Anti-correlated Random-dot Stereograms Research Articles

EEG response in humans for frequency-tagged anticorrelated random-dot stereograms: Increased coherency and alpha oscillations.

In humans, the presence of a neural mechanism triggered by anticorrelated random-dot stereograms have been theorized based on animal models from invasive studies, but have not been experimentally verified with the use of electroencephalography. In this study, we employed a phase-consistent, temporally modulated alternating depth stereogram stimulus, where we created anticorrelation by inverting the contrast between the eyes. We recorded the electrical response of the resulting brain oscillations of our four participants using EEG in both the correlated and anticorrelated conditions and whether they perceived depth movement. Our analysis found that the correlated stereograms elicited a strong coherency at the even harmonics of the depth alternation, and the anticorrelated stimulus created lower coherency peaks at the first harmonic of the depth alternation, even when participants did not report the depth movement to be visible. While both conditions created a diminishment of spectral power in the beta band, we found that the anticorrelated condition created increased spectral power in the alpha band. We experimentally verified the presence of a neural mechanism triggered by anticorrelated random-dot stereograms in the human brain with our coherency analysis and that it would not have been detected with the conventional spectral analysis due to the weakness of the response. We hypothesize that the decreased beta oscillations are related to either visual discomfort and visual attention to our stimulus, and that the increased alpha oscillations in the anticorrelated condition is a response to the incorrect depth information created by the stereogram.

Relationship between the disparity tuning symmetry and responses to anti-correlated random dot stereograms in macaque areas V2, V3 and V3A

Relationship between the disparity tuning symmetry and responses to anti-correlated random dot stereograms in macaque areas V2, V3 and V3A

Neural representation of illusory reversed depth in anti-correlated random-dot stereograms across visual cortical areas in central and peripheral visual fields: An fMRI study

Neural representation of illusory reversed depth in anti-correlated random-dot stereograms across visual cortical areas in central and peripheral visual fields: An fMRI study

First- and second-order contributions to depth perception in anti-correlated random dot stereograms

The binocular energy model of neural responses predicts that depth from binocular disparity might be perceived in the reversed direction when the contrast of dots presented to one eye is reversed. While reversed-depth has been found using anti-correlated random-dot stereograms (ACRDS) the findings are inconsistent across studies. The mixed findings may be accounted for by the presence of a gap between the target and surround, or as a result of overlap of dots around the vertical edges of the stimuli. To test this, we assessed whether (1) the gap size (0, 19.2 or 38.4 arc min) (2) the correlation of dots or (3) the border orientation (circular target, or horizontal or vertical edge) affected the perception of depth. Reversed-depth from ACRDS (circular no-gap condition) was seen by a minority of participants, but this effect reduced as the gap size increased. Depth was mostly perceived in the correct direction for ACRDS edge stimuli, with the effect increasing with the gap size. The inconsistency across conditions can be accounted for by the relative reliability of first- and second-order depth detection mechanisms, and the coarse spatial resolution of the latter.

The effect of edge separation and orientation on the perception of depth in anti-correlated random dot stereograms

The effect of edge separation and orientation on the perception of depth in anti-correlated random dot stereograms

Reversed Depth in Anticorrelated Random-Dot Stereograms and the Central-Peripheral Difference in Visual Inference.

In a random-dot stereogram, the percept of object surfaces in a three-dimensional scene is generated by images presented to left and right eyes that comprise interocularly corresponding random black and white dots. The spatial disparities between the corresponding dots determine the depths of object surfaces. If the dots are anticorrelated, such that a black dot in one monocular image corresponds to a white dot in the other, disparity-tuned neurons in the primary visual cortex (V1) respond as if their preferred disparities become nonpreferred and vice versa, thereby reversing the disparity signs reported to higher visual areas. Typically, when viewing anticorrelated random-dot stereograms presented in the central visual field, humans have great difficulty perceiving the reversed depth or indeed any coherent depth at all. We report that the reversed depth is more easily perceived in the peripheral visual field, supporting a recently proposed central-peripheral dichotomy in the way that feedback from higher to lower visual cortical areas implements visual inference.

A relative frame of reference underlies reversed depth perception in anticorrelated random-dot stereograms.

Binocular disparity is represented by interocular cross-correlation of visual images in the striate and some extrastriate cortices. This correlation-based representation produces reversed depth perception in a binocularly anticorrelated random-dot stereogram (aRDS) when it is accompanied by an adjacent correlated RDS (cRDS). Removal of the cRDS or spatial separation between the aRDS and cRDS abolishes reversed depth perception. However, how an immediate plane supports reversed depth perception is unclear. One possible explanation is that the correlation-based representation generates reversed depth based on the relative disparity between the aRDS and cRDS rather than the absolute disparity of the aRDS. Here, we psychophysically tested this hypothesis. We found that participants perceived reversed depth in an aRDS with zero absolute disparity when it was surrounded by a cRDS with nonzero absolute disparity (i.e., nonzero relative disparity), suggesting a role of relative disparity on the depth reversal. In addition, manipulation of the absolute disparities of the central aRDS and surrounding cRDS caused depth perception to reverse with respect to the depth of the surround. Further, depth reversal persisted after swapping the locations of the two RDSs. A model of relative-disparity encoding explains all these results. We conclude that reversed depth perception in aRDSs occurs in a relative frame of reference and suggest that the visual system contains correlation-based representation that encodes relative disparity.

Cross-matching: a modified cross-correlation underlying threshold energy model and match-based depth perception

Three-dimensional visual perception requires correct matching of images projected to the left and right eyes. The matching process is faced with an ambiguity: part of one eye's image can be matched to multiple parts of the other eye's image. This stereo correspondence problem is complicated for random-dot stereograms (RDSs), because dots with an identical appearance produce numerous potential matches. Despite such complexity, human subjects can perceive a coherent depth structure. A coherent solution to the correspondence problem does not exist for anticorrelated RDSs (aRDSs), in which luminance contrast is reversed in one eye. Neurons in the visual cortex reduce disparity selectivity for aRDSs progressively along the visual processing hierarchy. A disparity-energy model followed by threshold nonlinearity (threshold energy model) can account for this reduction, providing a possible mechanism for the neural matching process. However, the essential computation underlying the threshold energy model is not clear. Here, we propose that a nonlinear modification of cross-correlation, which we term “cross-matching,” represents the essence of the threshold energy model. We placed half-wave rectification within the cross-correlation of the left-eye and right-eye images. The disparity tuning derived from cross-matching was attenuated for aRDSs. We simulated a psychometric curve as a function of graded anticorrelation (graded mixture of aRDS and normal RDS); this simulated curve reproduced the match-based psychometric function observed in human near/far discrimination. The dot density was 25% for both simulation and observation. We predicted that as the dot density increased, the performance for aRDSs should decrease below chance (i.e., reversed depth), and the level of anticorrelation that nullifies depth perception should also decrease. We suggest that cross-matching serves as a simple computation underlying the match-based disparity signals in stereoscopic depth perception.

Depth Perception Not Found in Human Observers for Static or Dynamic Anti-Correlated Random Dot Stereograms

One of the greatest challenges in visual neuroscience is that of linking neural activity with perceptual experience. In the case of binocular depth perception, important insights have been achieved through comparing neural responses and the perception of depth, for carefully selected stimuli. One of the most important types of stimulus that has been used here is the anti-correlated random dot stereogram (ACRDS). In these stimuli, the contrast polarity of one half of a stereoscopic image is reversed. While neurons in cortical area V1 respond reliably to the binocular disparities in ACRDS, they do not create a sensation of depth. This discrepancy has been used to argue that depth perception must rely on neural activity elsewhere in the brain. Currently, the psychophysical results on which this argument rests are not clear-cut. While it is generally assumed that ACRDS do not support the perception of depth, some studies have reported that some people, some of the time, perceive depth in some types of these stimuli. Given the importance of these results for understanding the neural correlates of stereopsis, we studied depth perception in ACRDS using a large number of observers, in order to provide an unambiguous conclusion about the extent to which these stimuli support the perception of depth. We presented observers with random dot stereograms in which correlated dots were presented in a surrounding annulus and correlated or anti-correlated dots were presented in a central circular region. While observers could reliably report the depth of the central region for correlated stimuli, we found no evidence for depth perception in static or dynamic anti-correlated stimuli. Confidence ratings for stereoscopic perception were uniformly low for anti-correlated stimuli, but showed normal variation with disparity for correlated stimuli. These results establish that the inability of observers to perceive depth in ACRDS is a robust phenomenon.

Matching and correlation computations in stereoscopic depth perception

A fundamental task of the visual system is to infer depth by using binocular disparity. To encode binocular disparity, the visual cortex performs two distinct computations: one detects matched patterns in paired images (matching computation); the other constructs the cross-correlation between the images (correlation computation). How the two computations are used in stereoscopic perception is unclear. We dissociated their contributions in near/far discrimination by varying the magnitude of the disparity across separate sessions. For small disparity (0.03°), subjects performed at chance level to a binocularly opposite-contrast (anti-correlated) random-dot stereogram (RDS) but improved their performance with the proportion of contrast-matched (correlated) dots. For large disparity (0.48°), the direction of perceived depth reversed with an anti-correlated RDS relative to that for a correlated one. Neither reversed nor normal depth was perceived when anti-correlation was applied to half of the dots. We explain the decision process as a weighted average of the two computations, with the relative weight of the correlation computation increasing with the disparity magnitude. We conclude that matching computation dominates fine depth perception, while both computations contribute to coarser depth perception. Thus, stereoscopic depth perception recruits different computations depending on the disparity magnitude.

No evidence for the perception of depth in anticorrelated random dot stereograms in a large number of observers

No evidence for the perception of depth in anticorrelated random dot stereograms in a large number of observers

Responses of disparity-sensitive V3/V3A neurons to anti-correlated random-dot stereograms

Responses of disparity-sensitive V3/V3A neurons to anti-correlated random-dot stereograms

Reduced binocular disparity selectivity of V4 neurons to anti-correlated random-dot stereograms

Reduced binocular disparity selectivity of V4 neurons to anti-correlated random-dot stereograms

Responses of disparity selective neurons in V3/V3A to anti-correlated random-dot stereograms

Oftentimes, objects are only partially and transiently visible as parts of them become occluded during observer or object motion. The visual system can integrate such object fragments across space and time into perceptual wholes or spatiotemporal objects. This integrative and dynamic process may involve both ventral and dorsal visual processing pathways, along which shape and spatial representations are thought to arise. We measured fMRI BOLD response to spatiotemporal objects and used multi-voxel pattern analysis (MVPA) to decode shape information across 20 topographic regions of visual cortex. Object identity could be decoded throughout visual cortex, including intermediate (V3A, V3B, hV4, LO1–2,) and dorsal (TO1–2, and IPS0–1) visual areas. Shape-specific information, therefore, may not be limited to early and ventral visual areas, particularly when it is dynamic and must be integrated. Contrary to the classic view that the representation of objects is the purview of the ventral stream, intermediate and dorsal areas may play a distinct and critical role in the construction of object representations across space and time.

Spatial Frequency Integration for Binocular Correspondence in Macaque Area V4

Neurons in the primary visual cortex (V1) detect binocular disparity by computing the local disparity energy of stereo images. The representation of binocular disparity in V1 contradicts the global correspondence when the image is binocularly anticorrelated. To solve the stereo correspondence problem, this rudimentary representation of stereoscopic depth needs to be further processed in the extrastriate cortex. Integrating signals over multiple spatial frequency channels is one possible mechanism supported by theoretical and psychophysical studies. We examined selectivities of single V4 neurons for both binocular disparity and spatial frequency in two awake, fixating monkeys. Disparity tuning was examined with a binocularly correlated random-dot stereogram (RDS) as well as its anticorrelated counterpart, whereas spatial frequency tuning was examined with a sine wave grating or a narrowband noise. Neurons with broader spatial frequency tuning exhibited more attenuated disparity tuning for the anticorrelated RDS. Additional rectification at the output of the energy model does not likely account for this attenuation because the degree of attenuation does not differ among the various types of disparity-tuned neurons. The results suggest that disparity energy signals are integrated across spatial frequency channels for generating a representation of stereoscopic depth in V4.

Depth Perception with Opposite Contrast, Multiple-Match Stereograms.

Neurons that modulate their firing rate in response to binocular disparity have been observed in many visual cortical areas and are thought to form the neural substrate of stereopsis. V1 neurons which show disparity selectivity for random-dot stereograms (RDS), also modulate their firing rate in response to disparity changes in anti-correlated RDS. Disparity-tuning is often inverted as predicted by binocular energy models. However, the way that image correlation affects our perception of stereo depth is unclear, because anti-correlated stimuli give rise to either weak or no perception of depth. To gain further insight into the relation between activation of binocular cells in V1 and depth perception, we employed the Panum's limiting case (PLC) surface invented by Braddick. Here a horizontal dot pair in one eye matches a single dot in the other. One sees a pair of transparent surfaces with a depth difference proportional to the separation in the monocular pair. In the variant employed here, one element of the monocular pair has reversed constrast (e.g. black). We find that this gives rise to a reversal of depth sign of the reverse-contrast dots. Observers reported whether the reverse-contrast (black) dots were near, far, or unclear (the matching white dot surface appeared in the fixation plane). Tests were conducted with dynamic dots in 2 s trials. The results show a clear reversal of depth for the opposite-contrast dots. However, there are two important observations: 1. The depth of the opposite contrast dots did not vary with dot offset; and 2. The dots appear to form an amorphous cloud rather than a surface. Both observations contrast with same-contrast PLC-RDS results. We postulate that under these conditions the post-V1 mechanisms that integrate and reconcile the outputs of V1 disparity mechanisms fail. Hence our inability to see a coherent surface or quantitative depth. Our perception corresponds qualitatively (up to depth sign) to the incoherent output of V1 disparity cells.

Unconscious adaptation: a new illusion of depth induced by stimulus features without depth

Here, we show a new illusion of depth induced by psychophysical adaptation to dynamic random-dot stereograms (RDS) that are interocularly anticorrelated (i.e., in which the images for the two eyes have reversed contrast polarity with each other). After prolonged viewing of anticorrelated RDS, the presentation of uncorrelated RDS (i.e., in which two images are mutually independent random-dot patterns) produces the sensation of depth, although both anticorrelated and uncorrelated RDSs are perceptually rivalrous with no consistent depth by themselves. Contrary to other aftereffects demonstrated in a number of visual dimensions, including motion, orientation, and disparity, this illusion results from unconscious adaptation; observers are not aware of what they are being adapted to during the process of adaptation. We further demonstrate that this illusion can be predicted from the simulated responses of disparity-selective neurons based on a local filtering model. Model simulations indicate that the inspection of anticorrelated RDS causes the adaptation of all disparity detectors except one sensitive to its disparity; therefore, those selectively unadapted detectors show relatively strong activation in response to the subsequent presentation of uncorrelated RDS and produce depth perception.

At Least at the Level of Inferior Temporal Cortex, the Stereo Correspondence Problem Is Solved

Stereoscopic vision requires the correspondence problem to be solved, i.e., discarding “false” matches between images of the two eyes, while keeping correct ones. To advance our understanding of the underlying neuronal mechanisms, we compared single neuron responses to correlated and anticorrelated random dot stereograms (RDSs). Inferior temporal neurons, which respond selectively to disparity-defined three-dimensional shapes, showed robust selectivity for correlated RDSs portraying concave or convex surfaces, but unlike neurons in areas V1, MT/V5, and MST, were not selective for anticorrelated RDSs. These results show that the correspondence problem is solved at least in far extrastriate cortex, as it is in the monkey's perception.

Poor visibility of motion in depth is due to early motion averaging

Under a variety of conditions, motion in depth from binocular cues is harder to detect than lateral motion in the frontoparallel plane. This is surprising, as the nasal-temporal motion in the left eye associated with motion in depth is easily detectable, as is the nasal-temporal motion in the right eye. It is only when the two motions are combined in binocular viewing that detection can become difficult. We previously suggested that the visibility of motion-in-depth is low because early stereomotion detectors average left and right retinal motions. For motion in depth, a neural averaging process would produce a motion signal close to zero. Here we tested the averaging hypothesis further. Specifically we asked, could the reduced visibility observed in previous experiments be associated with depth and layout in the stimuli, rather than motion averaging? We used anti-correlated random dot stereograms to show that, despite no depth being perceived, it is still harder to detect motion when it is presented in opposite directions in the two eyes than when motion is presented in the same direction in the two eyes. This suggests that the motion in depth signal is lost due to early motion averaging, rather than due to the presence of noise from the perceived depth patterns in the stimulus.

Disparity detection in anticorrelated stereograms.

Recent physiological observations in which stimuli with opposite contrast signs in the two eyes have been used (anticorrelated stereograms) show that these stimuli evoke responses in primary visual cortex which are the reverse of responses to correlated stimuli. Psychophysical investigations reveal no such reversals: reversed-contrast bars with crossed disparities are seen in front of those with uncrossed disparities. For anticorrelated random-dot stereograms human subjects perceive no depth at all, except at low dot densities. However, these human studies were carried out with stimuli that differed in several ways from those used in physiological studies. We therefore reexamined psychophysical responses using stimuli similar to those used for physiological recordings. Our results confirm the previous findings: there is no evidence of a reversed depth sensation for bar stereograms (crossed disparities are never seen behind uncrossed disparities), and subjects are unable to detect depth in anticorrelated random-dot stereograms at the densities used for the physiological recordings. The discrepancy between the psychophysical data and the responses of single neurons in primary visual cortex suggests that further processing outside area V1 is necessary to provide the signals that produce the sensation of stereoscopic depth.