Zhi-Lei Zhang

Spatial interactions minimize relative disparity between adjacent surfaces.

Computational models of stereopsis employ a number of algorithms that constrain stereo matches to produce the smallest absolute disparity and to minimize the relative disparity between nearby features. In some natural scenes, such as large slanted textured surfaces, these two constraints lead to different matching solutions. The current study utilized a stimulus in which there was a large discrepancy in both the magnitude and direction of matches that solved for minimum absolute and minimum relative disparity. This discrepancy revealed a dominance for the minimum relative disparity over the minimum absolute disparity matching solution that increased with spatial proximity, spatial frequency and width of adjacent features. The likelihood of a minimum-relative-disparity matching solution also increased when the difference between the amplitudes of the alternative relative disparities was large. When alternative relative disparity matching solutions had similar amplitudes but opposite signs (crossed vs. uncrossed), an idiosyncratic depth bias served as a tie-breaker. The present results show that absolute disparity matches are constrained to minimize relative disparity between adjacent features.

Effects of luminance and saccadic suppression on perisaccadic spatial distortions.

Visual directions of foveal targets flashed just prior to the onset of a saccade are misperceived as shifted in the direction of the eye movement. We examined the effects of luminance level and temporal interactions on the amplitude of these perisaccadic spatial distortions (PSDs). PSDs were larger for both single and sequentially double-flashed stimuli with low than high luminance levels, and there was a reduction of PSDs for low luminance targets flashed immediately before the saccade. Significant temporal interactions were suggested by PSDs for a pair of sequentially presented flashes (ISI = 50 ms) that could not be predicted from the single-flash distortions: PSD increased for the first flash and decreased for the second compared to the single-flash distortions. We also found that when the flash pair was presented near saccade onset, the perceived distortion of the earlier flash overtook that of the later flash, even though the late flash occurred closer in time to the saccade. To explain these effects, we propose that stimulus-dependent nonlinearities (contrast gain control and saccadic suppression) influence the duration of the temporal impulse response of both single- and double-flashed stimuli.

Thresholds for stereo-slant discrimination between spatially separated targets are influenced mainly by visual and memory factors but not oculomotor instability

Surface-slant variations can be sensed either simultaneously with steady fixation or sequentially with saccadic gaze shifts. Stereo-slant discrimination thresholds are affected by visual, oculomotor, and memory factors. We have investigated the effects of fixation strategy, target separation, and exposure duration on stereo-slant discrimination. With long exposure durations (734 ms), stereo-slant discrimination thresholds measured with simultaneous presentation of test and reference stimuli were lower with gaze shifts than without them when target separations exceeded 4 deg. Above 4-deg target separations, the benefits of improved disparity resolution with foveal gaze shifts outweighed the costs of oculomotor variability associated with saccades. With short exposure durations (167 ms), as target separation increased, stereo-slant discrimination thresholds measured without gaze shifts increased with both sequential and simultaneous stimulus presentations, whereas thresholds with gaze shifts remained constant. This indicates that oculomotor errors are not an important factor in stereo-slant discrimination. In contrast to stereo-slant thresholds, sequential stereo-depth thresholds between two dots, measured with gaze shifts, increased with target separation. Thus, oculomotor error increases with target separation, and it is an important factor in stereo-depth discrimination.

Eye movements facilitate stereo-slant discrimination when horizontal disparity is noisy

Conditions in which saccadic gaze shifts within planar surfaces facilitate stereo-slant discrimination for slant about the horizontal and vertical axis were investigated. When horizontal disparity noise was added, large gaze shifts in the direction of the slant lowered stereo-slant discrimination thresholds compared to thresholds measured with steady central fixation, whereas eye movements orthogonal to the slant orientation did not lower slant-discrimination thresholds. When no horizontal noise was added, performance was the same with and without gaze shifts. These results suggest that slant is recovered from depth differences between target edges when horizontal disparity signals are variable and that foveal fixation improves the measures of disparity. Eye movements did not lower slant thresholds by providing multiple foveal samples of slant at different target locations that were averaged to reduce disparity noise levels, because eye movements only lowered the thresholds when there was a depth difference between the fixation points. To study which signals for azimuth are used when slant is recovered from the difference in depth between target edges, vertical disparity noise was added and stimulus height was reduced. Both methods elevated slant-discrimination thresholds when horizontal disparity noise was present, suggesting that vertical disparity is used as a cue for azimuth.

Temporal aspects of spatial interactions affecting stereo-matching solutions

Stereo-matching solutions minimize disparity relative to the horopter (minimum-absolute-disparity or MAD), and differences in disparity between adjacent features (minimum-relative-disparity or MRD). When placed in conflict, spatial proximity promotes MRD over MAD solutions. How does temporal proximity of neighboring features affect strength of these spatial interactions? We quantified the inter-stimulus interval (ISI) over which an unambiguous disparity pattern influenced stereo-matches for patterns with several possible solutions. Likelihood of MRD decreased as ISI increased (48.9 ms time constant) and increased as contrast was reduced for short ISIs, suggesting that monocular persistence (temporal impulse response) underlies the temporal interaction.

The effect of perceptual grouping on perisaccadic spatial distortions.

Perisaccadic spatial distortion (PSD) occurs when a target is flashed immediately before the onset of a saccade and it appears displaced in the direction of the saccade. In previous studies, the magnitude of PSD of a single target was affected by multiple experimental parameters, such as the targets luminance and its position relative to the central fixation target. Here we describe a contextual effect in which the magnitude of the PSD for a target was influenced by the synchronous presentation of another target: PSD for simultaneously presented targets was more uniform than when each was presented individually. Perisaccadic compression was ruled out as a causal factor, and the results suggest that both low- and high-level perceptual grouping mechanisms may account for the change in PSD magnitude. We speculate that perceptual grouping could play a key role in preserving shape constancy during saccadic eye movements.

Spatio- temporal interactions that promote the smoothness constraint for binocular matches

Early in his career, Bela Julesz introduced the stereo matching problem while working at Bell Labs on an encryption project. The common belief at that time was based on Wheatstone’s proposal that 2-D space perception of form preceded coding of disparity for 3-D space perception. However, with the random-dot stereogram, Julesz demonstrated that stereoscopic depth could be perceived in the absence of any identifiable objects or perspective cues available to either eye alone. This work inspired many algorithms for binocular matching including the smoothness constraint. Wheatstone’s and Julesz’s proposals as to whether binocular matches are solved at a low level, prior to form perception, or after form is perceived are still debated. We have examined spatio-temporal interactions that promote binocular matches and yield percepts of smooth surfaces in depth. We identified low-level processes for estimating depth differences between surface patches that require their proximity in both time and space, and a high level process that minimizes their depth differences when surface texture of adjacent patches appears to belong to the same surface. This suggests that the stereo-matching solution is influenced by a priori assumptions about the surface configuration of the scene and by monocular and binocular spatial cues.