Rivalrous texture stereograms

Coarse-to-fine interaction on perceived depth in compound grating

To encode binocular disparity, the visual system uses a pair of left eye and right eye bandpass filters with either a position or a phase offset between them. Such pairs are considered to exit at multiple scales to encode a wide range of disparity. However, local disparity measurements by bandpass mechanisms can be ambiguous, particularly when the actual disparity is larger than a half-cycle of the preferred spatial frequency of the filter, which often occurs in fine scales. In this study, we investigated whether the visual system uses a coarse-to-fine interaction to resolve this ambiguity at finer scales for depth estimation from disparity. The stimuli were stereo grating patches composed of a target and comparison patterns. The target patterns contained spatial frequencies of 1 and 4 cycles per degree (cpd). The phase disparity of the low-frequency component was 0° (at the horopter), -90° (uncrossed), or 90° (crossed), and that of the high-frequency components was changed independent of the low-frequency disparity, in the range between -90° (uncrossed) and 90° (crossed). The observers' task was to indicate whether the target appeared closer to the comparison pattern, which always shared the disparity with the low-frequency component of the target. Regardless of whether the comparison pattern was a 1-cpd + 4-cpd compound or a 1-cpd simple grating, the perceived depth order of the target and the comparison varied in accordance with the phase disparity of the high-frequency component of the target. This effect occurred not only when the low-frequency component was at the horopter, but also when it contained a large disparity corresponding to one cycle of the high-frequency component (±90°). Our findings suggest a coarse-to-fine interaction in multiscale disparity processing, in which the depth interpretation of the high-frequency changes based on the disparity of the low-frequency component.

Binocular rivalry produced by temporal frequency differences

When the eyes view images that are sufficiently different to prevent binocular fusion, binocular rivalry occurs and the images are seen sequentially in a stochastic alternation. Here we examine whether temporal frequency differences will trigger binocular rivalry by presenting two dynamic random-pixel arrays that are spatially matched but which modulate temporally at two different rates. We found that binocular rivalry between the two temporal frequencies did indeed occur, provided the frequencies were sufficiently different. Differences greater than two octaves (i.e., a factor of four) produced robust rivalry with clear-cut alternations similar to those experienced with spatial rivalry and with similar alternation rates. This finding indicates that temporal information can produce binocular rivalry in the absence of spatial conflict and is discussed in terms of rivalry requiring conflict between temporal channels.

Stereoscopic Depth Perception during Binocular Rivalry

When we view nearby objects, we generate appreciably different retinal images in each eye. Despite this, the visual system can combine these different images to generate a unified view that is distinct from the perception generated from either eye alone (stereopsis). However, there are occasions when the images in the two eyes are too disparate to fuse. Instead, they alternate in perceptual dominance, with the image from one eye being completely excluded from awareness (binocular rivalry). It has been thought that binocular rivalry is the default outcome when binocular fusion is not possible. However, other studies have reported that stereopsis and binocular rivalry can coexist. The aim of this study was to address whether a monocular stimulus that is reported to be suppressed from awareness can continue to contribute to the perception of stereoscopic depth. Our results showed that stereoscopic depth perception was still evident when incompatible monocular images differing in spatial frequency, orientation, spatial phase, or direction of motion engage in binocular rivalry. These results demonstrate a range of conditions in which binocular rivalry and stereopsis can coexist.

The extraction of features and disparities from images by a model based on the neurological organisation of the visual system

A computational simulation of the early stages of mammalian visual processing, from the retina to the primary visual cortex, is described. The simulation uses elements that are organised according to the anatomical connections of the biological visual system. It explores how observed responses of simple cells of the primary visual cortex can be generated by a small number of stages of the types of processing that are observed in the nervous system. Edge features are extracted from single images and disparities between stereoscopic image pairs are detected with good reliability. An important parameter affecting processing was found to be the strength of the surround inhibition between the elements that represent neurones of the primary visual cortex.

Interaction between binocular rivalry and depth in plaid patterns

Binocular rivalry was studied using plaids which were the sum of orthogonal diagonal gratings plus identical vertical gratings in the two eyes. The rivalry alternations sped up as the spatial frequency difference between the vertical and diagonal gratings was increased above about one octave, but slowed down for smaller differences. The interaction between depth and rivalry was studied using similar plaids but with depth introduced in the vertical components. Depth and rivalry coexisted when the spatial frequency difference between the vertical and diagonal gratings was greater than about one octave, but rivalry slowed down and depth perception was reduced for smaller differences. Plaids consisting of square wave gratings were used to compare: (1) added gratings; (2) vertical gratings superimposed on (i.e. occluding) diagonal gratings; (3) diagonal gratings superimposed on vertical gratings. Rivalry alternations were fastest in condition (3), indicating that grouping effects played a role. The final experiment indicated that depth and rivalry coexisted within a spatial frequency band if the orientation difference between the vertical and diagonal components was 60-70 degrees . These results place constraints on models of stereopsis and rivalry, indicating that depth and rivalry can coexist in different spatial frequency and orientation bands but that each interferes with the other in the same band.

An integrative model of binocular vision: a stereo model utilizing interocularly unpaired points produces both depth and binocular rivalry

Half-occluded points (visible only in one eye) are perceived at a certain depth behind the occluding surface without binocular rivalry, even though no disparity is defined at such points. Here we propose a stereo model that reconstructs 3D structures not only from disparity information of interocularly paired points but also from unpaired points. Starting with an array of depth detection cells, we introduce cells that detect unpaired points visible only in the left eye or the right eye (left and right unpaired point detection cells). They interact cooperatively with each other based on optogeometrical constraints (such as uniqueness, cohesiveness, occlusion) to recover the depth and the border of 3D objects. Since it is contradictory for monocularly visible regions to be visible in both eyes, we introduce mutual inhibition between left and right unpaired point detection cells. When input images satisfy occlusion geometry, the model outputs the depth of unpaired points properly. An interesting finding is that when we input two unmatched images, the model shows an unstable output that alternates between interpretations of monocularly visible regions for the left and the right eyes, thereby reproducing binocular rivalry. The results suggest that binocular rivalry arises from the erroneous output of a stereo mechanism that estimates the depth of half-occluded unpaired points. In this sense, our model integrates stereopsis and binocular rivalry, which are usually treated separately, into a single framework of binocular vision. There are two general theories for what the "rivals" are during binocular rivalry: the two eyes, or representations of two stimulus patterns. We propose a new hypothesis that bridges these two conflicting hypotheses: interocular inhibition between representations of monocularly visible regions causes binocular rivalry. Unlike the traditional eye theory, the level of the interocular inhibition introduced here is after binocular convergence at the stage solving the correspondence problem, and thus open to pattern-specific mechanisms.

Differential binocular input and local stereopsis

Using fractal noise images, we measured the dependence of Dmin and Dmax for stereo on the interocular differences of spatial frequency and contrast. Dmin exhibits a strong dependence on the highest spatial frequency contained in the image, while Dmax exhibits a weaker dependence on the lowest spatial frequency contained within the image. Neither relationship was found to be different when the filtering was restricted to only one eye's image, although the effect of differential lowpass filtering for Dmin was greater than that of binocular lowpass filtering. Contrast is thought to affect stereo performance particularly when it is reduced in only one eye's image. We show that, at least for broadband fractal images representative of everyday natural images, interocular contrast differences are no more disruptive than binocular ones. These results bear upon the nature of the matching process in stereopsis. The fact that these interocular spatial frequency and contrast manipulations do not selectively degrade stereopsis beyond that expected from a consideration of purely monocular effects is consistent with matching occurring within multiple spatial channels prior to their combination.

Luminance spatial scale and local stereo-sensitivity

Using filtered, broad band, fractal noise images we measured the dependence of D(min) and D(max) for stereo on luminance spatial frequency. D(min) was found to exhibit a simple dependence on the highest spatial frequency contained in the stimulus. D(max) depended on both image size and spatial frequency in a way that suggests an informational limit. Different rules govern D(min) and D(max) even for first order stereopsis, arguing against a common neural explanation based on independent access to the most pertinent spatial filter.

Macaque inferior temporal neurons are selective for three-dimensional boundaries and surfaces

The lower bank of the superior temporal sulcus (TEs), part of the inferior temporal cortex, contains neurons selective for disparity-defined three-dimensional (3-D) shape. The large majority of these TEs neurons respond to the spatial variation of disparity, i.e., are higher-order disparity selective. To determine whether curved boundaries or curved surfaces by themselves are sufficient to elicit 3-D shape selectivity, we recorded the responses of single higher-order disparity-selective TEs neurons to concave and convex 3-D shapes in which the disparity varied either along the boundary of the shape, or only along its surface. For a majority of neurons, a 3-D boundary was sufficient for 3-D shape selectivity. At least as many neurons responded selectively to 3-D surfaces, and a number of neurons exhibited both surface and boundary selectivity. The second aim of this study was to determine whether TEs neurons can represent differences in second-order disparities along the horizontal axis. The results revealed that TEs neurons can also be selective for horizontal 3-D shapes and can code the direction of curvature (vertical or horizontal). Thus, TEs neurons represent both boundaries and surfaces curved in depth and can signal the direction of curvature along a surface. These results show that TEs neurons use not only boundary but also surface information to encode 3-D shape properties.

Luminance spatial scale facilitates stereoscopic depth segmentation

Are differences in luminance spatial frequency between surfaces that overlap in depth useful for surface segmentation? We examined this question, using a novel stimulus termed a dual-surface disparity grating. The dual-surface grating was made from Gabor micropatterns and consisted of two superimposed sinusoidal disparity gratings of identical disparity-modulation spatial frequency and orientation but of opposite spatial phase. Corrugation amplitude thresholds for discrimination of the orientation of the dual-surface grating were obtained as a function of the difference in Gabor (luminance) spatial frequency between the two surfaces. When the Gabor micropatterns on the two surfaces were identical in spatial frequency, thresholds were very high and in some instances impossible to obtain. However, with as little as a 1-octave difference in spatial frequency between the surfaces, thresholds fell sharply to near-asymptotic levels. The fall in thresholds paralleled a change in the appearance of the stimulus from one of irregular depth to stereo transparency. The most parsimonious explanation for this finding is that the introduction of a between-surface luminance spatial-frequency difference reduces the number of spurious cross-surface binocular matches, thus helping to reveal the three-dimensional structure of the stimulus.

A transition between eye and object rivalry determined by stimulus coherence

Two orthogonal patterns presented to the two eyes, respectively, are perceived as alternating in time, a phenomenon often assumed to reflect competition between neuronal activities corresponding to the two eyes, presumably in the primary visual cortex. Recent evidence supports a competition between neuronal activities corresponding to the two patterns (objects) at some higher cortical processing stage after inputs from the two eyes have converged. Here, using textures made of Gabor signals, we present psychophysical data showing that the level of visual processing at which competition takes place and is resolved, is determined by the degree of stimulus coherence. Moreover, depending on stimulus parameters, competition may occur at several levels of processing at the same time.

Disparity modulation sensitivity for narrow-band-filtered stereograms

Stereo thresholds for 84% correct detection of sinusoidal disparity corrugations depicted by narrow-band-filtered random dot stereograms were determined for surfaces as a function of (i) luminance center spatial frequency and (ii) disparity modulation frequency. In addition, supra-threshold depth matching functions for two amplitudes of peak-to-trough depth were determined using similar stimuli. Disparity thresholds followed a U-shaped function when plotted against luminance centre spatial frequency from 1 to 8 c/deg. The threshold functions for the three highest corrugation frequencies (ranging from 0.25 to 1 c/deg) formed a single family with a similar bandpass shape and a peak sensitivity at ca 4 c/deg. At the lowest frequency of depth modulation (0.125 c/deg) the shape of the luminance spatial frequency threshold function showed a reduced sensitivity to depth modulations when portrayed by patterns with high luminance centre frequencies (8 c/deg). The similarity of the threshold functions reveals luminance and corrugation frequency to be largely independent dimensions. The finding that the functions are not identical provides some evidence to support a weak luminance spatial frequency selectivity in stereoscopic channels tuned to corrugation frequency.

Neural encoding of binocular disparity: energy models, position shifts and phase shifts

Neurophysiological data support two models for the disparity selectivity of binocular simple and complex cells in primary visual cortex. These involve binocular combinations of monocular receptive fields that are shifted in retinal position (the position-shift model) or in phase (the phase-shift model) between the two eyes. This article presents a formal description and analysis of a binocular energy model with these forms of disparity selectivity. We propose how one might measure the relative contributions of phase and position shifts in simple and complex cells. The analysis also reveals ambiguities in disparity encoding that are inherent in these model neurons, suggesting a need for a second stage of processing. We propose that linear pooling of the binocular responses across orientations and scales (spatial frequency) is capable of producing an unambiguous representation of disparity.

Fine-to-coarse scale disambiguation in stereopsis

Spatial frequency selectivity has been incorporated into various theories of stereo matching, along with spatial scale interactions operating from coarse-to-fine spatial scales. We concentrate here on the role of fine scale information in the stereo matching process and show that fine scale information is capable of disambiguating matches made at coarser scales. An ambiguous coarse scale stimulus was created by presenting a low frequency (2 c/deg) sine wave in anti-phase to the two eyes, whose endpoints betrayed no information about which way the sine waves should be matched. It could be seen with crossed or uncrossed disparity equally validly and at chance from trial to trial. To this was added a fine scale (8 c/deg) filtered random dot stimulus specifying unambiguously a certain disparity. Observers judged the apparent depth of the two stimuli as the disparity of the fine scale stimulus was varied. The sine wave was usually perceived to have the same sign disparity as the fine scale stimulus. Depth matching with the two superimposed stimuli confirmed that the coarse scale stimulus was actually disambiguated, and seen with disparities equal to half its spatial period. The results suggest the operation of a cross-spatial scale matching disambiguation process, which can operate in a fine-to-coarse fashion.

Size-disparity correlation in stereopsis at contrast threshold

Contrast thresholds for 75% correct depth identification in narrow-band filtered random dot stereograms were determined for different center spatial frequencies and binocular disparities. Rigorous control over vergence was maintained during testing, and a forced-choice procedure was used. The resulting contrast sensitivity function for stereopsis revealed sensitivity over a greater range of disparities at low than at high spatial frequencies. Sensitivity peaked for large disparities at low spatial frequencies and for small disparities at high spatial frequencies. When disparities were converted to effective binocular phase differences, the variation of contrast sensitivity with phase followed a consistent pattern across spatial frequencies, with peak sensitivity occurring mainly for binocular phases of between 90 degrees and 180 degrees. These results have implications for the extent of spatial integration at the input to the disparity sensing mechanism. A model postulating a spread of positional disparities independent of the spatial frequency selectivity of disparity-sensitive units cannot account for the results. But the size-disparity correlation strongly evident in our data is predicted by certain models of stereopsis, such as phase disparity encoding. An ideal observer analysis is developed that demonstrates that our results were not forced by the nature of the stimulus employed; rather, the quantum efficiency for stereopsis at contrast threshold follows the size-disparity correlation.

Binocular rivalry disrupts stereopsis

Does the shift from binocular rivalry to fusion or stereopsis take time? We measured stereoacuity after rivalry suppression of one half-image of a stereoacuity line target. After the observer signalled that the single stereo half-image had been suppressed, the other half-image was presented for a variable duration. Stereoacuity thresholds were elevated for 150-200 ms. A control experiment demonstrated that the threshold elevation was due to rivalry suppression per se, rather than masking effects associated with the rivalry-inducing target. Monocular Vernier thresholds, measured as the smallest identifiable abrupt shift in the upper line of an aligned Vernier target that had previously been suppressed by rivalry, were elevated for a much longer duration. This result shows that an appropriately matched stereo pair can break rivalry suppression more easily than can monocular changes in position. With the aid of a similar paradigm, we also measured the duration needed to detect a disparate feature in a random-dot stereogram after rivalry suppression of one half-image of the stereogram. Observers could correctly identify the location of the disparate feature (upper or lower visual field) when the other half-image was presented for a duration ranging from 150-650 ms. In the absence of the matching half-image, the first half-image was suppressed by the rival target for a far longer duration (a few seconds). These findings show that although stereopsis and fusion terminate rivalry, both are initially disrupted for a few hundred milliseconds by rivalry suppression.

Spatial frequency tuning of human stereopsis

A masking paradigm was employed to measure the spatial frequency selectivity of channels underlying human stereopsis. Observers viewed spatially filtered (0.4 octave bandwidth) random-dot stereograms in which a disparate bar appeared in either the top or bottom half of the display; superimposed on one RDS half-image was a noise target whose spatial frequency content was varied relative to that of the RDS. A staircase procedure was used to measure the monocular noise energy (and hence the signal-to-noise ratio) at which observers could judge the location of the disparate bar on 71% of trials. Statistical analyses showed that the resulting stereoscopic masking functions could be grouped into two sets, one with peak sensitivity at 3 c/deg and the other with peak sensitivity at 5 c/deg. These two channels were observed for both crossed and uncrossed disparities ranging from coarse to fine. Essentially the same results were obtained with binocular noise and with stereo displays flashed too briefly to be affected by eye movements. Our results are inconsistent with models of stereopsis in which the disparity range to which a channel is sensitive varies with that channel's peak spatial frequency. These data imply that the spatial frequency selectivity of stereopsis differs from the tuning of spatial channels underlying the detection and discrimination of form.

Real world occlusion constraints and binocular rivalry

A surface occluding a more distant surface gives rise to interocularly unpaired regions to its immediate left and right. The unpaired region on the left side is visible only to the left eye, whereas that on the right side is visible only to the right eye. Thus for real world scenes there are opto-geometrical constraints which determine whether particular combinations of relative depth and right-eye-only or left-eye-only stimuli are ecologically valid or invalid. We report a demonstration and experiments to show that opto-geometrically "valid" unpaired regions are seen as continuous with the rear plane and escape interocular suppression, whereas "invalid" unpaired regions are perceived as closer and are suppressed vigorously. An additional experiment indicates that the results cannot be understood in terms of correspondence solving, but require neural mechanisms that embody real-world occlusion constraints. These results suggest a rather close interaction between stereopsis and rivalry "modules". Since explicit eye-of-origin information is lost relatively early in the hierarchical organization of cortical visual processing, we argue that occlusion-related constraints must be embodied at such early levels.

Is edge information for stereoacuity spatially channeled?

Models of stereopsis generally assume that binocular correspondence is achieved through alignment of luminance edges in the two eyes. Yet the stimulus properties which constitute edge information for stereopsis have not been defined. Three experiments explored the nature of these stimulus properties. The first two experiments tested whether local luminance gradient and the relative phase of spatial components supply information about the position of edges which influences stereosensitivity. In Expt 1, stereothresholds were reduced with increased spatial frequency or contrast of sinusoidal luminance gratings, but no simple relationship between target luminance gradient and stereosensitivity was found. In Expt 2, stereothresholds were equivalent for targets having identical spatial frequency components, but differing in maximum luminance gradient and the relative spatial phase of their components. In addition, stereothresholds were lower for the target having the higher contrast in pairs of unequal-contrast targets having equal maximum luminance gradients. These results suggest that the properties of luminance gradient and relative spatial phase do not influence stereosensitivity independently of spatial frequency and contrast. Experiment 3 directly tested whether stereosensitivity depends on edge information whose disparity is detected independently at different spatial scales. Stereothresholds for IF + 5F compound targets were found to be equivalent to thresholds obtained separately with the more sensitive of the two components. Taken together with a compressive nonlinearity in the relationship between contrast and stereothreshold obtained by others (Halpern and Blake, 1989; Legge and Gu, 1989) and replicated in Expt 1, the results of Expt 3 indicate that, whatever the exact nature of the luminance discontinuity information utilized in disparity detection, it is processed independently at different spatial scales.

Compound binocular rivalry

Binocular rivalry was examined with random dot patterns consisting of three colours: red, green and grey. The microstructure of the patterns was defined by the individual dots, and the correspondence between the microstructures in the two eyes was manipulated. The macrostructures were defined by the distributions of red, green and grey dots over the displays, so that they consisted of orthogonally striped patterns. The degree of correspondence between the microstructures was varied in Expt 1, together with the spatial frequency of the microstructure. Rivalry periods of the macrostructures were briefer when the microstructures were in correspondence, In Expt 2 the spatial frequencies of the macrostructures were varied. The lower spatial frequency predominated for longer than the higher. The results are discussed in terms of independent pathways for corresponding and rivalry stimulation. In addition a stimulus pairing that produces clear dichoptic colour mixtures is presented.

Field processes in stereovision. A description of stereopsis appropriate to ophthalmology and visual perception

There is, as yet, no satisfactory theory of stereopsis, despite the fact that our overt knowledge of "solid seeing" is now about 150 years old, and that contributions to our understanding come today from many fields: ophthalmology, psychology, psychophysics, neurophysiology, computer modelling, and optical-TV display technology. We review herein, and demonstrate for the reader whenever possible, certain key perceptual properties of the stereoscopic event of which any general theory must take account: vector stereoscopy and the neural grid, depth in empty visual fields, the relationship between stereoscopic and cognitive contours, stereoscopic contour formation in the presence of blur (thus, at low levels of central visual acuity), the phenomenon of cortical locking and of neural grid evocation in the presence of either peripheral or central rivalry, certain unusual ranges of figural mismatch and the concept of the horopter in relation to modern single cell electroneurophysiology in animals and to the constancy of visual directions. Some comments are also made on the concept of disparity processing by single cortical neurons, together with a short discussion of the implications of certain views of the genetics of stereovision for the perception of novel random texture sine-wave stereograms. We conclude that any theory pertinent to ophthalmology and visual science must combine the global concepts of cortical integration, the neural lock and the neural grid, herein introduced, with the more classical concepts of particulate or local binocular cortical correspondence. Certain preliminary steps in this direction are presented.

Errors in the stereoscopic separation of surfaces represented with regular textures

Stereograms containing two similar or dissimilar linear textures, either on the same surface or at two different depths, were tested on seventy subjects. Whereas random textures usually produced correct percepts, regular textures consistently led to errors of stereoscopic interpretations, including a reversal of hollows into bumps, dissociation of single surfaces into two layers, and errors in relative positioning of two surfaces. Horizontal-vertical textures tended to be seen as flatter and further away from the observer than diagonal ones. Continuous textures tended to be seen closer than discontinuous ones. In the interpretation of the results, the possibility is raised that different textures are processed independently and that the brain has no reliable method for combining the conclusions into a rigorous global percept.

Binocular sensory fusion is limited by spatial resolution

Binocular sensory fusion which was previously thought to have a maximum spatial extent at the fovea of 1 deg is at least 600% larger when stimulated by low spatial frequency (coarse) detail. This upper limit for sensory fusion has a constant phase disparity limit of 90 deg which corresponds to the monocular Rayleigh criterion for spatial resolution of two diffraction patterns. At low spatial frequencies the sensory fusion limit equals the upper disparity limit for stereoscopic depth perception which suggests that a common mechanism underlies these two phenomena.

Stereopsis from disparity of complex grating patterns

Vertical grating patterns containing more than one spatial frequency component were presented stereoscopically. The depth percepts resulting from differences in relative horizontal position (or phase) in left- and right-eye views were measured using a depth-matching procedure. When the frequency components were similar in contrast, the depth percept was mediated by the overall disparity of the compound. However, a relatively low contrast component could make no contribution to the depth percept while still remaining clearly visible in the grating pattern. When two frequency components were equal in contrast but carried different individual disparities derived from local edge and spatial frequency information, the resulting percept contained multiple depth planes.

Spatial tuning of static and dynamic local stereopsis

The range of spatial tuning for channels that process static and dynamic disparities was investigated in the central visual field by measuring stereoscopic thresholds as a function of the difference in size of spatially filtered bar-like patterns presented to the two eyes. Spatial tuning functions were revealed by an elevation of stereothreshold as the difference between the widths of bar patterns increased. Functions tuned to low spatial frequencies (0.075-2 c/deg) were classified as transient since their stereosensitivity was greater for dynamic (1 Hz) than static disparities. Functions tuned to high spatial frequencies (2.4-19 c/deg) were classified as sustained since their stereosensitivity was equal for dynamic and static disparities. When equal width patterns were presented to the two eyes, stereothreshold increased with spatial periods greater than 0.4 deg according to a constant 6 deg phase disparity. This size-disparity correlation suggests that large disparities are processed by spatial filters tuned to disparities proportional to their receptive field dimensions.

Eye movements and neural remapping during fusion of misaligned random-dot stereograms

Fender and Julesz [J. Opt. Soc. Am. 57, 819 (1967)] found that fused retinally stabilized binocular line targets could be misaligned on the two retinas in the temporalward direction by at least 30 min of arc without loss of fusion and stereopsis and that random-dot stereograms could be misaligned 2 deg before fusion was lost. To test these results in normal vision, we recorded eye motions of four observers while they viewed a random-dot stereogram that subtended about 10 deg. The observers misaligned overlaid vectograph stereo images by moving them apart in a temporalward direction until fusion was lost. They then returned the vectographs to the overlaid position. Throughout this cycle the observers reported at frequent intervals if they could perceive strong or weak depth, loss of depth, or loss of fusion. For some observers the image separation could be increased to 5 deg beyond parallel before fusion was lost. The visual axes diverged to follow the image centers and varied from overconverged to overdiverged with respect to the image centers while the observers still reported depth and fusion. We call the difference between the image separation and eye vergence the vergence error. If a vergence error persisted for at least 10 sec without loss of the percepts of fusion and depth, we postulate that neutral remapping occurred that compensated for the retinal misalignment. We found that the average maximum neural remapping was 3.0 deg.(ABSTRACT TRUNCATED AT 250 WORDS)

Binocular rivalry: suppression depends on orientation and spatial frequency

In binocular rivalry the time during which different stimuli are perceived depends--amongst other things--on their spatial frequency (sf) contents, on contrast and on orientation. Limiting the sf-range of both periodic and aperiodic stimuli in different ways (while keeping the contrast constant) decreased their predominance. This result seems to corroborate the concept of spatial frequency channels in human vision. Decreasing the contrast also decreased predominance. Thus blurred patterns are suppressed by sharply focused ones because of both their lower contrast and their loss of high sf's. This has consequences for the therapy of strabismic amblyopia. Obliquely oriented patterns were almost as dominant as vertical ones and much more than horizontal ones. Instead of a conventional "oblique-effect" we found a "vertical-effect".

A computer implementation of a theory of human stereo vision

Recently, Marr & Poggio (1979) presented a theory of human stereo vision. An implementation of that theory is presented, and consists of five steps. (i) The left and right images are each filtered with masks of four sizes that increase with eccentricity; the shape of these masks is given by delta 2G, the Laplacian of a Gaussian function. (ii) Zero crossings in the filtered images are found along horizontal scan lines. (iii) For each mask size, matching takes place between zero crossings of the same sign and roughly the same orientation in the two images, for a range of disparities up to about the width of the mask's central region. Within this disparity range, it can be shown that false targets pose only a simple problem. (iv) The output of the wide masks can control vergence movements, thus causing small masks to come into correspondence. In this way, the matching process gradually moves from dealing with large disparities at a low resolution to dealing with small disparities at a high resolution. (v) When a correspondence is achieved, it is stored in a dynamic buffer, called the 2 1/2-dimensional sketch. To support the adequacy of the Marr-Poggio model of human stereo vision, the implementation was tested on a wide range of stereograms from the human stereopsis literature. The performance of the implementation is illustrated and compared with human perception. Also statistical assumptions made by Marr & Poggio are supported by comparison with statistics found in practice. Finally, the process of implementing the theory has led to the clarification and refinement of a number of details within the theory; these are discussed in detail.

A comparison of binocular depth mechanisms in areas 17 and 18 of the cat visual cortex

1. The retinal disparity sensitivity of neurones in areas 17 and 18 of the cat visual cortex was examined. The response of each cell to an optimally oriented slit was measured as disparity was varied orthogonally to the receptive field orientation. Eye movements were monitored with a binocular reference cell simultaneously recorded in area 17 (Hubel & Wiesel, 1970).2. Two types of disparity-sensitive cells were found, similar to those observed in the monkey by Poggio & Fischer (1977). The first type, tuned excitatory cells, were usually binocular and had a sharp peak in their disparity-response curve. They responded maximally at the disparity that brought their receptive fields into superposition on the tangent screen. This disparity closely coincided with the disparity at which the reference cell's receptive fields were also superimposed. By analogy with the monkey this point was taken to be the fixation point, or 0 degrees . The second type, near and far cells, were most often monocular. They gave their weakest response (which was usually no response at all) at 0 degrees . On one side of 0 degrees the response grew linearly for up to 4 degrees and then remained at the maximum. On the other side of zero, it remained at the minimum for up to several degrees before rising towards the maximum.3. The receptive field organization of several disparity-sensitive cells was examined using the activity profile method of Henry, Bishop & Coombs (1969). The size and strength of the discrete excitatory and inhibitory regions of the receptive fields of a cell could quantitatively account for the shape of its disparity-response curve.4. The laminar distribution of disparity sensitivity as well as of several other receptive field properties in areas 17 and 18 was studied. The organization of the two areas was remarkably similar in many respects. There was a difference, however, in the proportions of the two types of disparity-sensitive cells in the two areas. Area 17 contained many more tuned excitatory cells than near and far cells, while area 18 had the reverse distribution. In addition, the cells in area 18 were sensitive to a much broader range of disparities. While both areas contain disparity-sensitive neurones, these differences suggest that they play different roles in depth vision.5. Recent psychophysical and neurophysiological evidence has led to a new model of stereopsis in which depth is signalled by the pooled activity of large groups of cells (Richards, 1971). The current results are consistent with this model.

The computation of binocular edges

A computational model is described which effects the binocular combination of monocular edge information. The distinctive features of the model are: (i) it identifies edge locations in each monocular field by searching for zero crossings in nonorientated centre-surround convolution profiles; (ii) it selects amongst all possible binocular point-for-point combinations of edge locations only those which satisfy a (quasi-)collinear figural grouping rule; (iii) it presents a concept of the orientated and spatial-frequency-tuned channel as a nonlinear grouping operator. The success of the model is demonstrated both on a stereo pair of a natural scene and on a random-dot stereogram.

Surfaces with steep variations in depth pose difficulties for orientationally tuned disparity filters

Surfaces possessing steep variations in depth present severe difficulties for orientationally tuned filter models of stereopsis. These difficulties are discussed in connection with a random-dot stereogram depicting a surface with steep horizontal corrugations. As expected on theoretical grounds, we find that a vertical +/- 45 degrees orientationally filtered version of this stereogram cannot be fused. Moreover, it is demonstrated that a horizontal +/- 45 degrees filtered version can be fused only with difficulty and its stereo percept is poor compared to that of the unfiltered original. It is concluded that orientated filters seem ill-designed to mediate the extraction of disparity cues, at least in the cases under consideration.

A computational theory of human stereo vision

An algorithm is proposed for solving the stereoscopic matching problem. The algorithm consists of five steps: (1) Each image is filtered at different orientations with bar masks of four sizes that increase with eccentricity; the equivalent filters are one or two octaves wide. (2) Zero-crossings in the filtered images, which roughly correspond to edges, are localized. Positions of the ends of lines and edges are also found. (3) For each mask orientation and size, matching takes place between pairs of zero-crossings or terminationss of the same sign in the two images, for a range of disparities up to about the width of the mask's central region. (4) Wide masks can control vergence movements, thus causing small masks to come into correspondence. (5) When a correspondence is achieved, it is stored in a dynamic buffer, called the 2 1/2-D sketch. It is shown that this proposal provides a theoretical framework for most existing psychophysical and neurophysiological data about stereopsis. Several critical experimental predictions are also made, for instance about the size of Panum's area under various conditions. The results of such experiments would tell us whether, for example, cooperativity is necessary for the matching process.

The relationship between apparent depth and disparity in rivalrous-texture stereograms

A series of experiments is reported on rivalrous-texture stereograms composed of narrowband-filtered random noise. Experiment 1 found that the apparent deth-disparity function for such stereograms was different from that observed with similar but nonrivalrous stimuli. In particular, rivalrous divergent disparities produced the same depth as rivalrous zero disparity and this latter disparity itself produced a significant degree of protruding (i.e. 'convergent') depth in a certain type of rivalrous-texture stereogram. Free inspection was permitted and disparities were in the range 16 min convergent to 16 min divergent. Experiment 2 found no convincing evidence for reliable qualitative depth discriminations from tachistoscopic presentations of rivalrous-texture stereograms, using a forced-choice task requiring a discrimination between 16 min convergent and 16 min divergent conditions. This task was solved easily for equivalent nonrivalrous stimuli. Experiment 3 measured a hitherto unreported binocular depth effect, termed 'paradepth', which is produced by presenting a target in one field only. This effect appears to be a genuine biocular depth effect and not just the result of an ordinary monocular masking depth cue. The size of the depth effect was found to be a function of the width of the target. The overall conclusion derived from the series of experiments is that rivalrous-texture stereograms are complex stimuli capable of yielding curious and unexpected depth effects which are not readily explained in detail within any existing theoretical framework.

Contrast summation effects and stereopsis

Contrast thresholds for stereopsis were measured for a variety of bandpass-filtered random-dot stereograms in a series of experiments. The principal finding was that contrast thresholds for stereopsis from 'complex' stereograms composed of mixtures of (a) two widely different spatial frequencies or (b) two or more widely different oriented random textures, are considerably lower than would be expected if stereopsis from such stimuli is mediated by the first component to rise above its own stereopsis contrast threshold. Instead, it appears that stereopsis comes about whenever the supradetection-threshold contrast of a stereogram exceeds a certain level, regardless of whether this contrast is provided by a single component or by a mix of two different ones. The implications of these findings for models of stereopsis are discussed.

Contrast sensitivity function for stereopsis

Contrast thresholds for stereopsis from narrow-band-filtered random-dot stereograms were compared with contrast thresholds for simple detection of similar narrow-band noise. Centre frequencies of filters were in the range 2.5--15 cycles deg(-1). It was found that the contrast sensitivity function for stereopsis is similar in shape to that for detection, suggesting that as far as contrast requirements are concerned the mechanisms of global stereopsis do not show a bias in sensitivity to any particular spatial frequency but instead require a constant level of suprathreshold contrast regardless of spatial frequency.

A perspicuous technique for directly visualizing radiation-damage artefacts in biological electron microscopy

Levels of impairment of electron-microscopic images of biological specimens stemming from radiation damage are assessed in a rapid visual procedure that involves taking a pair of low-fluence micrographs of a specimen area before and after a fraction of the picture area has been more seriously damaged by applying a measured electron fluence. The pair of micrographs is treated as a mock-stereo pair and is given contrasting colours. Lateral displacements of specimen details appear as false relief and changes in electron lucency as false colour.

Is binocular vision always monocular?

Visual sensitivity of one eye was determined under binocular stimulus conditions yielding apparent fusion, stereopsis, monocular dominance, and monocular suppression. Marked losses in sensitivity accompanied monocular suppression but were not evident during stable singel vision. The results are inconsistent with the hypothesis that supression alone mediates binocular single vision.

Global processes in stereopsis: some comments on Ramachandran and Nelson (1976)

The use of the term 'global in the context of stereopsis is discussed. It is concluded that different meanings of this term need to be kept carefully distinguished at all times. The discussion centres around a series of demonstrations introduced by Ramachandran and Nelson, and interpretations are offered for these demonstrations in terms of spatial-frequency-tuned stereopsis channels.