Depth capture by kinetic depth and by stereopsis

The perceived depth of regions within a stereogram lacking explicit disparity information can be captured by the surface structure of regions where disparity is explicit: stereo capture. In two experiments, observers estimated surface curvature/depth of an untextured object (a 'ribbon') superimposed on a cylinder textured with dots, the cylinder curvature being defined by disparity (stereo depth) or by motion parallax (kinetic depth: KD). With the stereo-defined cylinder, depth capture was obtained under conditions where the disparity of the ribbon was ambiguous; with the KD, cylinder depth capture was obtained under conditions where the motion flow of the cylinder was in a direction parallel to that of the ribbon. These results demonstrate yet another similarity between KD and stereopsis.     

Global stereopsis in rhesus monkeys

In three separate experiments an attempt was made to demonstrate global stereopsis in two rhesus monkeys by using random dot stereograms projected and viewed through polarizing filters. Although both animals learned a number of discriminations, control tests showed that both were perceiving non-depth cues such as monocular identification of minute pattern differences or brightness differences caused by reflections of polarized light. In a final experiment red/green anaglyph forms of the stereograms were viewed through red/green filters. Both monkeys, together with a third experimentally naive animal, showed incontrovertible evidence of prompt discrimination based on stereopsis. This paper makes a number of recommendations about the use of random dot stereograms to demonstrate global stereopsis in animals.     

Perspective based on stereopsis and occlusion

Perspective is usually considered a monocular pictorial cue, distinct from other cues such as occlusion and stereopsis. We cut across these distinctions by asking whether purely binocular (cyclopean) contours, created by stereoscopically shifting a region of homogeneous texture nearer or further than its surround, can act as a linear-perspective cue and whether the contours' ability to do this is influenced by their surface belongingness. We found that the left/right orientation of cyclopean trapezoids nearer than a surround strongly influenced perceived slant, showing that perspective constraints are applied to stereoscopically derived contours. Further regions, however, appeared as surfaces seen through a trapezoidal aperture. Because the aperture "owned" the trapezoidal contours, their orientation had little effect on perceived slant. We conclude that the application of perspective constraints depends critically on how contours are classified by stereo-specified occlusion relationships among surfaces and that perspective, stereopsis, and occlusion are not distinct processing systems.     

Ecological relevance of stereopsis in one-handed ball-catching

The aim of this study was to compare one-handed catching performance between catchers with high (n = 10) and low (n = 10) binocular depth vision or stereopsis. In two sessions of 90 trials, tennis balls were projected at three different velocities towards the subject's shoulder region. Participants with good stereopsis were more successful, although the difference in number of correct catches fell short of significance. More specifically, catchers with low stereopsis made more temporal errors, but no differences in spatial errors. As the velocity of the ball increased, the initiation of the catch was delayed and catching performance decreased. The finding that stereopsis affected timing of the catch challenges the 'monocular tau hypothesis' in the control of interceptive timing, while the velocity effect shows that the act of catching a ball is not initiated at a constant time-to-contact.     

Binocular stereopsis without spatial disparity

Binocular stereopsis has traditionally been studied mainly under static viewing conditions. There has consequently been the tendency to view binocular stereopsis only in terms of the pickup of purely spatial (time-frozen) disparity. However, whenever there is movement of objects or the 0, the structure of the light entering each eye undergoes continuous change, and so a different type of disparity—kinetic disparity—is made potentially available to the binocular system. That kinetic disparity can, in fact, be picked up is shown by the present experiment, in which there was no spatial disparity information available about the three-dimensional motion path of an object; only kinetic disparity information was available. This suggests that a clear distinction should be made between binocular-static and binocular-kinetic space perception.     

Monocular without stereopsis with and head movement

Random dots moving with various velocity gradients were presented to observers; the motion was yoked to head movement in one condition and to no head movement in another. In Experiment 1, 12 observers were shown motion gradients with sine, triangle, sawtooth, and square waveforms with amplitudes (equivalent disparities) of 12′ and 1° 53′. In Experiment 2, 48 observers were shown only the sinewave or square-wave gradient of 1° 53′ disparity either with or without head movement so that the observers’ expectation to see depth in one condition did not transfer to another. The main findings were: (1) with 12′ disparity, the head-movement condition produced perceived depth but almost no perceived motion, whereas the no-head-movement condition produced both perceived depth and perceived motion; (2) with 1° 53′ disparity, both conditions produced perceived depth and perceived motion; and (3) when the expectation to see depth was removed, the no-head-movement condition with the square-wave gradient produced no perceived depth, only motion. We suggest that monocular stereopsis with head movement can be achieved without perception of motion but monocular stereopsis without head movement requires perception of motion.     

Monocular stereopsis with and without head movement

Random dots moving with various velocity gradients were presented to observers; the motion was yoked to head movement in one condition and to no head movement in another. In Experiment 1, 12 observers were shown motion gradients with sine, triangle, sawtooth, and square waveforms with amplitudes (equivalent disparities) of 12' and 1 degrees 53'. In Experiment 2, 48 observers were shown only the sinewave or square-wave gradient of 1 degrees 53' disparity either with or without head movement so that the observers' expectation to see depth in one condition did not transfer to another. The main findings were: (1) with 12' disparity, the head-movement condition produced perceived depth but almost no perceived motion, whereas the no-head-movement condition produced both perceived depth and perceived motion; (2) with 1 degrees 53' disparity, both conditions produced perceived depth and perceived motion; and (3) when the expectation to see depth was removed, the no-head-movement condition with the square-wave gradient produced no perceived depth, only motion. We suggest that monocular stereopsis with head movement can be achieved without perception of motion but monocular stereopsis without head movement requires perception of motion.     

Patent stereopsis with diplopia in random-dot stereograms

Fusional limits for an RD (random-dot) stereogram with overall horizontal retinal disparity due to the temporalward pulling of its two constituent RD patterns beyond the divergence limits of the eyes have been determined by using an afterimage method. Two criteria for fusion were used, viz, the perception ofsingle local RD elements and the perception of stereoscopic depth in the “hidden” square of side 1.38 deg with 8-min relative horizontal disparity. The diplopia thresholds were found to be in the range of 0.15–0.3 deg, and hence do not exceed the “classical” upper limit of about 0.3 deg, which has been reported for elementary line stereograms. The stereoscopic limits were found to be in the range of 0.5–1.3 deg, which is compatible with the precision of patent stereopsis from double images which has been reported for elementary line stereograms. The results of the present third look at the experiments performed by Fender and Julesz (1967) suggest that there are no special neuronal processes raising the fusional limits for RD stereograms above those for elementary line stereograms. Previous claims that such special neuronal processes may occur seem to be based on an evaluation of fusional limits obtained with different criteria for fusion. It is further argued that the major hysteresis effect that has been observed for fusional limits for RD stereograms should not be ascribed to a raising of the classical size of the diplopia threshold due to special neuronal processes initiated by RD stereograms, but to a lowering of the classical limits of patent stereopsis from double images due to the increased difficulty of solving the correspondence problem in RD stereograms.     

Contrast masking reveals spatial-frequency channels in stereopsis.

Yang and Blake (1991 Vision Research 31 1177-1189) investigated depth detection in stereograms containing spatially narrow-band signal and noise energies. The resulting masking functions led them to conclude that stereo vision was subserved by only two channels peaking at 3 and 5 cycles deg-1. Glennerster and Parker (1997 Vision Research 37 2143-2152) re-analysed these data, taking into account the relative attenuation of low- and high-frequency noise masks as a consequence of the modulation transfer function (MTF) of the early visual system. They transformed the data using an estimated MTF and found that peak masking was always at the signal frequency across a 2.8 octave range. Here we determine the MTF of the early visual system for individual subjects by measuring contrast thresholds in a 2AFC orientation-discrimination task (horizontal vs vertical) using band-limited stimuli presented in a 7 deg x 7 deg window at 4 deg eccentricity. The filtered stimuli had a bandwidth of 1.5 octaves in frequency and 15 degrees in orientation at half-height. In the subsequent stereo experiment, the same (vertical) filters were used to generate both signal and noise bands. The noise was binocularly uncorrelated and scaled by each subject's MTF. Subjects performed a 2AFC depth-discrimination task (crossed vs uncrossed disparity) to determine threshold signal contrast as a function of signal and mask frequency. The resulting functions showed that peak masking was at the signal frequency over the three octave range tested (0.4-3.2 cycles deg-1). Comparison with simple luminance-masking data from experiments with similar stimuli shows that bandwidths for stereo masking are considerably larger. These data suggest that there are multiple bandpass channels feeding into stereopsis but that their characteristics differ from luminance channels in pattern vision.     

Stimulus uncertainty does not impair stereopsis

The effect of stimulus uncertainty on the stereoscopic resolution of letters was examined for two classes of letters: (1) letters presented stereoscopically as random-element stereograms, and (2) letters presented as two-dimensional physical contours. The variables of stimulus discriminability (stereoscopic vs. physical contours) and stimulus uncertainty (number of alternative letter targets) were combined factorially. Stereoscopically presented letters were more difficult to resolve, but stimulus uncertainty had the same effect for both stereoscopic and physically defined letters. The additivity of these two variables suggests that the perception of stereoscopic forms is an automatic process not impaired by uncertainty about the form to be resolved.     

Perceptual latencies to discriminate surface orientation in stereopsis

The difference in sensitivity to stereoscopic surfaces oriented horizontally or vertically (the stereoscopic orientation anisotropy) can be redescribed as a difference in sensitivity to shear or compression transformations that relate the binocular images. The present experiment was designed to test this by dissociating the image transformation from the orientation of the surface. Surfaces were presented in isolation or in the presence of a surrounding frame that formed step and gradient discontinuities in the disparity field. Without discontinuities, observers required considerably more time to discriminate between surfaces differing in compression than between those differing in shear, irrespective of surface orientation. Disparity discontinuities facilitated the perception of the disparity gradients; minimum stimulus durations were reduced by over an order of magnitude when the reference frame was present. These results support the hypothesis that the disparity field is decomposed into different primitives during the recovery of depth and surface structure.     

Colour inputs to random-dot stereopsis.

Recently it has been claimed by Livingstone and Hubel that, of three anatomically and functionally distinct visual channels (the magnocellular, parvocellular interblob, and blob channels), only the magnocellular channel is involved in the processing of stereoscopic depth. Since the magnocellular system shows little overt colour opponency, the reported loss of the ability to resolve random-dot stereograms defined only by colour contrast seems consistent with this view. However, Julesz observed that reversed-contrast stereograms could be fused if correlated colour information was added. In the present study, 'noise' (non-corresponding) pixels were injected into random-dot stereograms in order to increase fusion time. All six subjects tested were able to achieve stereopsis in less than three minutes when there was only correspondence in colour and not in luminance, and three when luminance contrast was completely reversed. This ability depends on information about the direction of colour contrast, not just the presence of chromatic borders. When luminance and chromatic contrast are defined in terms of signal-to-noise ratios at the photoreceptor mosaic, chromatic information plays at least as important a role in stereopsis as does luminance information, suggesting that the magnocellular channel is not uniquely involved.     

The interplay between stereopsis and structure from motion

In a series of psychophysical experiments, an adaptation paradigm was employed to study the influence of stereopsis on perception of rotation in an ambiguous kinetic depth (KD) display. Without prior adaptation or stereopsis, a rotating globe undergoes spontaneous reversals in perceived direction of rotation, with successive durations of perceived rotation being random variables. Following 90 sec of viewing a stereoscopic globe undergoing unambiguous rotation, the KD globe appeared to rotate in a direction opposite that experienced during the stereoscopic adaptation period. This adaptation aftereffect was short-lived, and it occurred only when the adaptation and test figures stimulated the same retinal areas, and only when the adaptation and test figures rotated about the same axis. The aftereffect was just as strong when the test and adaptation figures had different shapes, as long as the adaptation figure contained multiple directions of motion imaged at different retinal disparities. Nonstereoscopic adaptation figures had no effect on the perceived direction of rotation of the ambiguous KD figure. These results imply that stereopsis and motion strongly interact in the specification of structure from motion, a result that complements earlier work on this problem.     

Seeing in three dimensions: the neurophysiology of stereopsis

From the pair of 2-D images formed on the retinas, the brain is capable of synthesizing a rich 3-D representation of our visual surroundings. The horizontal separation of the two eyes gives rise to small positional differences, called binocular disparities, between corresponding features in the two retinal images. These disparities provide a powerful source of information about 3-D scene structure, and alone are sufficient for depth perception. How do visual cortical areas of the brain extract and process these small retinal disparities, and how is this information transformed into non-retinal coordinates useful for guiding action? Although neurons selective for binocular disparity have been found in several visual areas, the brain circuits that give rise to stereoscopic vision are not very well understood. I review recent electrophysiological studies that address four issues: the encoding of disparity at the first stages of binocular processing, the organization of disparity-selective neurons into topographic maps, the contributions of specific visual areas to different stereoscopic tasks, and the integration of binocular disparity and viewing-distance information to yield egocentric distance. Some of these studies combine traditional electrophysiology with psychophysical and computational approaches, and this convergence promises substantial future gains in our understanding of stereoscopic vision.     

Postfusional latency in stereoscopic slant perception and the primitives of stereopsis

Random dot stereograms of slanted surfaces were constructed, each representing one or two slanted surfaces in different relative arrangements and with different axes. Latency to fusion and from fusion to stereoscopic resolution was measured for each stimulus. It was found that latency to fusion was always very brief but that latency to stereoscopic resolution varied markedly, depending upon the orientation and arrangement of the stereoscopic surfaces. A gradient of discontinuities at a surface boundary produced an instant slant response for that surface, whereas a gradient of absolute disparities across the surface did not, except under conditions where vertical declination (a form of orientation disparity) was present. We conclude that stereopsis is not based on the primitives used in matching the images for fusion and that it is, at least initially, a response to disparity discontinuities which play no role in the fusion process. We also conclude that vertical declination is responded to globally as a slant around a horizontal axis but that other forms of orientation disparity are ineffective. The evidence from our experiments does not support the existence of a stereoscopic ability to respond globally to differences in magnification (or spatial frequency). It is suggested that stereoscopic perception of slant around a vertical axis is slow because it results from the integration of local processes.