Reversed stereo depth and motion direction with anti-correlated stimuli

What's special about horizontal disparity

Horizontal disparity has been recognized as the primary signal driving stereoscopic depth since the invention of the stereoscope in the 1830s. It has a unique status in our understanding of binocular vision. The direction of offset of the eyes gives the disparities of corresponding image point locations across the two retinas a strong horizontal bias. Beyond the retina, other factors give shape to the effective disparity direction used by visual mechanisms. The influence of orientation is examined here. I argue that horizontal disparity is an inflection point along a continuum of effective directions, and its role in stereo vision can be reinterpreted. The pointwise geometric justification for its special status neglects the oriented structural elements of spatial vision, its physiological support is equivocal, and psychophysical support of its special status may partially reflect biased stimulus sampling. The literature shows that horizontal disparity plays no particular role in the processing of one-dimensional stimuli, a reflection of the stereo aperture problem. The resulting depth is non-veridical, even non-transitive. Although one-dimensional components contribute to the stereo depth of visual objects generally, two-dimensional stimuli appear not to inherit the aperture problem. However, a look at the two-dimensional stimuli that predominate in experimental studies shows regularities in orientation that give a new perspective on horizontal disparity.

Robust natural depth for anticorrelated random dot stereogram for edge stimuli, but minimal reversed depth for embedded circular stimuli, irrespective of eccentricity

The small differences between the images formed in our left and right eyes are an important cue to the three-dimensional structure of scenes. These disparities are encoded by binocular neurons in the visual cortex. At the earliest stage of processing, these respond to binocular correlation between images. We assessed the perception of depth in anticorrelated stimuli, in which the contrast polarity in one eye is reversed, as a function of their location in the retinal image, and their depth configuration (a horizontal edge or a circle surrounded by an annulus) We found that, regardless of stimulus eccentricity, participants perceived depth in the natural direction for edge stimuli, and weakened, reversed depth for circular stimuli.

A computational model of stereoscopic prey capture in praying mantises

We present a simple model which can account for the stereoscopic sensitivity of praying mantis predatory strikes. The model consists of a single “disparity sensor”: a binocular neuron sensitive to stereoscopic disparity and thus to distance from the animal. The model is based closely on the known behavioural and neurophysiological properties of mantis stereopsis. The monocular inputs to the neuron reflect temporal change and are insensitive to contrast sign, making the sensor insensitive to interocular correlation. The monocular receptive fields have a excitatory centre and inhibitory surround, making them tuned to size. The disparity sensor combines inputs from the two eyes linearly, applies a threshold and then an exponent output nonlinearity. The activity of the sensor represents the model mantis’s instantaneous probability of striking. We integrate this over the stimulus duration to obtain the expected number of strikes in response to moving targets with different stereoscopic disparity, size and vertical disparity. We optimised the parameters of the model so as to bring its predictions into agreement with our empirical data on mean strike rate as a function of stimulus size and disparity. The model proves capable of reproducing the relatively broad tuning to size and narrow tuning to stereoscopic disparity seen in mantis striking behaviour. Although the model has only a single centre-surround receptive field in each eye, it displays qualitatively the same interaction between size and disparity as we observed in real mantids: the preferred size increases as simulated prey distance increases beyond the preferred distance. We show that this occurs because of a stereoscopic “false match” between the leading edge of the stimulus in one eye and its trailing edge in the other; further work will be required to find whether such false matches occur in real mantises. Importantly, the model also displays realistic responses to stimuli with vertical disparity and to pairs of identical stimuli offering a “ghost match”, despite not being fitted to these data. This is the first image-computable model of insect stereopsis, and reproduces key features of both neurophysiology and striking behaviour.

The praying mantis is the only insect so far known to compute depth using stereoscopic (3D) vision. Mantis stereopsis appears to be simpler than human stereopsis and most machine sterovision algorithms. A computational model of mantis stereopsis may therefore be beneficial to the field of robotics, particularly where computational power is limited. Using a combination of behavioural observations and neurophysiological data, we propose a very simple model structure to describe the prey capture response in the praying mantis. We used the limited available data on the mantis’ size and distance preferences for its prey to train our model parameters. Our simple model is able to qualitatively reproduce previously unexplained characteristics of our training data, and predicts key observations in additional empirical data that was not included in the model training. Whilst we believe our model to be only a partial and heavily simplified account of mantis stereopsis, our results are supportive of our model structure as an approximation of the size and disparity sensors used by the mantis when catching its prey.

Associations Between Binocular Depth Perception and Performance Gains in Laparoscopic Skill Acquisition

The ability to perceive differences in depth is important in many daily life situations. It is also of relevance in laparoscopic surgical procedures that require the extrapolation of three-dimensional visual information from two-dimensional planar images. Besides visual-motor coordination, laparoscopic skills and binocular depth perception are demanding visual tasks for which learning is important. This study explored potential relations between binocular depth perception and individual variations in performance gains during laparoscopic skill acquisition in medical students naïve of such procedures. Individual differences in perceptual learning of binocular depth discrimination when performing a random dot stereogram (RDS) task were measured as variations in the slope changes of the logistic disparity psychometric curves from the first to the last blocks of the experiment. The results showed that not only did the individuals differ in their depth discrimination; the extent with which this performance changed across blocks also differed substantially between individuals. Of note, individual differences in perceptual learning of depth discrimination are associated with performance gains from laparoscopic skill training, both with respect to movement speed and an efficiency score that considered both speed and precision. These results indicate that learning-related benefits for enhancing demanding visual processes are, in part, shared between these two tasks. Future studies that include a broader selection of task-varying monocular and binocular cues as well as visual-motor coordination are needed to further investigate potential mechanistic relations between depth perceptual learning and laparoscopic skill acquisition. A deeper understanding of these mechanisms would be important for applied research that aims at designing behavioral interventions for enhancing technology-assisted laparoscopic skills.

Human primary visual cortex shows larger population receptive fields for binocular disparity-defined stimuli

The visual perception of 3D depth is underpinned by the brain's ability to combine signals from the left and right eyes to produce a neural representation of binocular disparity for perception and behaviour. Electrophysiological studies of binocular disparity over the past 2 decades have investigated the computational role of neurons in area V1 for binocular combination, while more recent neuroimaging investigations have focused on identifying specific roles for different extrastriate visual areas in depth perception. Here we investigate the population receptive field properties of neural responses to binocular information in striate and extrastriate cortical visual areas using ultra-high field fMRI. We measured BOLD fMRI responses while participants viewed retinotopic mapping stimuli defined by different visual properties: contrast, luminance, motion, correlated and anti-correlated stereoscopic disparity. By fitting each condition with a population receptive field model, we compared quantitatively the size of the population receptive field for disparity-specific stimulation. We found larger population receptive fields for disparity compared with contrast and luminance in area V1, the first stage of binocular combination, which likely reflects the binocular integration zone, an interpretation supported by modelling of the binocular energy model. A similar pattern was found in region LOC, where it may reflect the role of disparity as a cue for 3D shape. These findings provide insight into the binocular receptive field properties underlying processing for human stereoscopic vision.

Contrast-reversed binocular dot-pairs in random-dot stereograms for depth perception in central visual field: Probing the dynamics of feedforward-feedback processes in visual inference

In a random-dot stereogram (RDS), the spatial disparities between the interocularly corresponding black and white random dots determine the depths of object surfaces. If a black dot in one monocular image corresponds to a white dot in the other, disparity-tuned neurons in primary visual cortex (V1) respond as if their preferred disparities become non-preferred and vice versa, reversing the disparity sign reported to higher visual areas. Reversed depth is perceptible in the peripheral but not the central visual field. This study demonstrates that, in central vision, adding contrast-reversed dots to a noisy RDS (containing the normal contrast-matched dots) can augment or degrade depth perception. Augmentation occurs when the reversed depth signals are congruent with the normal depth signals to report the same disparity sign, and occurs regardless of the viewing duration. Degradation occurs when the reversed and normal depth signals are incongruent with each other and when the RDS is viewed briefly. These phenomena reflect the Feedforward-Feedback-Verify-and-reWeight (FFVW) process for visual inference in central vision, and are consistent with the central-peripheral dichotomy that central vision has a stronger top-down feedback from higher to lower brain areas to disambiguate noisy and ambiguous inputs from V1. When a RDS is viewed too briefly for feedback, augmentation and degradation work by adding the reversed depth signals from contrast-reversed dots to the feedforward, normal, depth signals. With a sufficiently long viewing duration, the feedback vetoes incongruent reversed depth signals and amends or completes the imperfect, but congruent, reversed depth signals by analysis-by-synthesis computation.

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.

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.

Neural architectures for stereo vision

Stereoscopic vision delivers a sense of depth based on binocular information but additionally acts as a mechanism for achieving correspondence between patterns arriving at the left and right eyes. We analyse quantitatively the cortical architecture for stereoscopic vision in two areas of macaque visual cortex. For primary visual cortex V1, the result is consistent with a module that is isotropic in cortical space with a diameter of at least 3 mm in surface extent. This implies that the module for stereo is larger than the repeat distance between ocular dominance columns in V1. By contrast, in the extrastriate cortical area V5/MT, which has a specialized architecture for stereo depth, the module for representation of stereo is about 1 mm in surface extent, so the representation of stereo in V5/MT is more compressed than V1 in terms of neural wiring of the neocortex. The surface extent estimated for stereo in V5/MT is consistent with measurements of its specialized domains for binocular disparity. Within V1, we suggest that long-range horizontal, anatomical connections form functional modules that serve both binocular and monocular pattern recognition: this common function may explain the distortion and disruption of monocular pattern vision observed in amblyopia.

This article is part of the themed issue ‘Vision in our three-dimensional world’.

Weighted parallel contributions of binocular correlation and match signals to conscious perception of depth

Binocular disparity is detected in the primary visual cortex by a process similar to calculation of local cross-correlation between left and right retinal images. As a consequence, correlation-based neural signals convey information about false disparities as well as the true disparity. The false responses in the initial disparity detectors are eliminated at later stages in order to encode only disparities of the features correctly matched between the two eyes. For a simple stimulus configuration, a feed-forward nonlinear process can transform the correlation signal into the match signal. For human observers, depth judgement is determined by a weighted sum of the correlation and match signals rather than depending solely on the latter. The relative weight changes with spatial and temporal parameters of the stimuli, allowing adaptive recruitment of the two computations under different visual circumstances. A full transformation from correlation-based to match-based representation occurs at the neuronal population level in cortical area V4 and manifests in single-neuron responses of inferior temporal and posterior parietal cortices. Neurons in area V5/MT represent disparity in a manner intermediate between the correlation and match signals. We propose that the correlation and match signals in these areas contribute to depth perception in a weighted, parallel manner.This article is part of the themed issue 'Vision in our three-dimensional world'.

A Single Mechanism Can Account for Human Perception of Depth in Mixed Correlation Random Dot Stereograms

In order to extract retinal disparity from a visual scene, the brain must match corresponding points in the left and right retinae. This computationally demanding task is known as the stereo correspondence problem. The initial stage of the solution to the correspondence problem is generally thought to consist of a correlation-based computation. However, recent work by Doi et al suggests that human observers can see depth in a class of stimuli where the mean binocular correlation is 0 (half-matched random dot stereograms). Half-matched random dot stereograms are made up of an equal number of correlated and anticorrelated dots, and the binocular energy model-a well-known model of V1 binocular complex cells-fails to signal disparity here. This has led to the proposition that a second, match-based computation must be extracting disparity in these stimuli. Here we show that a straightforward modification to the binocular energy model-adding a point output nonlinearity-is by itself sufficient to produce cells that are disparity-tuned to half-matched random dot stereograms. We then show that a simple decision model using this single mechanism can reproduce psychometric functions generated by human observers, including reduced performance to large disparities and rapidly updating dot patterns. The model makes predictions about how performance should change with dot size in half-matched stereograms and temporal alternation in correlation, which we test in human observers. We conclude that a single correlation-based computation, based directly on already-known properties of V1 neurons, can account for the literature on mixed correlation random dot stereograms.

Luminance, Colour, Viewpoint and Border Enhanced Disparity Energy Model

The visual cortex is able to extract disparity information through the use of binocular cells. This process is reflected by the Disparity Energy Model, which describes the role and functioning of simple and complex binocular neuron populations, and how they are able to extract disparity. This model uses explicit cell parameters to mathematically determine preferred cell disparities, like spatial frequencies, orientations, binocular phases and receptive field positions. However, the brain cannot access such explicit cell parameters; it must rely on cell responses. In this article, we implemented a trained binocular neuronal population, which encodes disparity information implicitly. This allows the population to learn how to decode disparities, in a similar way to how our visual system could have developed this ability during evolution. At the same time, responses of monocular simple and complex cells can also encode line and edge information, which is useful for refining disparities at object borders. The brain should then be able, starting from a low-level disparity draft, to integrate all information, including colour and viewpoint perspective, in order to propagate better estimates to higher cortical areas.

Stereo vision and strabismus

Binocular stereopsis, or stereo vision, is the ability to derive information about how far away objects are, based solely on the relative positions of the object in the two eyes. It depends on both sensory and motor abilities. In this review, I briefly outline some of the neuronal mechanisms supporting stereo vision, and discuss how these are disrupted in strabismus. I explain, in some detail, current methods of assessing stereo vision and their pros and cons. Finally, I review the evidence supporting the clinical importance of such measurements.

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.

The place of human psychophysics in modern neuroscience

Human psychophysics is the quantitative measurement of our own perceptions. In essence, it is simply a more sophisticated version of what humans have done since time immemorial: noticed and reflected upon what we can see, hear, and feel. In the 21st century, when hugely powerful techniques are available that enable us to probe the innermost structure and function of nervous systems, is human psychophysics still relevant? I argue that it is, and that in combination with other techniques, it will continue to be a key part of neuroscience for the foreseeable future. I discuss these points in detail using the example of binocular stereopsis, where human psychophysics in combination with physiology and computational vision, has made a substantial contribution.

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.

Binocular eye movement control and motion perception: what is being tracked?

PURPOSE

We investigated under what conditions humans can make independent slow phase eye movements. The ability to make independent movements of the two eyes generally is attributed to few specialized lateral eyed animal species, for example chameleons. In our study, we showed that humans also can move the eyes in different directions. To maintain binocular retinal correspondence independent slow phase movements of each eye are produced.

METHODS

We used the scleral search coil method to measure binocular eye movements in response to dichoptically viewed visual stimuli oscillating in orthogonal direction.

RESULTS

Correlated stimuli led to orthogonal slow eye movements, while the binocularly perceived motion was the vector sum of the motion presented to each eye. The importance of binocular fusion on independency of the movements of the two eyes was investigated with anti-correlated stimuli. The perceived global motion pattern of anti-correlated dichoptic stimuli was perceived as an oblique oscillatory motion, as well as resulted in a conjugate oblique motion of the eyes.

CONCLUSIONS

We propose that the ability to make independent slow phase eye movements in humans is used to maintain binocular retinal correspondence. Eye-of-origin and binocular information are used during the processing of binocular visual information, and it is decided at an early stage whether binocular or monocular motion information and independent slow phase eye movements of each eye are produced during binocular tracking.

Stereoscopic vision in the absence of the lateral occipital cortex

Both dorsal and ventral cortical visual streams contain neurons sensitive to binocular disparities, but the two streams may underlie different aspects of stereoscopic vision. Here we investigate stereopsis in the neurological patient D.F., whose ventral stream, specifically lateral occipital cortex, has been damaged bilaterally, causing profound visual form agnosia. Despite her severe damage to cortical visual areas, we report that DF's stereo vision is strikingly unimpaired. She is better than many control observers at using binocular disparity to judge whether an isolated object appears near or far, and to resolve ambiguous structure-from-motion. DF is, however, poor at using relative disparity between features at different locations across the visual field. This may stem from a difficulty in identifying the surface boundaries where relative disparity is available. We suggest that the ventral processing stream may play a critical role in enabling healthy observers to extract fine depth information from relative disparities within one surface or between surfaces located in different parts of the visual field.

Vertical binocular disparity is encoded implicitly within a model neuronal population tuned to horizontal disparity and orientation

Primary visual cortex is often viewed as a "cyclopean retina", performing the initial encoding of binocular disparities between left and right images. Because the eyes are set apart horizontally in the head, binocular disparities are predominantly horizontal. Yet, especially in the visual periphery, a range of non-zero vertical disparities do occur and can influence perception. It has therefore been assumed that primary visual cortex must contain neurons tuned to a range of vertical disparities. Here, I show that this is not necessarily the case. Many disparity-selective neurons are most sensitive to changes in disparity orthogonal to their preferred orientation. That is, the disparity tuning surfaces, mapping their response to different two-dimensional (2D) disparities, are elongated along the cell's preferred orientation. Because of this, even if a neuron's optimal 2D disparity has zero vertical component, the neuron will still respond best to a non-zero vertical disparity when probed with a sub-optimal horizontal disparity. This property can be used to decode 2D disparity, even allowing for realistic levels of neuronal noise. Even if all V1 neurons at a particular retinotopic location are tuned to the expected vertical disparity there (for example, zero at the fovea), the brain could still decode the magnitude and sign of departures from that expected value. This provides an intriguing counter-example to the common wisdom that, in order for a neuronal population to encode a quantity, its members must be tuned to a range of values of that quantity. It demonstrates that populations of disparity-selective neurons encode much richer information than previously appreciated. It suggests a possible strategy for the brain to extract rarely-occurring stimulus values, while concentrating neuronal resources on the most commonly-occurring situations.

Mechanisms underlying the transformation of disparity signals from V1 to V2 in the macaque

Stereo vision relies on cortical signals that encode binocular disparity. In V1, the disparity energy model explains many features of binocular interaction, but it overestimates the responses to anticorrelated images. Combining the outputs of two, or more, energy model-like subunits [two-subunit (2SU) model] can resolve this discrepancy and provides an alternative explanation for disparity signals previously thought to indicate phase disparity between the receptive fields (RFs) of each eye. The 2SU model naturally explains how "near/far" (odd-symmetric) tuning becomes dominant in extrastriate cortex. To compare the energy and the 2SU models, we used a broadband compound grating and applied a common interocular phase difference to all spatial frequency components (a stimulus phase disparity), combined with a common spatial displacement (a stimulus position disparity). This produces binocular images that never occur in natural viewing, for which the 2SU model and the energy model make distinctively different predictions. Responses of neurons recorded from both V1 and V2 of awake rhesus macaques systematically deviated from the predictions of the energy model, in accordance with the 2SU model. These deviations correlated with the symmetry of the tuning curve, indicating that the 2SU mechanism is exploited to produce odd symmetry. Nonetheless, individual subunits also contain RF phase disparity that contributes to odd symmetry. The results suggest that neurons in V2 probably inherit phase disparity signals from V1 neurons, but systematically combine input from V1 neurons with different position disparities, in a way that elaborates odd-symmetric tuning and extends the range of disparities encoded by single neurons.

Multivoxel pattern selectivity for perceptually relevant binocular disparities in the human brain

Processing of binocular disparity is thought to be widespread throughout cortex, highlighting its importance for perception and action. Yet the computations and functional roles underlying this activity across areas remain largely unknown. Here, we trace the neural representations mediating depth perception across human brain areas using multivariate analysis methods and high-resolution imaging. Presenting disparity-defined planes, we determine functional magnetic resonance imaging (fMRI) selectivity to near versus far depth positions. First, we test the perceptual relevance of this selectivity, comparing the pattern-based decoding of fMRI responses evoked by random dot stereograms that support depth perception (correlated RDS) with the decoding of stimuli containing disparities to which the perceptual system is blind (anticorrelated RDS). Preferential disparity selectivity for correlated stimuli in dorsal (visual and parietal) areas and higher ventral area LO (lateral occipital area) suggests encoding of perceptually relevant information, in contrast to early (V1, V2) and intermediate ventral (V3v, V4) visual cortical areas that show similar selectivity for both correlated and anticorrelated stimuli. Second, manipulating disparity parametrically, we show that dorsal areas encode the metric disparity structure of the viewed stimuli (i.e., disparity magnitude), whereas ventral area LO appears to represent depth position in a categorical manner (i.e., disparity sign). Our findings suggest that activity in both visual streams is commensurate with the use of disparity for depth perception but the neural computations may differ. Intriguingly, perceptually relevant responses in the dorsal stream are tuned to disparity content and emerge at a comparatively earlier stage than categorical representations for depth position in the ventral stream.

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.

Binocular depth perception and the cerebral cortex

Our ability to coordinate the use of our left and right eyes and to make use of subtle differences between the images received by each eye allows us to perceive stereoscopic depth, which is important for the visual perception of three-dimensional space. Binocular neurons in the visual cortex combine signals from the left and right eyes. Probing the roles of binocular neurons in different perceptual tasks has advanced our understanding of the stages within the visual cortex that lead to binocular depth perception.

Early computational processing in binocular vision and depth perception

Stereoscopic depth perception is a fascinating ability in its own right and also a useful model of perception. In recent years, considerable progress has been made in understanding the early cortical circuitry underlying this ability. Inputs from left and right eyes are first combined in primary visual cortex (V1), where many cells are tuned for binocular disparity. Although the observation of disparity tuning in V1, combined with psychophysical evidence that stereopsis must occur early in visual processing, led to initial suggestions that V1 was the neural correlate of stereoscopic depth perception, more recent work indicates that this must occur in higher visual areas. The firing of cells in V1 appears to depend relatively simply on the visual stimuli within local receptive fields in each retina, whereas the perception of depth reflects global properties of the stimulus. However, V1 neurons appear to be specialized in a number of respects to encode ecologically relevant binocular disparities. This suggests that they carry out essential pre-processing underlying stereoscopic depth perception in higher areas. This article reviews recent progress in developing accurate models of the computations carried out by these neurons. We seem close to achieving a mathematical description of the initial stages of the brain's stereo algorithm. This is important in itself--for instance, it may enable improved stereopsis in computer vision--and paves the way for a full understanding of how depth perception arises.

Comparing Perceptual Signals of Single V5/MT Neurons in Two Binocular Depth Tasks

Neurons in the extrastriate visual area V5/MT show perceptually relevant signals in binocular depth tasks, which can be measured as a choice probability (CP) for the neuron. The presence of a CP in a particular paradigm may be an indicator that the neuron is generally part of the substrate for the perception of binocular depth. We compared the responses of those single neurons that show CPs in one stereoscopic depth task with their responses in another stereo task. Each neuron was tested for the presence of 1) CPs during a task in which macaques responded to the sign of binocular depth in a structure-from-motion stimulus, to judge its direction of three-dimensional rotation and 2) a consistent response to the stereo disparity of binocularly anti-correlated stimuli. Previous work, confirmed here, shows that changing the disparity of these binocularly anti-correlated stimuli often fails to yield a coherent change in the depth percept. For each test alone, there are V5/MT neurons that carry signals that are congruent with the perceptual effects. However, on comparing tests, there is no fixed pool of neurons that can account for the binocular depth percept. Excitation of neurons with a measurable CP does not necessarily lead to a change in perception. The cortical circuitry must be able to make dynamic changes in the pools of neurons that underlie perceptual judgments according to the demands of the task.

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.

Detecting disparity in two-dimensional patterns

One can measure the disparities between two retinal images in several different ways. Experiments were conducted to identify the measure that is invariant at the threshold for detecting the disparity of two-dimensional patterns. The patterns used were stereo plaids, which permit a partial dissociation between the disparity of the pattern and the disparities of its one-dimensional components. For plaids with near-horizontal disparities, thresholds are limited by a disparity phase shift equal to the threshold phase shift for single gratings. For non-horizontal disparities, thresholds are elevated, yet are still phase-limited. In no disparity direction are thresholds for detecting disparity determined by the spatial extent of the plaids' disparity. Effects of the number and the orientation of components with task-relevant disparities indicate that plaid thresholds are limited by the disparity of the plaid's one-dimensional components. No evidence was found that these components form any higher-order pattern that can be used in detecting disparity. Oblique and near-vertical disparities generate elevated thresholds at a stage beyond component disparity detection. This second stage combines component disparities, which are ambiguous about depth, into pattern disparities capable of supporting veridical depth perception.

A Bayesian approach to the stereo correspondence problem

I present a probabilistic approach to the stereo correspondence problem. Rather than trying to find a single solution in which each point in the left retina is assigned a partner in the right retina, all possible matches are considered simultaneously and assigned a probability of being correct. This approach is particularly suitable for stimuli where it is inappropriate to seek a unique partner for each retinal position--for instance, where objects occlude each other, as in Panum's limiting case. The probability assigned to each match is based on a Bayesian analysis previously developed to explain psychophysical data (Read, 2002). This provides a convenient way to incorporate constraints that enable the ill-posed correspondence problem to be solved. The resulting model behaves plausibly for a variety of different stimuli.

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.