Orientation of stimuli and binocular disparity coding

An experiment is described which attempts to relate physiological work on disparity coding in the cat to a psychophysical situation using human subjects and Julesz stereograms composed of small line elements. It was found that depth perception occurred only if matching disparate lines in each stereogram shared a similar orientation. Depth began to deteriorate if an orientation difference exceeded 10° and it was extinguished at about 60°. The results are interpreted as supporting the hypothesis that shape-sensitive disparity detectors of the kind found in the cat exist also in man.     

How configurations of binocular disparity determine whether stereoscopic slant or stereoscopic occlusion is seen

A partially occluded contour and a slanted contour may generate identical binocular horizontal disparities. We investigated conditions promoting an occlusion resolution indicated by an illusory contour in depth along the aligned ends of horizontally disparate line sets. For a set of identical oblique lines with a constant width added to one eye's view, strength, depth, and stability of the illusory contour were poor, whereas for oblique lines of alternating orientations the illusory contours were strong, indicating a reliance on vertical size disparities rather than vertical positional disparities in generating perceived occlusion. For horizontal lines, occlusion was seen when the lines were of different lengths and absolute width disparity was invariant across the set. In all line configurations, when the additional length was on the wrong eye to be attributed to differential occlusion, lines appeared slanted consistent with their individual horizontal disparities. This rules out monocular illusory contours as the determining factor.     

Aging and the perception of slant from optical texture, motion parallax, and binocular disparity

The ability of younger and older observers to perceive surface slant was investigated in four experiments. The surfaces possessed slants of 20°, 35°, 50°, and 65°, relative to the frontoparallel plane. The observers judged the slants using either a palm board (Experiments 1, 3, and 4) or magnitude estimation (Experiment 2). In Experiments 1–3, physically slanted surfaces were used (the surfaces possessed marble, granite, pebble, and circle textures), whereas computer-generated 3-D surfaces (defined by motion parallax and binocular disparity) were utilized in Experiment 4. The results showed that the younger and older observers' performance was essentially identical with regard to accuracy. The younger and older age groups, however, differed in terms of precision in Experiments 1 and 2: The judgments of the older observers were more variable across repeated trials. When taken as a whole, the results demonstrate that older observers (at least through the age of 83 years) can effectively extract information about slant in depth from optical patterns containing texture, motion parallax, or binocular disparity.     

An analysis of binocular slant contrast

When a small frontoparallel surface (a test strip) is surrounded by a larger slanted surface (an inducer), the test strip is perceived as slanted in the direction opposite to the inducer. This has been called the depth-contrast effect, but we call it the slant-contrast effect. In nearly all demonstrations of this effect, the inducer's slant is specified by stereoscopic signals; and other signals, such as the texture gradient, specify that it is frontoparallel. We present a theory of slant estimation that determines surface slant via linear combination of various slant estimators; the weight of each estimator is proportional to its reliability. The theory explains slant contrast because the absolute slant of the inducer and the relative slant between test strip and inducer are both estimated with greater reliability than the absolute slant of the test strip. The theory predicts that slant contrast will be eliminated if the signals specifying the inducer's slant are consistent with one another. It also predicts reversed slant contrast if the inducer's slant is specified by nonstereoscopic signals rather than by stereo signals. These predictions were tested and confirmed in three experiments. The first showed that slant contrast is greatly reduced when the stereo-specified and nonstereo-specified slants of the inducer are made consistent with one another. The second showed that slant contrast is eliminated altogether when the stimulus consists of real planes rather than images on a display screen. The third showed that slant contrast is reversed when the nonstereo-specified slant of the inducer varies and the stereo-specified slant is zero. We conclude that slant contrast is a byproduct of the visual system's reconciliation of conflicting information while it attempts to determine surface slant.     

A statistical model of binocular disparity

Binocular disparity provides important information about the three-dimensional structure of the environment. The current study sought to complement our geometrical understanding of binocular vision by considering the distributions of horizontal and vertical disparities that might be expected in images of the natural environment, using a simple environmental model. It was observed that the distribution of disparities depends critically on fixation, and varies greatly from one image location to another. The results were considered in relation to computational models of binocular stereopsis, and compared to two known properties of the visual system—the small disparity preference in disparity matching, and the influence of eccentricity on Panum's fusional limit. Overall, the study characterizes the binocular disparities that are likely to be encountered in the real world scenes, and discusses the implications of these for our understanding of binocular visual systems.     

Intersubject variability in perceived oscillation as a function of threshold for binocular disparity.

Four groups of 15 female subjects each were classified along a quantitative dimension for proportion of perceived oscillation and threshold for binocular disparity. Analyses of variance showed that significant differences in proportion of perceived oscillation were accompanied by significant differences in threshold for binocular disparity for perceivers of "high" and "low" oscillation (p less than .05). For perceivers of "intermediate" oscillation significant differences in proportion of perceived oscillation but not threshold for binocular disparity were found. It was suggested that: (1) intersubject variability in perceived oscillation may be governed by the threshold for binocular disparity, (2) "low" perceivers may be especially sensitive to the magnitude of the cue, (3) "intermediate" perceivers' subjective reports may be primarily dependent on response criteria and the multiplicity of subjective factors which constitute it, (4) "high" perceivers apparently have least response sensitivity and they cannot maintain a consistent response criterion.     

Fusion frequency as a function of number and phase of binocular stimuli

The relation of fusion hertz to the number of pulses in a train was explored under three conditions: monoptically, dichoptically inphase, and dichoptically antiphase. All three conditions show an increase in fusion hertz as the number of pulses in the stimulating train increases. Over the range of pulse numbers investigated, fusion hertz varies principally with the number of pulses delivered to one eye regardless of the stimulating condition of the other eye.     

Orientation disparity, deformation, and stereoscopic slant perception.

Koenderink and van Doorn's theory, that the basis of stereoscopic slant perception is the deformation component of the disparity, field, was tested for slant around a horizontal axis, which produces images with a vertical ramp of horizontal disparity (horizontal shear) characterised by a global orientation disparity at the vertical meridian. The disparity field in this case can be parsed into two components, deformation and curl, which each contribute half of the orientation disparity. This case was compared with similar random-dot stimuli in which the deformation component was doubled and the curl component eliminated or vice versa. All three types of stimuli had identical orientation disparity at the vertical meridian. A condition in which there was no such orientation disparity, but deformation was present, was also included. It was found that perceived slant was not related to the deformation present, as Koenderink and van Doorn's theory would predict, but was predictable from the orientation disparity at the vertical meridian per se.     

Role of convergence and binocular disparity in size constancy

Summary The effect of convergence on the perceived size of a light disk presented against a dark background was investigated by means of a projector stereoscope with polarizing filters. The results obtained with four subjects indicate that the logarithm of matched size decreases linearly as the convergence angle increases. The effect of binocular disparity was also examined by presenting a vertical bar beside the disk, but this did not add to the convergence effect. The results of a previous study on binocular disparity were reinterpreted as an effect of convergence difference between two objects. Implications of the present findings to the phenomenon of size constancy were discussed.

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Zusammenfassung Der Effekt der Konvergenz auf die wahrgenommene Größe einer gegen einen dunklen Hintergrund dargebotenen Lichtscheibe ist durch ein Projektorstereoskop anhand Polarisationsfiltern untersucht worden. Die Ergebnisse, die mit vier Versuchspersonen erworben wurden, zeigen, daß der Logarithmus der subjektiv gleichgestellten Größe sich linear mit zunehmendem Konvergenzwinkel verkleinert. Außerdem wurde der Effekt der Querdisparation durch das Darbieten eines vertikalen Lichtbalkens neben der Lichtscheibe untersucht; aber dieser war ohne Effekt. Die Ergebnisse einer vorhergehenden Untersuchung über die Querdisparation wurde neu interpretiert als ein Effekt der Konvergenzdifferenz zwischen zwei Objekten. Die Bedeutung des Versuches für das Phänomen der Größenkonstanz wurde erläutert.

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This study was performed at Chiba University in 1967 during the sabbatical year of the second author.     

Orientational versus horizontal disparity in the stereoscopic appreciation of slant

Twenty stereograms with needles either plunging in depth or untilted were constructed. When the geometry of the needles was unbiased, the tilt of the needles was correctly and rapidly appreciated. When the needles were biased so as to remove either their orientational disparity, or the difference in horizontal disparities at the tips, they could be seen, depending on the subject and the nature of the bias, either with or without slant. Orientational disparity proved to be, with two different testing methods, clearly more effective than horizontal disparity in conveying the information of slant. Biased needles at -45 degrees were more often rejected as untilted than biased needles at +45 degrees. The orientational disparity information was ineffective with crosses that combined +45 degrees and -45 degrees needles. The reaction time and the nature of the percept were correlated, the tilted percept taking longer to mature than the untilted one in biased stereograms. Of the seventy tested subjects, one appeared to make no use at all of horizontal disparity in the stereoscopic appreciation of slant.     

Perspective, orientation disparity, and anisotropy in stereoscopic slant perception.

Stereoscopic depth estimates are not predictable from the geometry of point disparities. The configural properties of surfaces (surface contours) may play an important role in determining, for example, slant responses to a disparity gradient, and the marked anisotropy in favour of slant around a horizontal axis. It has been argued that variation in slant magnitude are attributable to the degree of perspective conflict present and that anisotropy is attributable to orientation disparity, which varies with the axis of slant. Three experiments were conducted in which configural properties were varied to try and tease apart the respective roles of orientation disparity and conflicting perspective in determining stereoscopic slant perception and slant axis anisotropy. The results could not be accounted for by the magnitude of the orientation disparities present. Conflicting perspective cues appeared to play a role but only for slant around a vertical axis. It was concluded that there are important configural effects in stereopsis attributable neither to orientation disparity nor to perspective.     

Relationship between binocular disparity and motion parallax in surface detection

The ability to detect surfaces was studied in a multiple-cue condition in which binocular disparity and motion parallax could specify independent depth configurations. On trials on which binocular disparity and motion parallax were presented together, either binocular disparity or motion parallax could indicate a surface in one of two intervals; in the other interval, both sources indicated a volume of random points. Surface detection when the two sources of information were present and compatible was not better than detection in baseline conditions, in which only one source of information was present. When binocular disparity and motion specified incompatible depths, observers’ ability to detect a surface was severely impaired if motion indicated a surface but binocular disparity did not. Performance was not as severely degraded when binocular disparity indicated a surface and motion did not. This dominance of binocular disparity persisted in the presence of foreknowledge about which source of information would be relevant.     

The appearance of surfaces specified by motion parallax and binocular disparity

The experiments reported in this paper were designed to investigate how depth information from binocular disparity and motion parallax cues is integrated in the human visual system. Observers viewed simulated 3-D corrugated surfaces that translated to and fro across their line of sight. The depth of the corrugations was specified by either motion parallax, or binocular disparities, or some combination of the two. The amount of perceived depth in the corrugations was measured using a matching technique.

A monocularly viewed surface specified by parallax alone was seen as a rigid, corrugated surface translating along a fronto-parallel path. The perceived depth of the corrugations increased monotonically with the amount of parallax motion, just as if observers were viewing an equivalent real surface that produced the same parallax transformation. With binocular viewing and zero disparities between the images seen by the two eyes, the perceived depth was only about half of that predicted by the monocular cue. In addition, this binocularly viewed surface appeared to rotate about a vertical axis as it translated to and fro. With other combinations of motion parallax and binocular disparity, parallax only affected the perceived depth when the disparity gradients of the corrugations were shallow. The discrepancy between the parallax and disparity signals was typically resolved by an apparent rotation of the surface as it translated to and fro. The results are consistent with the idea that the visual system attempts to minimize the discrepancies between (1) the depth signalled by disparity and that required by a particular interpretation of the parallax transformation and (2) the amount of rotation required by that interpretation and the amount of rotation signalled by other cues in the display.     

The combined influence of binocular disparity and shading on pictorial shape

The combined influence of binocular disparity and shading on pictorial shape was studied. Stimuli were several pairs of stereo photographs of real objects. The stereo base was 0, 7, or 14 cm, and the location of the light source was varied over three positions (one from about the viewpoint of the camera, one about perpendicular to the line of sight, and one in between the two). Therefore, in total, nine different combinations were studied. Subjects had to perform surface attitude settings at about 300 positions in the image plane. From the settings, depth maps were calculated on which a principal components analysis was performed. It was found that three components were enough to account for at least 97.8% of the variance in the data. The first component accounted for shape constancy. The effects of the two cues could be isolated as a linear combination of the other two components. The effects of the disparity and the shading cue variation were found to combine in almost linear fashion.     

The combined influence of binocular disparity and shading on pictorial shape

The combined influence of binocular disparity and shading on pictorial shape was studied. Stimuli were several pairs of stereo photographs of real objects. The stereo base was 0, 7, or 14 cm, and the location of the light source was varied over three positions (one from about the viewpoint of the camera, one about perpendicular to the line of sight, and one in between the two). Therefore, in total, nine different combinations were studied. Subjects had to perform surface attitude settings at about 300 positions in the image plane. From the settings, depth maps were calculated on which a principal components analysis was performed. It was found that three components were enough to account for at least 97.8% of the variance in the data. The first component accounted for shape constancy. The effects of the two cues could be isolated as a linear combination of the other two components. The effects of the disparity and the shading cue variation were found to combine in almost linear fashion.