Depth inversion despite stereopsis: the appearance of random-dot stereograms on surfaces seen in reverse perspective.

Inside-out relief masks of faces can be depth-inverted (i.e. seen in reverse perspective) during close-up binocular viewing. If a random-dot stereogram is projected onto such a mask, stereopsis can be achieved for the stereogram, and its depth planes are correctly seen while the mask itself, including the region covered by the stereogram, is simultaneously perceived as depth-inverted. This demonstration shows that binocular depth inversion cannot be explained by a complete loss of stereoscopic information (e.g. through monocular suppression), or by a process analogous to pseudoscopic viewing whereby retinal disparities are incorporated into perception, but with their signs uniformly reversed.     

Learning to see random-dot stereograms.

In the present study some specific properties of the learning effects reported for random-dot stereograms are examined. In experiment 1 the retinal position-specific learning effect was reproduced and in a follow-up experiment it was shown that the position specificity of learning can be accounted for by selective visual attention. In experiments 2 and 3 evidence was obtained that suggests that observers can learn, to a certain degree, monocular random-dot patterns and that this learning facilitates the depth percept. This result indicates that the traditional belief that random-dot stereograms are devoid of monocularly recognizable or useful forms should be reconsidered. In the second set of experiments the learning of two binocular surface properties of random-dot stereograms, depth edges and internal depth regions, was investigated. It was shown in experiment 4 that the depth edges of random-dot stereograms are not learned, whereas the results of experiment 5 indicate that the internal depth regions are learned. Finally, in experiment 6 it was shown that depth edges are learned when the internal depth regions of the stereogram are ambiguous. The results are discussed in terms of the importance of the particular type of stimulus used in the learning process and in terms of perceptual learning and attention.     

Patent stereopsis with diplopia in random-dot stereograms

Fusional limits for an RD (random-dot) stereogram with overall horizontal retinal disparity due to the temporalward pulling of its two constituent RD patterns beyond the divergence limits of the eyes have been determined by using an afterimage method. Two criteria for fusion were used, viz, the perception ofsingle local RD elements and the perception of stereoscopic depth in the “hidden” square of side 1.38 deg with 8-min relative horizontal disparity. The diplopia thresholds were found to be in the range of 0.15–0.3 deg, and hence do not exceed the “classical” upper limit of about 0.3 deg, which has been reported for elementary line stereograms. The stereoscopic limits were found to be in the range of 0.5–1.3 deg, which is compatible with the precision of patent stereopsis from double images which has been reported for elementary line stereograms. The results of the present third look at the experiments performed by Fender and Julesz (1967) suggest that there are no special neuronal processes raising the fusional limits for RD stereograms above those for elementary line stereograms. Previous claims that such special neuronal processes may occur seem to be based on an evaluation of fusional limits obtained with different criteria for fusion. It is further argued that the major hysteresis effect that has been observed for fusional limits for RD stereograms should not be ascribed to a raising of the classical size of the diplopia threshold due to special neuronal processes initiated by RD stereograms, but to a lowering of the classical limits of patent stereopsis from double images due to the increased difficulty of solving the correspondence problem in RD stereograms.     

Hysteresis,cooperativity, and depth averaging in dynamic random-dot stereograms

Experiments were performed to assess the response of the human visual system to dynamic random-dot patterns composed of disparity mixtures. In Experiment 1, the perceived depth and relative stability of two patterns were compared; one pattern depicted two transparent layers of dots, and the other depicted a volume of dots. Two effects were found: (1) the volume pattern exhibited a large degree of disparity averaging; and (2) asymmetries were observed in the relative stability of these two patterns. Experiment 2 was designed to determine whether these findings could be attributed to spatially localized processes occurring-at the location of disparity discontinuities. This was accomplished by introducing unpaired noise points localized either along the disparity discontinuities or in the center of the layered and volume patterns. The amount of depth averaging and the direction of the asymmetry did not appear to depend on processes localized along the disparity discontinuities. Results of these experiments, taken in conjunction with those of previous studies, suggest that hysteresis is independent of cooperative persistence mechanisms.     

Temporal properties of disparity processing revealed by dynamic random-dot stereograms

In studies of the temporal flexibility of the stereoscopic system, it has been suggested that two different processes of binocular depth perception could be responsible for the flexibility: tolerance for interocular delays and temporal integration of correlation. None has investigated the relationship between tolerance for delays and temporal integration mechanisms and none has revealed which mechanism is responsible for depth perception in dynamic random-dot stereograms. We address these questions in the present study. Across five experiments, we investigated the temporal properties of stereopsis by varying interocular correlation as a function of time in controlled ways. We presented different types of dynamic random-dot stereograms, each consisting of two pairs of alternating random-dot patterns. Our experimental results demonstrate that (i) disparities from simultaneous monocular inputs dominate those from interocular delayed inputs; (ii) stereopsis is limited by temporal properties of monocular luminance mechanisms; and (iii) depth perception in dynamic random-dot stereograms results from cross-correlation-like operation on two simultaneous monocular inputs that represent the retinal images after having been subjected to a process of monocular temporal integration of luminance.     

Ecologically invalid monocular texture leads to longer perceptual latencies in random-dot stereograms

Two experiments were conducted to explore Gillam and Borsting's (1988, Perception 17 603-608) report that uncorrelated monocular texture facilitates stereopsis by shortening the latency to see depth in random-dot stereograms. Experiment 1 used stereograms similar, in pattern but not disparity, to Gillam and Borsting's with monocular texture present or absent. A third condition, where monocular texture was dissimilar to the binocular panels and background, was also used. We were unable to generalize the findings of Gillam and Borsting for a depth step of 6 min of arc to a larger depth step of 24 min of arc. That is, we observed no significant difference in latencies between the conditions with monocular texture absent and present at a disparity of 24 min of arc. We found latencies to be significantly longer in the monocular-texture-different condition than the monocular-texture-absent condition, however. We account for this, ad hoc, by arguing that the monocular-texture-different stereogram depicts a rare or 'accidental' visual scenario. This account was supported by the results of experiment 2 which showed that stereograms depicting accidental views yielded longer latencies than those depicting generic views. We conclude that the ecological validity of monocular texture must also be considered when assessing the effects of monocular texture on stereopsis.     

Hysteresis, cooperativity, and depth averaging in dynamic random-dot stereograms.

Experiments were performed to assess the response of the human visual system to dynamic random-dot patterns composed of disparity mixtures. In Experiment 1, the perceived depth and relative stability of two patterns were compared; one pattern depicted two transparent layers of dots, and the other depicted a volume of dots. Two effects were found: (1) the volume pattern exhibited a large degree of disparity averaging; and (2) asymmetries were observed in the relative stability of these two patterns. Experiment 2 was designed to determine whether these findings could be attributed to spatially localized processes occurring at the location of disparity discontinuities. This was accomplished by introducing unpaired noise points localized either along the disparity discontinuities or in the center of the layered and volume patterns. The amount of depth averaging and the direction of the asymmetry did not appear to depend on processes localized along the disparity discontinuities. Results of these experiments, taken in conjunction with those of previous studies, suggest that hysteresis is independent of cooperative persistence mechanisms.     

The use of numerical and graphical statistical methods in the analysis of data on learning to see complex random-dot stereograms

Several numerical and graphical statistical methods are illustrated in an analysis of data from an experiment that investigated a hypothesis of Julesz that giving a person a priori information about the structure of a complex random-dot stereogram reduces the time needed to perceive it when it is viewed. The data are divided into two groups, one consisting of those observers who received no cue or verbal cues (NV) and the other consisting of those who received verbal-visual cues (VV). A quantile-quantile plot shows that the NV times (mean = 7.6) are longer than the VV times (mean =5.6). By using probability plots, it is shown that the perception times have an exponential probability distribution. A hypothesis test based upon this distribution is used to show that the difference between the NV and VV times has significance slightly below 0.05.     

Generation of random-dot stereogratings

Stereogratings are an extension of periodic stimulation to the Cyclopean domain. A program for the generation of random-dot stereogratings is described, with discussion of the advantages and disadvantages of the program.     

Depth of ankle inversion and discrimination of foot positions

Ankle inversion injuries are common, yet little is known about the error associated with different positions as inversion depth increases. In this study, absolute judgments made without feedback were used to measure discrimination of different extents of ankle inversion which arose from active movements made to physical stops by 20 self-reported right side-dominant participants. Testing was conducted over three sets of five inversion depths that were within a range of 1.4 degrees and centered around mean depths of 8,11, and 14 degrees. Discrimination of ankle inversion movements decreased linearly with depths of movement further into inversion, both within and across the sets of inversion depths. Thus, error in assessing movement position increased with inversion depth. Inversion movements that were made with the left foot were significantly better discriminated at all depths than those made with the right foot.     

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.     

Illusions prepared as stereograms

The loci of organization and the modes of operation of certain perceptual mechanisms may be determined by presenting appropriate stimuli independently to each eye in such a way that they become superimposed in stereoscopic vision. It is possible that understanding of the mechanisms responsible for the appearance of certain “geometrical illusions” may be furthered by adopting this procedure. The two functional components of a sample of illusions are distinguished and illustrated in the form of stereograms.     

Generation of internally restricted random-dot patterns

The probability of a successful draw of a dot position within a random dot pattern is considered for the special case where a minimal city block distance is imposed separating any two dots within the random pattern. An analytical solution is derived and is tested against Monte Carlo simulations. The agreement is considered to be good, except at extremely low probabilities of a successful draw. An alternative method, based upon the utilization of successively coarser grids, is also given. Formulas are also provided for circular and for diamond-shaped separation regions.     

Colour inputs to random-dot stereopsis.

Recently it has been claimed by Livingstone and Hubel that, of three anatomically and functionally distinct visual channels (the magnocellular, parvocellular interblob, and blob channels), only the magnocellular channel is involved in the processing of stereoscopic depth. Since the magnocellular system shows little overt colour opponency, the reported loss of the ability to resolve random-dot stereograms defined only by colour contrast seems consistent with this view. However, Julesz observed that reversed-contrast stereograms could be fused if correlated colour information was added. In the present study, 'noise' (non-corresponding) pixels were injected into random-dot stereograms in order to increase fusion time. All six subjects tested were able to achieve stereopsis in less than three minutes when there was only correspondence in colour and not in luminance, and three when luminance contrast was completely reversed. This ability depends on information about the direction of colour contrast, not just the presence of chromatic borders. When luminance and chromatic contrast are defined in terms of signal-to-noise ratios at the photoreceptor mosaic, chromatic information plays at least as important a role in stereopsis as does luminance information, suggesting that the magnocellular channel is not uniquely involved.     

The absence of depth constancy in contour stereograms

Stereoscopic surfaces constructed from Kanizsa-type illusory contours or explicit luminance contours were tested for three-dimensional (3-D) shape constancy. The curvature of the contours and the apparent viewing distance between the surface and the observer were manipulated. Observers judged which of two surfaces appeared more curved. Experiment 1 allowed eye movements and revealed a bias in 3-D shape judgment with changes in apparent viewing distance, such that surfaces presented far from the observer appeared less curved than surfaces presented close to the observer. The lack of depth constancy was approximately the same for illusory-contour surfaces and for explicit-contour surfaces. Experiment 2 showed that depth constancy for explicit-contour surfaces improved slightly when fixation was required and eye movements were restricted. These experiments suggest that curvature in depth is misperceived, and that illusory-contour surfaces are particularly sensitive to this distortion.