Brian J. Rogers

Motion parallax as an independent cue for depth perception

The perspective transformations of the retinal image, produced by either the movement of an observer or the movement of objects in the visual world, were found to produce a reliable, consistent, and unambiguous impression of relative depth in the absence of all other cues to depth and distance. The stimulus displays consisted of computer-generated random-dot patterns that could be transformed by each movement of the observer or the display oscilloscope to simulate the relative movement information produced by a three-dimensional surface. Using a stereoscopic matching task, the second experiment showed that the perceived depth from parallax transformations is in close agreement with the degree of relative image displacement, as well as producing a compelling impression of three-dimensionality not unlike that found with random-dot stereograms.

Similarities between motion parallax and stereopsis in human depth perception.

Random dot techniques were used to investigate the human visual systems sensitivity to sinusoidal depth modulations specified by motion parallax information. Thresholds for perceiving depth were found to be smallest when the spatial frequency of the depth corrugations was between 0.2 and 0.5 c/deg visual angle. These data were compared with the equivalent thresholds for perceiving depth corrugations specified by binocular disparity using similar apparatus and psychophysical procedures. The similarity between the sensitivity functions is suggestive of a closer relationship between the two systems than has previously been thought.

Vertical disparities, differential perspective and binocular stereopsis

TO calculate the depth difference between a pair of points on a three-dimensional surface from binocular disparities, it is necessary to know the absolute distance to the surface1,2. Traditionally, it has been assumed that this information is derived from non-visual sources such as the vergence angle of the eyes3,4. It has been shown5,6 that the horizontal gradient of vertical disparity between the images in the two eyes also contains information about the fixation distance7–9. Recent results10,11, however, indicated that manipulations of the vertical disparity gradient have no effect on either the perceived shape or the perceived depth of surfaces defined by horizontal disparities. Following the reasoning of Longuet-Higgins12 and Tyler13, we suggest that vertical disparities are best understood as a consequence of perspective viewing from two different vantage points and the results we report here show that the human visual system is able to exploit vertical disparities and use them to scale the perceived depth and size of stereoscopic surfaces, if the field of view is sufficiently large.

Illusory reversal of visual depth and movement during changes of contrast

Abstract The visual system usually sees phi apparent movement when two similar pictures are exposed successively, and stereoscopic depth when the pictures are exposed one to each eye. But when a picture was followed via a dissolve by its own photographic negative, overlapping but displaced, strong apparent movement was seen in the opposite direction to the image displacement (“reversed phi”). When both eyes saw a positive picture, and one eye also saw an overlapping low-contrast negative containing binocular disparity, “reversed stereo” was seen, with the apparent depth opposite to the physical disparity. Results were explained with a model of spatial summation by visual receptive fields.

Disparity Scaling and the Perception of Frontoparallel Surfaces

Binocular disparity can be defined in a variety of ways and its measurement depends upon the particular coordinate framework chosen. As a result of the inverse square law, binocular disparities need to be scaled by some estimate of absolute distance if they are to be interpreted correctly. The experiments described in this paper investigated the extent to which (i) the vergence angle and (ii) the horizontal gradient of vertical disparities or ‘differential perspective’ provide the necessary information for judging that a stereoscopic surface is flat and frontoparallel. For small displays (<20 deg) vergence is more effective than differential perspective in scaling frontoparallel surfaces but for larger displays (>30 deg), differential perspective plays the major role. When both cues together specify the viewing distance, the constancy of frontoparallel-surface scaling is close to perfect for all sizes of display up to 80 deg. Analysis of the geometry of stereoscopic images shows that when a surface patch lies in a frontal plane, the binocular horizontal size ratio of any surface feature is equal to the square of its binocular vertical size ratio, whatever its distance from the observer.

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 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.

Simultaneous and successive contrast effects in the perception of depth from motion-parallax and stereoscopic information.

Prolonged inspection of a three-dimensional corrugated surface resulted in a successive contrast effect, or aftereffect, of depth, whereby a subsequently-viewed physically-flat test surface appeared to be corrugated in depth with the opposite phase to the adapting surface. The aftereffect occurred both when the depth was specified by motion parallax, in the absence of all other sources of depth information, and when it was specified solely by stereoscopic information. The depth aftereffect was measured by ‘nulling’ the apparent depth in the test surface with physical relative motion or binocular disparity until the test surface appeared flat. Up to 70% of the depth in the adapting surface was necessary to null the aftereffect. Simultaneous contrast effects in the perception of three-dimensional surfaces were used to investigate the spatial interactions that exist in the processing of motion-parallax and stereoscopic information. A physically vertical surface appeared to slope in depth in the opposite direction to the slope of a surrounding surface. In this case up to 50% of the slope of the inducing surface was necessary to null the contrast effect. Similar results were again obtained for motion-parallax and stereoscopic depth.

The interaction of binocular disparity and motion parallax in the computation of depth.

Depth from binocular disparity and motion parallax has traditionally been assumed to be the product of separate and independent processes. We report two experiments which used classical psychophysical paradigms to test this assumption. The first tested whether there was an elevation in the thresholds for detecting the 3D structure of corrugated surfaces defined by either binocular disparity or motion parallax following prolonged viewing (adaptation) of supra-threshold surfaces defined by either the same or different cue (threshold elevation). The second experiment tested whether the depth detection thresholds for a compound stimulus, containing both binocular disparity and motion parallax, were lower than the thresholds determined for each of the components separately (sub-threshold summation). Experiment 1 showed a substantial amount of within- and between-cue threshold elevation and experiment 2 revealed the presence of sub-threshold summation. Together, these results support the view that the combination of binocular disparity and motion parallax information is not limited to a linear, weighted addition of their individual depth estimates but that the cues can interact non-linearly in the computation of depth.

A Craik-O'Brien-Cornsweet illusion for visual depth

Abstract A stereo analogue of the Cornsweet luminance illusion was discovered, and measured by a null method. Two flat vertical textured surfaces in the frontoparallel plane met at a vertical boundary, at which the left-hand surface curved slightly forward and the right-hand surface curved back by an equal amount. The protruding left edge was jointed to the receding right edge by a step. Result: although the two flat surfaces were equidistant, the left surface appeared to be about half a centimetre nearer to the observer than the right surface.