Anisotropy in Werner's binocular depth-contrast effect

Double fusion, a depth perception mechanism in Panum's limiting case

The origin of depth in Panum's limiting case is unclear at present, so we investigated the depth perception mechanism using a triangle type of Panum's stimulus with a slant effect and clear criterion. Experiment 1 explored whether participants can correctly perceive fixation and nonfixation features using the fixation point and quick representation of stimuli, then examined whether participants' depth judgments supported double fusion or single fusion. The results of Experiment 1 showed that participants could correctly perceive the depth of fixation and nonfixation features. That is, it supported double fusion. In Experiment 2, we examined whether the depth perceived by observers comes from depth contrast. The results of Experiment 2 showed that the depth of the two features perceived after binocular fusion did not originate from the depth contrast. The findings suggest that the depth perception mechanism of Panum's limiting case is more likely to be double fusion.

Stereoscopic Slant Contrast and the Perception of Inducer Slant at Brief Stimulus Presentations

Slant contrast refers to a stereoscopic phenomenon in which the perceived slant of a test object is affected by the disparity of a surrounding inducer object. Slant contrast has been proposed to involve cue conflict, but it is unclear whether this idea is useful in explaining slant contrast at short stimulus presentations (<1 s). We measured both slant contrast and perceived inducer slant while varying the presentation duration (100-800 ms) of stereograms with several spatial configurations. In three psychophysical experiments, we found that (a) both slant contrast and perceived inducer slant increased as a function of stimulus duration, and (b) slant contrast was relatively stable across different test and inducer shapes at each short stimulus duration, whereas perceived inducer slant increased when cue conflict was reduced. These results suggest that at brief, not long stimulus presentations, the cue conflict between disparity and perspective plays a smaller role in slant contrast than other depth cues.

Stereoscopic Depth Contrast in a 3D Müller-Lyer Configuration: Evidence for Local Normalization

Depth contrast is a stereoscopic visual phenomenon in which the slant of an element is affected by that of adjacent elements. Normalization has been proposed to be a possible cause of depth contrast, but it is still unclear how depth contrast involves normalization. To address this issue, we devised stereograms consisting of a vertical test line accompanied by several inducer lines, like a three-dimensional variation of the well-known Müller-Lyer configuration. The inducer lines had horizontal binocular disparities that defined a stereoscopic slant about a horizontal axis with respect to the endpoints of the test line. The observer's task was to adjust the slant of the test line about a horizontal axis until it appeared subjectively vertical. The results of two psychophysical experiments found that slant settings were affected by the slant of local inducers, but not by the overall slant of the whole stimulus. These results suggest that, at least for line patterns, the stereo system normalizes depth locally.

Binocular spatial induction for the perception of depth does not cross the midline

Although horizontal binocular retinal disparity between images in the two eyes resulting from their different views of the world has long been the centerpiece for understanding the unique characteristics of stereovision, it does not suffice to explain many binocular phenomena. Binocular depth contrast (BDC), the induction of an appearance of visual pitch in a centrally located line by pitched-from-vertical flanking lines, has particularly been the subject of a good deal of attention in this regard. In the present article, we show that BDC does not cross the median plane but is restricted to the side of the visual field containing a unilateral inducer. These results cannot be explained by the use of retinal disparity alone or in combination with any additional factors or processes previously suggested to account for stereovision. We present a two-channel three-stage neuromathematical model that accounts quantitatively for present and previous BDC results and also accounts for a large number of the most prominent features of binocular pitch perception: Stage 1 of the differencing channel obtains the difference between the retinal orientations of the images in the two eyes separately for the inducer and the test line; stage 1 of the summing channel obtains the corresponding sums. Signals from inducer and test stimuli are combined linearly in each channel in stage 2, and in stage 3 the outputs from the two channels are combined along with a bias signal from the body-referenced mechanism to yield ', the model's prediction for the perception of pitch.

Hinge versus twist: the effects of 'reference surfaces' and discontinuities on stereoscopic slant perception

Stereoscopic slant perception around a vertical axis (horizontal slant) is often found to be strongly attenuated relative to geometric prediction. Stereo slant is much greater, however, when an adjacent surface, stereoscopically in the frontal plane, is added. This slant enhancement is often attributed to the presence of a 'reference surface' or to a spatial change in the disparity gradient (introducing second and higher derivatives of disparity). Gillam, Chambers, and Russo (1988 Journal of Experimental Psychology: Human Perception and Performance 14 163-175) questioned the role of these factors in that placement of the frontal-plane surface in a direction collinear with the slant axis (twist configuration) sharply reduced latency for perceiving slant whereas placing the same surface in a direction orthogonal to the slant axis (hinge configuration) had little effect. We here confirm these findings for slant magnitude, showing a striking advantage for twist over hinge configurations. We also examined contrast slant measured on the frontal-plane surface in the hinge and twist configurations. Under conditions where test and inducer surfaces have centres at the same depth for twist and hinge, we found that twist configurations produced strong negative slant contrast, while hinge configurations produced significant positive contrast or slant assimilation. We conclude that stereo slant and contrast effects for neighbouring surfaces can only be understood from the patterns and gradients of step disparities present. It is not adequate to consider the second surface merely as a reference slant for the first or as having its effect via a spatial change in the disparity gradient.

Dissociations between slant-contrast and reversed slant-contrast

A vertical test probe is misperceived as slanted in the opposite direction to an inducer when disparity specifies the inducer slant while monocular cues specify a frontoparallel surface (slant-contrast). In reversed cue conditions with vertical axis slant the test probe is misperceived as slanted in the same direction as the inducer (reversed slant-contrast). We found reliable slant-contrast and reversed slant-contrast with inducers having horizontal-axis slant. The reversed slant-contrast was not influenced when the inducer and probe were separated in the frontal plane or in disparity depth whereas slant contrast was degraded, especially in the latter condition. Slant contrast was most pronounced when the inducer was slanted like a ceiling compared to like a ground. No such difference was found for the reversed slant-contrast. When the cue conflict was minimized slant-contrast was reduced, but only with inducers having ground-like slant. Implications for an existing model explaining the slant effects are discussed.

The effect of surface placement and surface overlap on stereo slant contrast and enhancement

Stereoscopic slant contrast is an apparent slant induced in a stereoscopically frontal plane surface (the test) opposite in direction to the specified stereoscopic slant of a neighbouring surface (the inducer). Test surfaces offset from the inducer in a direction collinear with the axis of slant (twist) show more contrast than those offset in a direction orthogonal to the axis of slant (hinge). We attribute this anisotropy to the presence and extent of a gradient of relative disparity in twist configurations and the absence of such a gradient in hinge configurations. This hypothesis was tested by measuring the perceived slant of the test and inducer surfaces for horizontal and vertical axes of inducer slant and collinear and orthogonal surface offsets. For vertical axis slant, the hypothesis was supported; contrast variations with position of the test surface could be explained by variations in relative slant. For horizontal axis slant, variations in contrast could be accounted for by normalisation of the slanted surface, with relative slant remaining constant. Two further experiments showed that the extent of the gradient of relative disparity rather than the area of texture overlap of the two surfaces best predicted the contrast results and that perceived relative slant did not vary with the absolute slants of the two surfaces. The arrangement of stereo surfaces is critical in predicting their relative slant.

Differences in perceived depth for temporally correlated and uncorrelated dynamic random-dot stereograms

We investigated the influence of temporal frequency on binocular depth perception in dynamic random-dot stereograms (DRS). We used (i) temporally correlated DRS in which a single pair of images alternated between two disparity values, and (ii) temporally uncorrelated DRS consisting of the repeated alternation of two uncorrelated image pairs each having one of two disparity values. Our results show that disparity-defined depth is judged differently in temporally correlated and temporally uncorrelated DRS above a temporal frequency of about 3 Hz. The results and simulations indicate that (i) above about 20 Hz, the complete absence of stereomotion is caused by temporal integration of luminance, (ii) the difference in perceived depth in temporally correlated and temporally uncorrelated DRS for temporal frequencies between 20 and 3 Hz, is caused by temporal integration of disparity.

The stereoscopic anisotropy: individual differences and underlying mechanisms

Observers are more sensitive to variations in the depth of stereoscopic surfaces in a vertical than in a horizontal direction; however, there are large individual differences in this anisotropy. The authors measured discrimination thresholds for surfaces slanted about a vertical axis or inclined about a horizontal axis for 50 observers. Orientation and spatial frequency discrimination thresholds were also measured. For most observers, thresholds were lower for inclination than for slant and lower for orientation than for spatial frequency. There was a positive correlation between the 2 anisotropies, resulting from positive correlations between (a) orientation and inclination thresholds and (b) spatial frequency and slant thresholds. These results support the notion that surface inclination and slant perception is in part limited by the sensitivity of orientation and spatial frequency mechanisms.

Effects of disparity-perspective cue conflict on depth contrast

The role of disparity-perspective cue conflict in depth contrast was examined. A central square and a surrounding frame were observed in a stereoscope. Five conditions were compared: (1) only disparity was introduced into either the centre or surround stimulus, (2) only perspective was introduced into the centre or surround, (3) concordant perspective and disparity were introduced into the centre or surround, (4) disparity was introduced into one stimulus and perspective into the other, and (5) only the centre stimulus was presented with horizontal shear disparity and perspective manipulated independently. The results show that individual differences in depth contrast were related to individual differences in the weighting of disparity and perspective in the single-stimulus conditions. We conclude that conflict between disparity and perspective contributes to depth contrast. However, significant depth contrast occurred when there was no disparity-perspective cue conflict, indicating that this cue conflict is not the sole mechanism producing depth contrast.

Temporal dependencies in resolving monocular and binocular cue conflict in slant perception

Observers viewed large dichoptic patterns undergoing smooth temporal modulations or step changes in simulated slant or inclination under various conditions of disparity-perspective cue conflict and concordance. After presentation of each test surface, subjects adjusted a comparison surface to match the perceived slant or inclination of the test surface. Addition of conflicting perspective to disparity affected slant and inclination perception more for brief than for long presentations. Perspective had more influence for smooth temporal changes than for step changes in slant or inclination and for surfaces presented in isolation rather than with a zero disparity frame. These results indicate that conflicting perspective information plays a dominant role in determining the temporal properties of perceived slant and inclination.

Change in perceived spatial directions due to context

We examined the influence of context on exocentric pointing. In a virtual three-dimensional set-up, we asked our subjects to aim a pointer toward a target in two conditions. The target and the pointer were visible alone, or they were visible with planes through each of them. The planes consisted of a regular grid of horizontal and vertical lines. The presence of the planes had a significant influence on the indicated direction. These changes in indicated direction depended systematically on the orientation of the planes relative to the subject and on the angle between the planes. When the orientation of the (perpendicular) planes varied from asymmetrical to symmetrical to the frontoparallel plane, the indicated direction varied over a range of 15 degrees--from a slightly larger slant to a smaller slant--as compared with the condition without the contextual planes. When the dihedral angle between the two planes varied from 90 degrees to 40 degrees, the indicated direction varied over a range of less than 5 degrees: A smaller angle led to a slightly larger slant. The standard deviations in the indicated directions (about 3 degrees) did not change systematically. The additional structure provided by the planes did not lead to more consistent pointing. The systematic changes in the indicated direction contradict all theories that assume that the perceived distance between any two given points is independent of whatever else is present in the visual field--that is, they contradict all theories of visual space that assume that its geometry is independent of its contents (e.g., Gilinsky, 1951; Luneburg, 1947; Wagner, 1985).

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.

Surface separation decreases stereoscopic slant but a monocular aperture increases it

When an isolated surface is stereoscopically slanted around its vertical axis, perceived slant is attenuated relative to prediction, whereas when a frontal-plane surface is placed above or below the slanted surface, slant is close to the predicted magnitude. Gillam et al (1988 Journal of Experimental Psychology: Human Perception and Performance 14 163-175) have argued that this slant enhancement is due to the introduction of a gradient of relative disparities across the abutment of the two surfaces which is a more effective stimulus for slant than is the gradient of absolute disparities present when the slanted surface is presented alone. To test this claim we varied the separation between the two surfaces, along either the vertical or depth axis. Since these manipulations have been reported to reduce the depth response to individual relative disparities, they should similarly affect any slant response based on a gradient of relative disparities. As predicted, increasing the separation, vertically or in depth, systematically reduced both the perceived slant of the stereoscopically slanted surface and also the stereo contrast slant induced in the frontal-plane surface. These results are not predicted by alternative accounts of slant enhancement (disparity-gradient contrast, normalisation, frame of reference). We also demonstrated that sidebands of monocular texture, when added to equate the half-image widths of the slanted surface, increased the perceived slant of this surface (particularly when presented alone) and reduced the contrast slant. Monocular texture, by signalling occlusion, appeared to provide absolute slant information which determined how the total relative slant perceived between the surfaces was allocated to each.

Spatial interactions modulate stereoscopic processing of horizontal and vertical disparities

Stereoscopic processing of horizontal and vertical disparities was assessed by measuring how the stereoscopic appearance of test dots near the fixation point was influenced by inducing stimuli in the near periphery. The inducing stimuli were differentially magnified in the two eyes and varied in horizontal eccentricity. As expected, when the inducers were horizontally magnified, the test dots exhibited depth contrast, slanting in depth in a direction opposite the slant of the inducing dots. When the inducers were vertically magnified, the test dots slanted in depth around a vertical axis toward the eye with the larger vertical image (the induced-size effect). However, two lines of evidence suggested that an eccentricity-dependent weighted average of horizontal and vertical components of inducer-dot magnification determined the slant of the test dots. First, as the horizontal eccentricity of the inducing dots was varied, the trend of test-dot slants measured with vertical inducer magnifications was predicted by the trend of test-dot slants measured with horizontal inducer magnifications. Second, test-dot slants measured with a combination of both horizontal and vertical inducer magnification could be predicted by simply adding test-dot slants measured with either horizontal or vertical inducer magnification alone.

Definition and detection of binocular disparity

Stereoacuity experiments tested definitions of binocularly disparate spatial positions by perturbing the binocular correspondence of the two half-images. Dichoptic translations perturbed zero-order retinal positions; expansions perturbed first-order horizontal separations; rotations perturbed first-order orientations; and anisotropic expansions deformed first-order two-dimensional (2D) structure. Each transformation perturbed relative positions in the two half-images by more than 100 arcsec, but stereoacuity thresholds remained about 10 arcsec. Binocular disparity involves second-order 2D differential structure of the monocular half-images, specifying local surface shape. Stereoacuity is much better than nonstereo acuity, suggesting that monocular spatial signals are binocularly correlated.

Stability of binocular depth perception with moving head and eyes

We systematically analyse the binocular disparity field under various eye, head and stimulus positions and orientations. From the literature we know that certain classes of disparity which involve the entire disparity field (such as those caused by horizontal lateral shift, differential rotation, horizontal scale and horizontal shear between the entire half-images of a stereogram) lead to relatively poor depth perception in the case of limited observation periods. These classes of disparity are found to be similar to the classes of disparities which are brought about by eye and head movements. Our analysis supports the suggestion that binocular depth perception is based primarily (for the first few hundred milliseconds) on classes of disparity that do not change as a result of ego-movement.