dot stereogram. A reference panel carried equal texture and sinusoid disparities; the second panel carried a different texture disparity and a sinusoid of variable phase. Near the horopter, transparency was the norm. However, with larger disparity offsets from the horopter, dispa rity averaging occurred, even when the texture and sinusoid disparities differed by over 10 min arc. Either two disparity estimates are extracted and then averaged at each point, or else the trade-off between fine and coarse scales occurs at the input to the disparity sensing mechanism. We have considered two schemes of the latter kind. An explanation based on low-pass monocular filtering and windowed cross-correlation fails to model the results. A more successful scheme postulates a disparity code inv olving the ratio of excitation of coarsely tuned mechanisms away from the horopter.
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