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Modelling human depth perception in binocular vision: obtaining the horizontal disparity map.

The paper presents a computer application developed as a tool for implementing, developing, and testing computational models for stereopsis. Two models for solving the correspondence problem and computing the stereo disparity map have been implemented. One of them is biologically inspired (it models the behaviour of simple and complex cells from the striate cortex) and the paper details the results obtained on random-dot stereograms and on pairs of real images.

Algorithms↗

A computational model of binocular depth perception.

We point out that the horizontal disparities between a pair of retinal images are inadequate for computing the three-dimensional structure of a scene unless supplemented by independent information about the distance and direction of the fixation point. We suggest that this supplementary information is derived not from non-visual sources, but from the vertical disparities of a few non-meridional image points. This hypothesis is shown to account quantitatively for Ogle's induced effect--the marked distortion of a scene by a vertically magnifying lens placed in front of one eye.

Depth Perception↗

Deficits in stereoscopic depth perception by mildly mentally retarded adults.

The ability of mildly mentally retarded adults to perceive specific perceptual phenomena attendant to global stereopsis produced by random element stereograms was investigated. From the standpoint of computational vision, these phenomena are difficult to process, yet nonretarded persons perceive them effortlessly and without error. Retarded subjects in this study, however, exhibited large qualitative deficits not attributable to an absence of stereopsis or a failure to comprehend. These results suggest that the computational requirements of the stimuli exceeded resources and imply the presence of a substantial structural deficit in an automatic preattentive perceptual stage quite distant from the domain of cognition.

Adult↗

Frequency of fusion and of loss of fusion, and binocular depth perception with alternating stimulus presentation.

Stereoscopic vision was investigated with an experimental design allowing dichoptic stimulus presentation at different frequencies of image alternation. For twenty subjects the frequency of binocular fusion and the frequency of loss of fusion to one stereoscopic image was measured as a function of the convergence angle. In thirteen subjects no dependence of the fusion frequency was found, while seven subjects showed a marked increase of the fusion frequency with increasing angle of convergence. In all cases the frequency of fusion was higher than the frequency of loss of fusion. Both frequencies, however, are lower than the flicker fusion frequency. Under conditions where no monocular cues and no references for stereoptic depth comparisons were presented, the apparent distance of the image from the observer could not be assessed, but perception of relative motion in depth was possible. All subjects assessed the direction of motion accurately down to changes of the convergence angle of 0.2 deg s-1.

Adolescent↗

Sensory modalities in depth perception by golden hamsters.

Golden hamsters are able to detect differences in the height of a platform from which they jump, as measured by their increasing latencies prior to jumping from increased elevations. This ability is very effective when optical information is available, but it is also present when hamsters jump in total darkness. A second experiment shows that, when hamsters are placed on a real physical cliff, they preferentially use tactile information over visual information to guide their choice of the side from which to descend. In a nonvisual setting, tactile stimulation is used in conjunction with other types of cues. Evidence is provided to suggest that these cues are of an acoustical nature.

Animals↗

A possible neurophysiological basis for depth perception in frogs: existence of a horopter surface.

In frogs, multi-unit receptive fields (MURF) of rostral binocular tectal points (BTP) show a crossed disparity when mapped at a distance equal to the perimeter radius (i.e., 33 cm). The shape of the spatial surface where MURF of all BTP are in-register is investigated in two planes: (a) in the longitudinal plane, the locus of superimposition is a circumference passing through both eyes; (b) in the vertical plane, it corresponds to a straight line tilted towards the animal's head. This surface can be defined as the frog's horopter surface since it represents the spatial locus where objects can simultaneously stimulate corresponding retinal areas. Behavioural and electrophysiological correlations are discussed.

Animals↗

Modelling biological depth perception in binocular vision: the local disparity estimation.

This paper presents an approach to solving the correspondence problem in binocular vision and to computing the local horizontal disparity map using a biologically inspired algorithm. A computer application was developed as a tool for implementing, developing, and testing computational models for stereopsis, and also as a framework for integrating the disparity map with other perspective clues. Two models for stereopsis have been implemented. One of them is biologically inspired (it models the behaviour of simple and complex cells from the striate cortex) and the other is the 'classical' model of David Marr and Tomaso Poggio, implemented in order to have a comparison term for the simulation results. The paper details the results obtained on random-dot stereograms and on pairs of real images.

Algorithms↗

Effect of meridional disparity on depth perception.

When a meridional-size lens is used to provide magnification in the horizonal meridan for one eye the resulting stereopsis distortion is readily accounted for in the terms of the binocular disparity caused by changed angular relations. When the same size lens is used to magnify the vertical meridian for one eye there is an opposite stereoscopic distortion for which is no ready geometric explanation. A perceptually induced mechanism operating in the vertical meridian has been suggested by Ogle. In the present experiment, apparatus was designed to introduce disparity of binocularly fused targets successively in each of several oblique meridians independent of the stereopsis measuring targets. Unlike the above-mentioned results obtained with size lenses, the induced stereoscopic distortion was in the same direction and of essentially the same magnitude for disparity in every meridian. It would follow that the perceptually induced mechanism is not exclusive to the vertical meridian.

Depth Perception↗

Stereoscopic depth perception at high velocities.

The view of the world from different perspectives provided by the two eyes is used by the human visual system to compute the relative distances and solid shapes of objects. However, the traditional theory of binocular disparity takes little account of the fact that a moving target will stimulate many different sets of disparate points in the two eyes with a range of temporal delays. Here we show that stereoacuity for periodic grating is not degraded by velocities of up to 640 degrees s-1 provided that they do not move at a greater rate than 30 cycles s-1. The minimum detectable spatial phase difference between the eyes was equivalent to a spatial phase difference of about 5 degrees and an interocular temporal delay as small as 450 microseconds. We suggest that stereopsis for moving targets is accomplished by neurons having a spatial-temporal phase shift in their receptive fields between the eyes.

Depth Perception↗

Electrophysiological assessment of the human depth-perception threshold.

The cortical response to stereoscopic stimuli was measured as a function of disparity using visual evoked potentials (VEP). The stereoscopic stimulus consisted of a dynamic random-dot pattern that portrayed a three-dimensional horizontal grating. Disparity of the grating was variable between 0 and 18 arc min, step size being 4.22 arc s. Evoked responses were recorded using a "random-sequence sweep technique." The VEP amplitude increased approximately linearly with the logarithm of disparity and allowed an estimation of the stereo threshold by linear extrapolation. The evoked potential estimates of the stereo threshold of 16 subjects were compared to psychophysically obtained thresholds. Several threshold-estimation techniques are discussed. Evoked potential and psychophysical threshold estimates had the lowest discrepancy when the VEP amplitude was linearly extrapolated to the logarithmic disparity axis. The difference between the evoked potential estimate and the psychophysical threshold was less than 20% in 56% of all cases; 16 of 18 cases (89%) agreed within a factor of 2.

Depth Perception↗

Differential sparing of depth perception, orienting, and optokinetic nystagmus after neonatal versus adult lesions of cortical areas 17, 18, and 19 in the cat.

Performance by cats with lesions of the visual cortex made in infancy or adulthood was examined on tasks of visually guided behavior that do not require specific training. Cats with lesions confined to areas 17, 18, and 19 made during the 1st postnatal week showed more sparing of function on a visual cliff, at orienting to targets suddenly appearing in the visual field, and at optokinetic nystagmus than did cats with equivalent damage incurred as adults. Cats with lesions that included areas 17, 18, 19 and most of the contiguous visual areas were severely impaired at all tasks whether the lesions were incurred neonatally or in adulthood. These findings suggest that sparing of vision after neonatal lesions of cortical areas 17, 18, and 19 is not confined to pattern learning tasks and that remaining lateral cortical visual areas are importantly involved in such sparing.

Aging↗

[Computer-assisted determination of parameters of depth perception: studies with the 3-rod device].

Psychophysical determination of the thresholds of stereoscopic vision takes about 20 min. During this procedure, you may have the feeling that the thresholds are shifting. To verify this phenomenon, the thresholds must be determined in a period shorter than 20 min, e.g., 4-6 min. This is one of the reasons we constructed a computerized machine to detect the stereoscopic thresholds. The heart of this device is a micrometric screw driven by a stepping motor that moves the central rod of the three-rod apparatus. This motor is controlled by a microcomputer with a basic program. A special program has been designed that functions in a manner similar to that of the Octopus perimeter and detects the thresholds with in a few steps. It is thus possible to reduce the detection time for one threshold dramatically. The first results with this device are not only very precise, but also demonstrate the minute values between stereoscopic thresholds. For an observation distance of 380 mm, we were able to calculate the disparation angles down to 3 s of arc. If a number of measurements are taken, the threshold fluctuations and physiological zero position can be calculated.

Depth Perception↗

Chromatic imbalance due to commonly used red-green filters reduces accuracy of stereoscopic depth perception.

This study was designed to determine the effect on stereopsis of interocular retinal chromatic and illuminance imbalance in 30 subjects with normal binocularity. A Randot 3 Circle Stereotest, viewed through polarizing glasses only, was the control condition. In each of three additional conditions, illuminance and chromatic imbalances were created by commonly used red and green filters and neutral density filters combined with the polarizing filters. The effect of each of these experimental conditions on stereopsis was determined by comparing total stereo judgement errors on the Randot Circle Stereotest for each condition to the control condition. Total average flux through the filter combinations was held constant by adjusting the luminance level of light reflected from the target. The chromatic imbalance created by the red-green filters significantly increased the number of stereo judgment errors (37%, p less than 0.05). However, illuminance imbalance (0.2 log units) of the magnitude created by the red-green filters did not significantly increase the number of errors (2.9%, p less than 0.65). Finally, the combined illuminance and chromatic imbalance created by the red-green filters significantly increased the error frequency (46%, p less than 0.05). The chromatic imbalance caused by red-green glasses significantly degrades stereopsis, whereas the illuminance imbalance caused by these filters has no significant effect on stereopsis.

Adolescent↗

Size-disparity correlation in human binocular depth perception.

To use the small horizontal disparities between images projected to the eyes for the recovery of three-dimensional information, our visual system must first identify which feature in one eye's image corresponds with which in the other. The earliest level of disparity processing in primates (V1) contains cells that are spatial-frequency tuned. If such cells have a disparity range that covers only a single period of their mean tuning frequency, there will always be exactly one potential match within this range. Here, this 'size-disparity' hypothesis was tested by measuring the contrast sensitivity of stereopsis as a function of disparity for single bandpass-filtered items. It was found that thresholds were low and relatively constant up to disparities an order of magnitude larger than is predicted by this constraint. Furthermore, peak sensitivity was relatively independent of spatial frequency. A control experiment showed that binocular correlation of the carrier is necessary for this task. In a third experiment, the maximum disparity that supports threshold performance was compared for an isolated bandpass item and bandpass-filtered noise. This limit was found to be five times larger for the isolated stimuli. In summary, these findings show that the initial stage of disparity detection is not limited by the size-disparity constraint. For stimuli with multiple false targets, however, processes subsequent to this stage reduce the disparity range over which the correspondence problem can be solved.

Depth Perception↗

Shape and depth perception from parallel projections of three-dimensional motion.

Parallel projections of dots on the surface of a transparent sphere rotating about a vertical axis provide strong impressions of depth and spherical shape. The hypothesis was tested that these impressions are the result of three perceptual heuristics: (a) The sinusoidal projected velocity function of each dot in the horizontal dimension tends to be perceived as a rotary motion in depth; (b) the projected velocity gradient in the vertical dimension is perceived as curvature in depth; and (c) the simultaneously visible fields of dots moving in opposite directions are perceived as surfaces separated in depth. When each factor was varied independently, all three significantly affected judgments of spherical shape and depth. Similar results were obtained with cylinders. The first factor was more important for shape judgments; the second was generally more important for depth judgments. These results, together with those of earlier studies in which these factors led to similar effects for different stimuli and transformations, suggest that these are general principles applicable to the perception of structure from both rigid and nonrigid motion.

Depth Perception↗

Pictorial and motion-based information for depth perception.

When computer-generated objects approached the viewpoint in midair, a large far object appeared to be nearer than a small near object and appeared to hit the viewpoint before the small object, which was specified by time-to-contact information to arrive sooner. These judgements were consistent with relative size and occurred even when motion-based information was potentially above threshold. The effects of relative size persisted with higher resolution animated films of approaching objects, were weakened by ground-intercept information, and were not as robust with laterally translating objects. Although it is often asserted that the kinds of information that have traditionally been called static depth cues are superseded by motion-based depth information, this article attempts to show that the reverse also can occur in distance perception, as has been shown in form perception.

Adult↗

Interactions between self-motion and depth perception in the processing of optic flow.

Moving and acting in a 3D environment requires the perception of its 3D structure. Vision is known to play a crucial role in the control of self-motion, particularly through the changes in the retinal image subsequent to movements of the observer. Reciprocally, signals related to self-motion can also influence our visual perception of 3D space. These interactions between 3D visual perception and self-motion, as demonstrated behaviourally, are now better understood thanks to the development of computational models for processing moving images. They also bear a particular interest in the context of the recent intensive exploration of the inferior parietal lobe (IPL) by neurophysiologists. The IPL is now firmly established as one site of interaction between 3D visual perception and motor control. The parallel between behaviour and neurophysiology leads to a set of crucial, yet unanswered, questions.

Humans↗