Stereoacuity thresholds in the presence of a reference surface.

With isolated binocular targets, the best depth discrimination is found in the fixation plane (Blakemore, C., Journal of Physiology 211 (1970) 599). More recent studies have suggested that stereoscopic thresholds are not always a simple function of absolute disparity, but depend on the relative disparities in the stimulus. Here, we explored the effects of relative disparity in more detail, taking particular care to control for the possibility that subjects might change their binocular eye position or exploit monocular information provided by additional reference cues. Subjects judged the depth of a vertical target line presented above a comparison line in a blank window within a fronto-parallel reference surface composed of randomly positioned dots. On individual trials, the reference surface was presented at one of three disparities (-10, 0 and +10 arc min). To control for changes in binocular eye position, exposure duration was 150 ms, and experimental conditions with different disparities of the reference surface and comparison line were randomly interleaved. To control for monocular cues, changes in threshold were determined with respect to a disparity noise condition that was in all ways identical to the reference plane condition, except that the disparities of the dots were randomly assigned between 10 and +10 arc min. Stereo-thresholds were lowered by a factor of about 2 when the surface was at the same depth as the comparison line. Thresholds were also lowered when the comparison disparity was close to the same depth as the reference surface, but were often raised when the comparison disparity had the opposite disparity sign. These results provide unequivocal evidence that the fundamental sensitivity of the disparity detecting system can be influenced by relative disparity cues that are not related to the task.

Fixation could simplify, not complicate, the interpretation of retinal flow.

The visual system must generate a reference frame to relate retinal images in spite of head and eye movements. We show how a reference frame for storing the visual direction and depth of points can be composed from the angles and changes in angles between pairs and triples of points. The representation has no unique origin in 3-D space nor a unique set of cardinal directions (basis vectors). We show how this relative representation could be built up over a series of fixations and for different directions of translation of the observer. Maintaining gaze on a point as the observer translates helps in building up this representation. In our model, retinal flow is divided into changes in eccentricity and changes in meridional angle. The latter, called 'polar angle disparities' for binocular viewing (Weinshall, 1990. Computer Vision Graphics and Image Processing, 49 222-241), can be used to recover the relief structure of the scene in a series of stages up to full Euclidean structure. We show how the direction of heading can be recovered by a similar series of stages.

The task-dependent use of binocular disparity and motion parallax information.

Binocular disparity and motion parallax are powerful cues to the relative depth between objects. However to recover absolute depth, either additional scaling parameters are required to calibrate the information provided by each cue, or it can be recovered through the combination of information from both cues (Richards, W. (1985). Structure from stereo and motion. Journal of the Optical Society of America, 2, 343-349). However, not all tasks necessarily require a full specification of the absolute depth structure of a scene and so psychophysical performance may vary depending on the amount of information available, and the degree to which absolute depth structure is required. The experiments reported here used three different tasks that varied in the type of geometric information required in order for them to be completed successfully. These included a depth nulling task, a depth-matching task, and an absolute depth judgement (shape) task. Real world stimuli were viewed (i) monocularly with head movements, (ii) binocularly and static, or (iii) binocularly with head movements. No effect of viewing condition was found whereas there was a large effect of task. Performance was accurate on the matching and nulling tasks and much less accurate on the shape task. The fact that the same perceptual distortions were not evident in all tasks suggests that the visual system can switch strategy according to the demands of the particular task. No evidence was found to suggest that the visual system could exploit the simultaneous presence of disparity and motion parallax.

Bias and sensitivity of stereo judgements in the presence of a slanted reference plane.

The perceived depth of features is known to be affected by the presence of a slanted reference plane. Mitchison and Westheimer ((1984). Vision Research, 24, 1063-1070) reported that two lines appear to be at the same depth when they lie in a plane approximately parallel with the reference plane. We measured the perceived depth of two lines presented in front of a regular grid of dots that was either fronto-parallel or slanted about a vertical axis. The effect of the slanted grid on perceived depth diminished as the grid was moved further in disparity from the lines. We also found that the slanted grid affected the sensitivity to differences in disparity. The minimum threshold for detecting changes in disparity is normally lowest in the fixation plane and rises systematically with increasing pedestal disparity. In the presence of a slanted reference plane, the minimum threshold is at or close to the plane of equal perceived depth and rises with increasing disparity from this plane.

dmax for stereopsis and motion in random dot displays.

The upper displacement limit for motion was compared with the upper disparity limit for stereopsis using two-frame random dot kinematograms or briefly presented stereograms. dmax (the disparity/displacement at which subjects make 20% errors in a forced-choice paradigm) was found to be very similar for motion and stereo at all dot densities, and to fall with increasing dot density (0.006% or two dots to 50%) according to a power law (exponent -0.2). If dmax is limited by the spacing of false targets, this pattern of results suggests that the spatial primitives in the input to the correspondence process may be derived from multiple spatial scales. A model using MIRAGE centroids provides a good fit to the data.

Cues to viewing distance for stereoscopic depth constancy.

A veridical estimate of viewing distance is required in order to determine the metric structure of objects from binocular stereopsis. One example of a judgment of metric structure, which we used in our experiment, is the apparently circular cylinder task (E B Johnston, 1991 Vision Research 31 1351-1360). Most studies report underconstancy in this task when the stimulus is defined purely by binocular disparities. We examined the effect of two factors on performance: (i) the richness of the cues to viewing distance (using either a naturalistic setting with many cues to viewing distance or a condition in which the room and the monitors were obscured from view), and (ii) the range of stimulus disparities (cylinder depths) presented during an experimental run. We tested both experienced subjects (who had performed the task many times before under full-cue conditions) and naïve subjects. Depth constancy was reduced for the naïve subjects (from 62% to 46%) when the position of the monitors was obscured. Under similar conditions, the experienced subjects showed no reduction in constancy. In a second experiment, using a forced-choice method of constant stimuli, we found that depth constancy was reduced from 64% to 23% in naïve subjects and from 77% to 55% in experienced subjects when the same set of images was presented at all viewing distances rather than using a set of stimulus disparities proportional to the correct setting. One possible explanation of these results is that, under reduced-cue conditions, the range of disparities presented is used by the visual system as a cue to viewing distance.

Computing stereo channels from masking data.

The detection of stereoscopic depth in random-dot patterns that have been spatially band-pass filtered is adversely affected by the addition of noise at spatial frequencies in the neighbourhood of the frequencies present in the stereogram. This elevation of threshold is generally termed masking and recent data have been interpreted as evidence for a pair of spatial-frequency-tuned stereo "channels" whose peak spatial frequencies are either at 3 and 5 c/deg or 2.5 and 7 c/deg. This interpretation was re-examined. In particular, we have studied how the characteristics of masking interactions might be affected by taking account of the presence of an initial modulation transfer function (including the optical m.t.f. of the eye) that precedes the stage at which signal and mask interact. Using this approach, we reach the conclusion that the peak of the internal masking function for stereo detection coincides with the signal spatial frequency over the whole range tested (1.7-11.6 c/deg). We conclude that the recent data of Yang and Blake [(1991). Vision Research, 31, 1177-1189] are consistent with a multiple channel model in much the form proposed by Julesz and Miller [(1975). Perception, 4, 125-143]. The analysis presented in this paper has general implications for the interpretation of masking studies in spatial contrast vision.

Stereoscopic depth constancy depends on the subject's task.

Under identical viewing conditions, observers made two types of judgement about the shape of stereoscopically defined surfaces: one required an estimate of viewing distance for correct performance (e.g. setting the depth of a hemi-cylinder to equal its half-height or a dihedral angle to 90 deg), the other did not (matching the depth of, for example, sinusoidal corrugations or hemi-cylinders presented at two distances). Depth constancy for the two types of task was about 75% and 100%, respectively. We argue that observers may use a simple "direct" strategy to perform the depth matching task rather than constructing and comparing a metric representation of each surface.

The time course of 2-D shape discrimination in random dot stereograms.

Predictions of a coarse-to-fine and co-operative stereo matching algorithm were compared using a 2-D shape discrimination task for disparity-defined targets in 50% random dot stereograms. Uniform disparity targets, square wave modulated targets with a different mean disparity to the background, or uncorrelated dots could be seen at much briefer exposures (down to 33 msec) than square wave modulated targets with the same mean disparity as the background. In the latter case, performance at brief exposures was improved by using coarser disparity corrugations. The results are readily explained by a coarse-to-fine matching scheme such as that proposed by Marr & Poggio (1979) [Proceedings of the Royal Society of London (B), 204, 301-328] and suggest that the correspondence problem is not the limiting step in the perception of simple cyclopean forms.

The effect of display size on disparity scaling from differential perspective and vergence cues.

The present study compared the relative effectiveness of differential perspective and vergence angle manipulations in scaling depth from horizontal disparities. When differential perspective and vergence angle were manipulated together (to simulate a range of different viewing distances from 28 cm to infinity), approximately 35% of the scaling required for complete depth constancy was obtained. When manipulated separately the relative influence of each cue depended crucially on the size of the visual display. Differential perspective was only effective when the display size was sufficiently large (i.e., greater than 20 deg) whereas the influence of vergence angle, although evident at each display size, was greatest in the smaller displays. For each display size the independent effects of the two cues were approximately additive. Perceived size (and two-dimensional spacing of elements) was also affected by manipulations of differential perspective and vergence. These results confirm that both differential perspective and vergence are effective in scaling the perceived two-dimensional size of elements and the perceived depth from horizontal disparities. They also show that the effect of the two cues in combination is approximately equal to the sum of their individual effects.

Memory in myasthenia gravis: neuropsychological tests of central cholinergic function before and after effective immunologic treatment.

There are reports of central cholinergic deficits in myasthenia gravis (MG) describing impaired performance on a variety of tests of memory with varying benefits from plasmapheresis. We tested 11 patients with symptomatic MG at the start of a trial of immunosuppressive treatment (prednisolone plus azathioprine or placebo) and again when in remission. The tests included the Logical Memory and Design Reproduction parts of the Wechsler Memory Scale, the Rey Auditory Verbal Learning Test, Peterson-Peterson task, and an auditory vigilance task. Muscle strength improved significantly over the period of treatment, but overall performance on tests of memory or attention did not. These results fail to substantiate reports of functionally significant and reversible central deficits in myasthenia gravis.

New depth to the Müller-Lyer illusion.

It is demonstrated that when the two halves of the Müller-Lyer illusion are shown separately to the two eyes this can result in a perception of the binocularly viewed shaft as slanted in depth. For short fin lengths, the magnitude of this slant can be predicted by the extent of the ordinary two-dimensional illusion. This result is discussed in relation to Julesz's claim that stereoscopic matching of the images in the two eyes must precede whatever process is responsible for the Müller-Lyer illusion (whereas the reported illusion seems to imply the reverse). The cyclopean Müller-Lyer demonstration on which Julesz's argument is based is reexamined. It is suggested that the matching of coarse-scale features in the images in the two eyes may help to explain both the cyclopean and the reported three-dimensional Müller-Lyer illusion.

Efficiency of locating centres of dot-clusters by human observers.

A spatial interval acuity task was used to determine the efficiency with which observers located the centroids of circular clusters of individually-small elements. A cluster was defined by its radius and by the number of elements within it. The observer's task was to compare the horizontal distance between the centres of two such clusters to a standard distance, and to decide whether it was greater or smaller. The standard distance was made explicit by two markers on the display screen. As expected on statistical grounds, thresholds increased with the radius of the clusters, and decreased as a function of the number of elements. There were considerable individual differences in efficiency between observers, but the best observers achieved efficiencies close to 100% in many of the conditions. One anomalous observer showed virtually no decrease in thresholds as the number of elements increased, and thus her efficiencies declined to as little as 10%. The ability to combine positional information over spatially-separated elements to obtain an estimate of their central tendency appears in general to be high, and may underlie the perceptual biases revealed in certain geometric illusions, such as the Müller-Lyer.

Biases and sensitivities in geometrical illusions.

Psychometric functions were collected to measure biases and sensitivities in certain classical illusory configurations, such as the Müller-Lyer. We found that sensitivities (thresholds or just noticeable differences) were generally not affected by the introduction of illusory biases, and the implications of this for theories of the illusions are discussed. Experiments on the Müller-Lyer figure showed that the effect depends upon mis-location of the ends of the figure, rather than upon a global expansion as demanded by the size-constancy theory. A new illusion is described in which the perceived position of a dot is displaced towards the centre of a surrounding cluster of dots, even though it is clearly discriminable from other members of the cluster by their colour. We argue that illusions illustrate powerful constraints upon visual processing: they arise when subjects are instructed to carry out a task to which the visual system is not adapted.