Stereopsis from interocular spatial frequency differences is not robust

Stereo slant discrimination of planar 3D surfaces: Frontoparallel versus planar matching

Binocular stereo cues are important for discriminating 3D surface orientation, especially at near distances. We devised a single-interval task where observers discriminated the slant of a densely textured planar test surface relative to a textured planar surround reference surface. Although surfaces were rendered with correct perspective, the stimuli were designed so that the binocular cues dominated performance. Slant discrimination performance was measured as a function of the reference slant and the level of uncorrelated white noise added to the test-plane images in the left and right eyes. We compared human performance with an approximate ideal observer (planar matching [PM]) and two subideal observers. The PM observer uses the image in one eye and back projection to predict a test image in the other eye for all possible slants, tilts, and distances. The estimated slant, tilt, and distance are determined by the prediction that most closely matches the measured image in the other eye. The first subideal observer (local planar matching [LPM]) applies PM over local neighborhoods and then pools estimates across the test plane. The second suboptimal observer (local frontoparallel matching [LFM]) uses only location disparity. We find that the ideal observer (PM) and the first subideal observer (LPM) outperforms the second subideal observer (LFM), demonstrating the additional benefit of pattern disparities. We also find that all three model observers can account for human performance, if two free parameters are included: a fixed small level of internal estimation noise, and a fixed overall efficiency scalar on slant discriminability.

Interocular Differences in Spatial Frequency Influence the Pulfrich Effect

The Pulfrich effect is a stereo-motion phenomenon. When the two eyes are presented with visual targets moving in fronto-parallel motion at different luminances or contrasts, the perception is of a target moving-in-depth. It is thought that this percept of motion-in-depth occurs because lower luminance or contrast delays the speed of visual processing. Spatial properties of an image such as spatial frequency and size have also been shown to influence the speed of visual processing. In this study, we use a paradigm to measure interocular delay based on the Pulfrich effect where a structure-from-motion defined cylinder, composed of Gabor elements displayed at different interocular phases, rotates in depth. This allows us to measure any relative interocular processing delay while independently manipulating the spatial frequency and size of the micro elements (i.e., Gabor patches). We show that interocular spatial frequency differences, but not interocular size differences of image features, produce interocular processing delays.

Stereopsis is adaptive for the natural environment

Humans and many animals have forward-facing eyes providing different views of the environment. Precise depth estimates can be derived from the resulting binocular disparities, but determining which parts of the two retinal images correspond to one another is computationally challenging. To aid the computation, the visual system focuses the search on a small range of disparities. We asked whether the disparities encountered in the natural environment match that range. We did this by simultaneously measuring binocular eye position and three-dimensional scene geometry during natural tasks. The natural distribution of disparities is indeed matched to the smaller range of correspondence search. Furthermore, the distribution explains the perception of some ambiguous stereograms. Finally, disparity preferences of macaque cortical neurons are consistent with the natural distribution.

Encoding of three-dimensional surface slant in cat visual areas 17 and 18

How are surface orientations of three-dimensional objects and scenes represented in the visual system? We have examined an idea that these surface orientations are encoded by neurons with a variety of tilts in their binocular receptive field (RF) structure. To examine whether neurons in the early visual areas are capable of encoding surface orientations, we have recorded from single neurons extracellularly in areas 17 and 18 of the cat using standard electrophysiological methods. Binocular RF structures are obtained using a binocular version of the reverse correlation technique. About 30% of binocularly responsive neurons have RFs with statistically significant tilts from the frontoparallel plane. The degree of tilts is sufficient for representing the range of surface slants found in typical visual environments. For a subset of neurons having significant RF tilts, the degrees of tilt are correlated with the preferred spatial frequency difference between the two eyes, indicating that a modified disparity energy model can account for the selectivity, at least partially. However, not all cases could be explained by this model, suggesting that multiple mechanisms may be responsible. Therefore an alternative hypothesis is also examined, where the tilt is generated by pooling of multiple disparity detectors whose preferred disparities progressively shift over space. Although there is evidence for extensive spatial pooling, this hypothesis was not satisfactory either, in that the neurons with extensive pooling tended to prefer an untilted surface. Our results suggest that encoding of surface orientations may begin with the binocular neurons in the early visual cortex.

The structure of stereoscopic masking: Position, disparity, and size tuning

The masking effect of a Gaussian blob on detection of a Gaussian target was measured as a function of the position, disparity, width and polarity of the mask. The data reveal a large degree of disparity-specific masking that cannot be explained by the masking of its monocular constituents. At 5 degrees eccentricity, the masking range extends about +/-1 degrees around the lines of sight of the two eyes and 1-3 degrees in disparity, depending on the size of the test stimuli. The masking effects can be modeled as having three additive components, one that has a fixed disparity range and is polarity independent, one with a center/surround form keyed to both the disparity and the polarity of the mask, and one that derives from the monocular masking in each eye. Thus, the profound disparity interaction behavior is not limited to the simple monocular masking properties of the stimuli but reveals extensive connectivity across the disparity domain. Future models of disparity encoding will need to take these properties into account.

Binocular fusion/suppression to spatial frequency differences at the border of areas 17/18 of the cat

As shown by various human psychophysical studies, interocular spatial frequency disparities can yield a variety of percepts. In order to examine how binocular fusion is affected by spatial frequency differences, we have recorded cells in the border region of areas 17/18 of anesthetized cats. The optic axes of the eyes were deviated onto cathode-ray screens, and the optimal spatial frequency of each eye was assessed by monocular stimulations using drifting sinusoidal gratings. The optimal relative phase using identical spatial frequencies in both eyes was first determined. Spatial frequency differences were then introduced by keeping the optimal spatial frequency constant in one eye and varying the spatial frequency in the other. Results indicate that cells (39%) responded with an increased firing rate (facilitation) to similar spatial frequencies in each eye and with a gradual attenuation (occlusion or suppression) when spatial frequency differences were increased. However, binocular facilitation did not always occur to the presentation of identical stimuli. For 16% of the cells, maximal responses were observed when lower spatial frequencies than the optimal one were presented in one eye while higher spatial frequencies produced suppression. The opposite pattern was observed only for two cells. These findings are discussed in terms of binocular fusion and suppression.

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.

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.