Paired and unpaired features can be equally effective in human depth perception

Monocular gap stereopsis in infants

In monocular gap stereopsis, one eye perceives a complete rectangular surface while the other eye perceives two small adjacent rectangular surfaces separated by a narrow vertical gap. Our visual system interprets the difference caused by the unmatched monocular images as a depth difference between two small rectangles. In a spontaneous visual preference study, it was asked whether participants aged 4 months responded to the depth effect generated by a monocular gap. Two experimental conditions were conducted. In one (large outer edge disparity condition), the monocular depth effect was twice as strong as in the other one (small outer edge disparity condition), according to the experimental research with adult participants conducted by Pianta and Gillam (2003, Vision Research, Vol. 43, pp. 1937-1950). In both conditions, it was tested whether the stimulus bearing monocular gap stereopsis was preferred over a comparison stimulus without depth. According to the results, the participants preferred looking at the stimulus with monocular stereopsis in the large outer edge disparity condition over doing so in the small outer edge disparity condition. Moreover, the difference between experimental conditions was significant; that is, the infants displayed a stronger spontaneous preference in the condition with the large outer edge disparity than in the condition with the small outer edge disparity. These findings provide evidence to suggest that infants aged 4 months are able to respond to monocular vertical gap information.

A motion-in-depth model based on inter-ocular velocity to estimate direction in depth

Perception of motion in depth is one of the most important visual functions for living in the three-dimensional world. Two binocular cues have been investigated for motion in depth: inter-ocular velocity difference (IOVD) and changing disparity (CD). IOVD provides direction information directly by comparing velocity signals from the two retinas. In this study, we propose for the first time a motion-in-depth model of IOVD that predicts motion-in-depth direction. The model is based on a psychophysical assumption that there are four channels tuned to different directions in depth (Journal of Physiology 235 (1973) 17-29). We modeled these channels by combining outputs of low-level motion detectors that are sensitive to left and right retinal stimulation. Using these channels, we constructed a model of motion in depth that successfully predicted a variety of psychophysical results including direction discrimination, perceived direction, spatial frequency tuning, effect of speed on rotation in depth, effect of lateral motion direction, and effect of binocular and temporal correlations.

The Stereoscopic Sliver: A Comparison of Duration Thresholds for Fully Stereoscopic and Unmatched Versions

Just as positional disparities of image features seen with both eyes provide depth information, the presence of an area visible to one eye but not the other within a binocularly viewed scene can indicate an occlusion at a depth discontinuity,. The close geometrical association between these two kinds of cues suggests they may both be exploited by stereopsis. To investigate this, we developed a novel binocular stimulus entirely lacking in classical disparity that contains an unmatched vertical sliver which elicits a warping of the surrounding surface to accommodate a depth discontinuity. We measured depth-discrimination performance at a range of stimulus durations, correcting for variations in stimulus visibility, to characterise the decline of the efficacy of the depth signal with limited integration time. Results show a close correspondence of performance for similar stimuli with unmatched features and classical binocular disparity across a sixtyfold range of viewing durations, supporting the notion of a close association between the two types of cues in human stereopsis. Control experiments excluded simple eye-of-origin cues and long-range false matches as explanatory factors.

Temporal integration property of stereopsis after higher-order aberration correction

Based on a binocular adaptive optics visual simulator, we investigated the effect of higher-order aberration correction on the temporal integration property of stereopsis. Stereo threshold for line stimuli, viewed in 550nm monochromatic light, was measured as a function of exposure duration, with higher-order aberrations uncorrected, binocularly corrected or monocularly corrected. Under all optical conditions, stereo threshold decreased with increasing exposure duration until a steady-state threshold was reached. The critical duration was determined by a quadratic summation model and the high goodness of fit suggested this model was reasonable. For normal subjects, the slope for stereo threshold versus exposure duration was about -0.5 on logarithmic coordinates, and the critical duration was about 200 ms. Both the slope and the critical duration were independent of the optical condition of the eye, showing no significant effect of higher-order aberration correction on the temporal integration property of stereopsis.

Electrophysiological correlates of binocular stereo depth without binocular disparities

A small region of background presented to only one eye in an otherwise binocular display may, under certain conditions, be resolved in the visual system by interpreting the region as a small gap between two similar objects placed at different depths, with the gap hidden in one eye by parallax. This has been called monocular gap stereopsis. We investigated the electrophysiological correlate of this type of stereopsis by means of sum potential recordings in 12 observers, comparing VEP's for this stimulus ("Gillam Stereo", Author BG has strong reservations about this term) with those for similar stimuli containing disparity based depth and with no depth (flat). In addition we included several control stimuli. The results show a pronounced early negative potential at a latency of around 170 ms (N170) for all stimuli containing non- identical elements, be they a difference caused by binocular disparity or by completely unmatched monocular contours. A second negative potential with latency around 270 ms (N270), on the other hand, is present only with stimuli leading to fusion and the perception of depth. This second component is similar for disparity-based stereopsis and monocular gap, or "Gillam Stereo" although slightly more pronounced for the former. We conjecture that the first component is related to the detection of differences between the images of the two eyes that may then either be fused, leading to stereopsis and the corresponding second potential, or else to inhibition and rivalry without a later trace in the VEP. The finding that that "Gillam Stereo" leads to cortical responses at the same short latencies as disparity based stereopsis indicates that it may partly rely on quite early cortical mechanisms.

The role of transparency in da Vinci stereopsis

The majority of natural scenes contains zones that are visible to one eye only. Past studies have shown that these monocular regions can be seen at a precise depth even though there are no binocular disparities that uniquely constrain their locations in depth. In the so-called da Vinci stereopsis configuration, the monocular region is a vertical line placed next to a binocular rectangular occluder. The opacity of the occluder has been mentioned to be a necessary condition to obtain da Vinci stereopsis. However, this opacity constraint has never been empirically tested. In the present study, we tested whether da Vinci stereopsis and perceptual transparency can interact using a classical da Vinci configuration in which the opacity of the occluder varied. We used two different monocular objects: a line and a disk. We found no effect of the opacity of the occluder on the perceived depth of the monocular object. A careful analysis of the distribution of perceived depth revealed that the monocular object was perceived at a depth that increased with the distance between the object and the occluder. The analysis of the skewness of the distributions was not consistent with a double fusion explanation, favoring an implication of occlusion geometry in da Vinci stereopsis. A simple model that includes the geometry of the scene could account for the results. In summary, the mechanism responsible to locate monocular regions in depth is not sensitive to the material properties of objects, suggesting that da Vinci stereopsis is solved at relatively early stages of disparity processing.

Transfer of perceptual learning of depth discrimination between local and global stereograms

Several previous studies reported differences when stereothresholds are assessed with local-contour stereograms vs. complex random-dot stereograms (RDSs). Dissimilar thresholds may be due to differences in the properties of the stereograms (e.g. spatial frequency content, contrast, inter-element separation, area) or to different underlying processing mechanisms. This study examined the transfer of perceptual learning of depth discrimination between local and global RDSs with similar properties, and vice versa. If global and local stereograms are processed by separate neural mechanisms, then the magnitude and rate of training for the two types of stimuli are likely to differ, and the transfer of training from one stimulus type to the other should be minimal. Based on previous results, we chose RDSs with element densities of 0.17% and 28.3% to serve as the local and global stereograms, respectively. Fourteen inexperienced subjects with normal binocular vision were randomly assigned to either a local- or global- RDS training group. Stereothresholds for both stimulus types were measured before and after 7700 training trials distributed over 10 sessions. Stereothresholds for the trained condition improve for approximately 3000 trials, by an average of 0.36+/-0.08 for local and 0.29+/-0.10 for global RDSs, and level off thereafter. Neither the rate nor the magnitude of improvement differ statistically between the local- and global-training groups. Further, no significant difference exists in the amount of improvement on the trained vs. the untrained targets for either training group. These results are consistent with the operation of a single mechanism to process both local and global stereograms.

The role of monocularly visible regions in depth and surface perception

The mainstream of binocular vision research has long been focused on understanding how binocular disparity is used for depth perception. In recent years, researchers have begun to explore how monocular regions in binocularly viewed scenes contribute to our perception of the three-dimensional world. Here we review the field as it currently stands, with a focus on understanding the extent to which the role of monocular regions in depth perception can be understood using extant theories of binocular vision.

Binocular spatial induction for the perception of depth does not cross the midline

Although horizontal binocular retinal disparity between images in the two eyes resulting from their different views of the world has long been the centerpiece for understanding the unique characteristics of stereovision, it does not suffice to explain many binocular phenomena. Binocular depth contrast (BDC), the induction of an appearance of visual pitch in a centrally located line by pitched-from-vertical flanking lines, has particularly been the subject of a good deal of attention in this regard. In the present article, we show that BDC does not cross the median plane but is restricted to the side of the visual field containing a unilateral inducer. These results cannot be explained by the use of retinal disparity alone or in combination with any additional factors or processes previously suggested to account for stereovision. We present a two-channel three-stage neuromathematical model that accounts quantitatively for present and previous BDC results and also accounts for a large number of the most prominent features of binocular pitch perception: Stage 1 of the differencing channel obtains the difference between the retinal orientations of the images in the two eyes separately for the inducer and the test line; stage 1 of the summing channel obtains the corresponding sums. Signals from inducer and test stimuli are combined linearly in each channel in stage 2, and in stage 3 the outputs from the two channels are combined along with a bias signal from the body-referenced mechanism to yield ', the model's prediction for the perception of pitch.

Globally consistent depth sorting of overlapping 2D surfaces in a model using local recurrent interactions

The human visual system utilizes depth information as a major cue to group together visual items constituting an object and to segregate them from items belonging to other objects in the visual scene. Depth information can be inferred from a variety of different visual cues, such as disparity, occlusions and perspective. Many of these cues provide only local and relative information about the depth of objects. For example, at occlusions, T-junctions indicate the local relative depth precedence of surface patches. However, in order to obtain a globally consistent interpretation of the depth relations between the surfaces and objects in a visual scene, a mechanism is necessary that globally propagates such local and relative information. We present a computational framework in which depth information derived from T-junctions is propagated along surface contours using local recurrent interactions between neighboring neurons. We demonstrate that within this framework a globally consistent depth sorting of overlapping surfaces can be obtained on the basis of local interactions. Unlike previous approaches in which locally restricted cell interactions could merely distinguish between two depths (figure and ground), our model can also represent several intermediate depth positions. Our approach is an extension of a previous model of recurrent V1-V2 interaction for contour processing and illusory contour formation. Based on the contour representation created by this model, a recursive scheme of local interactions subsequently achieves a globally consistent depth sorting of several overlapping surfaces. Within this framework, the induction of illusory contours by the model of recurrent V1-V2 interaction gives rise to the figure-ground segmentation of illusory figures such as a Kanizsa square.

Depth from binocular half-occlusions in stereoscopic images of natural scenes

Over the past two decades psychophysical experiments have firmly established that binocular half-occlusions are useful sources of information for the human visual system. The existing literature has focused on simplified stimuli that have no additional cues to depth, apart from stereopsis. From this large body of work we can be confident that the visual system is able to exploit binocular half-occlusions to aid depth perception; however, we do not know if this signal has any influence on perception when observers view complex stereoscopic stimuli with multiple sources of depth information. This issue is addressed here with the use of stereoscopic images of natural scenes, some of which have been digitally altered to manipulate a major half-occlusion signal. Our results show that depth-ordering judgments for these relatively complex stimuli are significantly affected by the nature of the half-occlusion signal, but only when highly textured surfaces are viewed. Under such conditions, the replacement of a binocular half-occlusion with background texture slows reaction time relative to performance when the occluded region is consistent with the foreground object. This result is specific to conditions when the depth ordering is correct (ie not reversed) and depends upon the size of the half-occlusion. The influence of the half-occlusion information in the presence of potent depth cues such as perspective, texture gradient, shading, and interposition is convincing evidence that this information plays a significant role in human depth perception.

The role of binocular stereopsis in monoptic depth perception

In his study of depth from monocular elements, Kaye (1978) [Kaye, M. (1978). Stereopsis without binocular correlation. Vision Research, 18(8), 1013-1022] reported that monocular stimuli, briefly presented to one eye in a stereoscopic display, generated reliable depth percepts. Here we replicate and extend Kaye's findings in an effort to identify the mechanism underlying the phenomenon. Our experiments show that the perception of depth is not a simple result of monocular local sign, for the percept of depth disappears when one eye is patched. In subsequent experiments we assess the possibility that the percept results from a very coarse stereoscopic match to either the centroid of the luminance distribution in the unstimulated eye or a simple match to the line of sight in the unstimulated eye. Our results consistently support the match-to-fovea account, and lead us to conclude that monoptic depth is a stereoscopic phenomenon.

Amodal completion with background determines depth from monocular gap stereopsis

Grove, Gillam, and Ono [Grove, P. M., Gillam, B. J., & Ono, H. (2002). Content and context of monocular regions determine perceived depth in random dot, unpaired background and phantom stereograms. Vision Research, 42, 1859-1870] reported that perceived depth in monocular gap stereograms [Gillam, B. J., Blackburn, S., & Nakayama, K. (1999). Stereopsis based on monocular gaps: Metrical encoding of depth and slant without matching contours. Vision Research, 39, 493-502] was attenuated when the color/texture in the monocular gap did not match the background. It appears that continuation of the gap with the background constitutes an important component of the stimulus conditions that allow a monocular gap in an otherwise binocular surface to be responded to as a depth step. In this report we tested this view using the conventional monocular gap stimulus of two identical grey rectangles separated by a gap in one eye but abutting to form a solid grey rectangle in the other. We compared depth seen at the gap for this stimulus with stimuli that were identical except for two additional small black squares placed at the ends of the gap. If the squares were placed stereoscopically behind the rectangle/gap configuration (appearing on the background) they interfered with the perceived depth at the gap. However when they were placed in front of the configuration this attenuation disappeared. The gap and the background were able under these conditions to complete amodally.

Monocular transparency and unpaired stereopsis

Howard and Duke [Howard, I. P. & Duke, P. A. (2003). Monocular transparency generates quantitative depth. Vision Research, 43, 2615-2621] recently proposed a new source of binocular information they claim is used to recover depth in stereoscopic displays. They argued that these displays lack conventional disparity and that the metrical depth experienced results from transparency rather than occlusion relations. Using a variety of modified versions of their stimuli, we show here that the conditions for transparency are not required to elicit the depth experienced in their stereograms. We demonstrate that quantitative and precise depth depended not on the presence of transparency but horizontal contours of the same contrast polarity. Depth was attenuated, particularly at larger target offsets, when horizontal contours had opposite contrast polarity for at least a portion of their length. We also show that a demonstration they used to control for the role of horizontal contours can be understood with previously identified mechanisms involved in the computations associated with stereoscopic occlusion. These results imply that the findings reported by Howard and Duke can be understood with mechanisms responsible for the computation of binocular disparity and stereoscopic occlusion.

Monocular transparency and unpaired stereopsis

Howard and Duke [Howard, I. P. & Duke, P. A. (2003). Monocular transparency generates quantitative depth. Vision Research, 43, 2615-2621] recently proposed a new source of binocular information they claim is used to recover depth in stereoscopic displays. They argued that these displays lack conventional disparity and that the metrical depth experienced results from transparency rather than occlusion relations. Using a variety of modified versions of their stimuli, we show here that the conditions for transparency are not required to elicit the depth experienced in their stereograms. We demonstrate that quantitative and precise depth depended not on the presence of transparency but horizontal contours of the same contrast polarity. Depth was attenuated, particularly at larger target offsets, when horizontal contours had opposite contrast polarity for at least a portion of their length. We also show that a demonstration they used to control for the role of horizontal contours can be understood with previously identified mechanisms involved in the computations associated with stereoscopic occlusion. These results imply that the findings reported by Howard and Duke can be understood with mechanisms responsible for the computation of binocular disparity and stereoscopic occlusion.

Pictorial cues constrain depth in da Vinci stereopsis

"da Vinci stereopsis" is defined as depth seen in a monocular object occluded by a binocular one, and the visual system must solve its depth ambiguity [Nakayama, K., & Shimojo, S. (1990). da Vinci stereopsis: Depth and subjective occluding contours from unpaired image points. Vision Research, 30, 1811-1825]. Although fused images include various pictorial features, effects of pictorial depth cues have never been systematically investigated in da Vinci stereopsis. To examine this, we created stereograms consisting of a monocular bar flanked by binocular bars with a fixed large horizontal separation, in which the monocular bar induced a subjective occluding edge. Manipulating vertical size or contrast of the bars could affect the depth of the monocular bar. Conflicting these cues revealed that the effect of vertical size was stronger than that of contrast in all our subjects. Measurements of the depth indicated that the relative vertical size of the bars quantitatively determined the perceived depth, of which levels had large inter-subject differences. All these experiments indicate that the visual system can use the pictorial depth cues as a constraint to determine the depth of monocular elements.

Evidence for the correcting-mechanism explanation of the Kanizsa amodal shrinkage

An object phenomenally shrinks in its horizontal dimension when shown on a 2-D plane as if the central portion of the object were partially occluded by another vertical one in 3-D space (the Kanizsa amodal shrinkage). We examined the predictions of the correcting-mechanism hypothesis proposed by Ohtsuka and Ono (2002, Proceedings of SPIE 4864 167-174), which states that an inappropriate operation of the mechanism that corrects a phenomenal increase in monocularly visible areas accompanied by a stereoscopic occluder gives rise to the illusion. In this study we measured the perceived width (or height in experiment 3) of a square seen behind a rectangle, while controlling other factors which potentially influence the illusion, such as the division of space or depth stratification. The results of five experiments showed that (a) the perceived width was not influenced when the occluder had a relatively large binocular disparity, but was underestimated when the occluder did not have disparity, and (b) the shrinkage diminished when the foreground rectangle was transparent, was horizontally oriented, or contained no pictorial occlusion cues. These results support the hypothesis that the correcting mechanism, triggered by pictorial occlusion cues, contributes to the Kanizsa shrinkage.

Greater depth seen with phantom stereopsis is coded at the early stages of visual processing

A visual search task was used to investigate the spatially parallel coding of depth from binocular disparity and from binocularly unmatched features. Experiment 1, using disparity noise, showed that detectability is higher for illusory phantom targets defined by unmatched features than for disparity-defined targets, although the two targets were equated as to theoretically minimum depth. Experiment 2, using binocularly unmatched noise whose width was equal to the disparity of the noise used in Experiment 1, showed that noise severely interferes with the detection of both the disparity and the phantom targets. These results are consistent with the idea that the greater depth seen with phantom stereopsis is coded at the early stages of visual processing.

Monocular gap stereopsis: manipulation of the outer edge disparity and the shape of the gap

A binocular stimulus that arises when two black frontal plane surfaces located at different depths have a gap between them for one eye but not for the other eye is interesting since the gap is monocular--it has no matching contours in the other eye--and yet binocular processes resolve a depth step effortlessly (Vision Research, 39, 493). In two experiments we investigate the processes and constraints underlying this depth resolution by varying the width of the solid image (the one without the gap) and the shape of the gap. The results show that the processes underlying monocular gap stereopsis can handle a situation in which the images of two surfaces in depth are effectively overlapping for one eye's view with the other eye seeing between them and that binocular depth is seen even when there is no disparity present. We also show that under ecologically appropriate conditions, depth curvature and warping can result when the monocular gap has a curved or warped edge. Both these experiments imply that the visual system responds to the ambiguity of the stimulus by adopting a minimum slant constraint.