Depth Discrimination Thresholds Research Articles

The impact of retinal motion on stereoacuity for physical targets

In a series of studies using physical targets, we examined the effect of lateral retinal motion on stereoscopic depth discrimination thresholds. We briefly presented thin vertical lines, along with a fixation marker, at speeds ranging from 0 to 16 deg·s−1. Previous investigations of the effect of retinal motion on stereoacuity consistently show that there is little impact of retinal motion up to 2 deg·s−1, however, thresholds appear to rise steeply at higher velocities (greater than 3 deg·s−1). These prior experiments used computerized displays to generate their stimuli. In contrast, with our physical targets we find that stereoacuity is stable up to 16 deg·s−1, even in the presence of appreciable smearing due to visual persistence. We show that this discrepancy cannot be explained by differences in viewing time, prevalence of motion smear or by high frequency flicker due to display updates. We conclude that under natural viewing conditions observers are able to make depth discrimination judgements using binocular disparity signals that are rapidly acquired at stimulus onset.

Lateral interference, effects of flankers and reference bar configuration on foveal depth discrimination thresholds

Lateral interference, effects of flankers and reference bar configuration on foveal depth discrimination thresholds

Stereoacuity in the periphery is limited by internal noise.

It is well-established that depth discrimination is finer in the fovea than the periphery. Here, we study the decline in depth discrimination thresholds with distance from the fovea using an equivalent noise analysis to separate the contributions of internal noise and sampling efficiency. Observers discriminated the mean depth of patches of "dead leaves" composed of ellipses varying in size, orientation, and luminance at varying levels of disparity noise between 0.05 and 13.56 arcmin and visual field locations between 0° and 9° eccentricity. At low levels of disparity noise, depth discrimination thresholds were lower in the fovea than in the periphery. At higher noise levels (above 3.39 arcmin), thresholds converged, and there was little difference between foveal and peripheral depth discrimination. The parameters estimated from the equivalent noise model indicate that an increase in internal noise is the limiting factor in peripheral depth discrimination with no decline in sampling efficiency. Sampling efficiency was uniformly low across the visual field. The results indicate that a loss of precision of local disparity estimates early in visual processing limits fine depth discrimination in the periphery.

Differential motion parallax as a monocular depth cue?

Computing the distance of an object from motion parallax involves the comparison of the displacement or velocity of the observer’s eye with the hereby induced displacement or velocity of the object on the retina. Motion parallax computation therefore requires knowledge about the relative speed between the observer and the object. In many situations this information is not available to the observer -either because the observer or the object moves with an unknown velocity. Theoretically, one could still determine distance by moving with two different speeds and employing only knowledge about the difference between them. We refer to this mechanism as “differential motion parallax” and we assume that many birds use this mechanism to monocularly measure distance in the lateral visual field. Here, we examine whether humans are capable of using differential motion parallax. Observers had to indicate whether a central, horizontal array of small squares was before or behind a plane represented by two flanking horizontal arrays. We measured depth discrimination thresholds for the monocularly viewed patterns with and without adding a constant, but from trial to trial unpredictibly varying motion component to the stimulus. Since motion parallax was the only cue, subjects had to make lateral translational movements with their upper body in order to solve the task. If the stimulus did not move, subjects demonstrated a high accuracy (in average 0.2 % of the viewing distance). Adding a constant speed of the same magnitude to both the central pattern and the flanking arrays did only slightly impair this performance. However, when adding constant, randomly chosen speeds independently to both patterns, the threshold increased dramatically, suggesting that the human visual system is not able not take advantage of differential motion parallax.

The intrinsic constraint approach to cue combination: An empirical and theoretical evaluation

We elucidate two properties of the intrinsic constraint (IC) model of depth cue combination (F. Domini, C. Caudek, & H. Tassinari, 2006). First, we show that IC combines depth cues in a weighted sum that maximizes the signal-to-noise ratio of the combined estimate. Second, we show that IC predicts that any two depth-matched pairs of stimuli are separated by equal numbers of just noticeable differences (JNDs) in depth. That is, IC posits a strong link between perceived depth and depth discrimination, much like some Fechnerian theories of sensory scaling. We test this prediction, and we find that it does not hold. We also find that depth discrimination performance approximately follows Weber's law, whereas IC assumes that depth discrimination thresholds are independent of baseline stimulus depth.

Comparison of level discrimination, increment detection, and comodulation masking release in the audio- and envelope-frequency domains.

In general, the temporal structure of stimuli must be considered to account for certain observations made in detection and masking experiments in the audio-frequency domain. Two such phenomena are (1) a heightened sensitivity to amplitude increments with a temporal fringe compared to gated level discrimination performance and (2) lower tone-in-noise detection thresholds using a modulated masker compared to those using an unmodulated masker. In the current study, translations of these two experiments were carried out to test the hypothesis that analogous cues might be used in the envelope-frequency domain. Pure-tone carrier amplitude-modulation (AM) depth-discrimination thresholds were found to be similar using both traditional gated stimuli and using a temporally modulated fringe for a fixed standard depth (ms = 0.25) and a range of AM frequencies (4-64 Hz). In a second experiment, masked sinusoidal AM detection thresholds were compared in conditions with and without slow and regular fluctuations imposed on the instantaneous masker AM depth. Release from masking was obtained only for very slow masker fluctuations (less than 2 Hz). A physiologically motivated model that effectively acts as a first-order envelope change detector accounted for several, but not all, of the key aspects of the data.

Neural Rate and Timing Cues for Detection and Discrimination of Amplitude-Modulated Tones in the Awake Rabbit Inferior Colliculus

Neural responses to amplitude-modulated (AM) tones in the unanesthetized rabbit inferior colliculus (IC) were studied in an effort to establish explicit relationships between physiological and psychophysical measures of temporal envelope processing. Specifically, responses to variations in modulation depth (m) at the cell's best modulation frequency, with and without modulation maskers, were quantified in terms of average rate and synchronization to the envelope over the entire perceptual dynamic range of depths. Statistically significant variations in the metrics were used to define neural AM detection and discrimination thresholds. Synchrony emerged at modulation depths comparable with psychophysical AM detection sensitivities in some neurons, whereas the lowest rate-based neural thresholds could not account for psychoacoustical thresholds. The majority of rate thresholds (85%) were -10 dB or higher (in 20 log m), and 16% of the population exhibited no systematic dependence of average rate on m. Neural thresholds for AM detection did not decrease systematically at higher SPLs (as observed psychophysically): thresholds remained constant or increased with level for most cells tested at multiple sound-pressure levels (SPLs). At depths higher than the rate-based detection threshold, some rate modulation-depth functions were sufficiently steep with respect to the across-trial variability of the rate to predict depth discrimination thresholds as low as 1 dB (comparable with the psychophysics). Synchrony, on the other hand, did not vary systematically with m in many cells at high modulation depths. A simple computational model was extended to reproduce several features of the modulation frequency and depth dependence of both transient and sustained pure-tone responders.

Stereopsis, cyclovergence and the backwards tilt of the vertical horopter

It is generally recognized that the vertical horopter has a backwards tilt such that it passes through the fixation point and a point near the feet of the observer. The basis of the tilt has been attributed to either a shear in binocular retinal correspondence along the vertical meridian or the presence of cyclovergence eye movements. In an attempt to determine empirically the mechanisms underlying the tilt of the vertical horopter, retinal correspondence along the vertical meridian was investigated as a function of viewing distance. In addition, binocular measurements of torsional eye position were made in the same observers under similar viewing conditions. The vertical horopter was determined using two criteria. In the first instance, increment depth discrimination thresholds for both crossed and uncrossed disparities were measured as a function of retinal eccentricity along the vertical meridian, up to 5° superiorly and inferiorly, and the horopter was defined by the region in space which had the lowest stereo-threshold. Secondly, subjective alignment of dichoptically presented nonius lines defined the horopter by identical visual directions. Both criteria were used to determine the horopter at 2 m while only the criterion of identical visual direction was used at the nearer distance of 50 cm. The vertical horopter showed a backwards tilt that decreased from an average of about 12° at 2 m to 3° at 50 cm, with some variability between observers. Torsional eye position did not change significantly between fixation distances. These results confirmed the geometric relation between the backwards tilt in the vertical horopter and fixation distance and support Helmholtz’s original contention that the tilt is a consequence of a shear in retinal correspondence in the vertical meridian.

Stereopsis, spatial frequency and retinal eccentricity

Stereoscopic depth discrimination thresholds increase with retinal eccentricity and distance from the horopter. However, in contrast to spatial resolution, the effects of spatial frequency on stereothresholds in the periphery are unknown. For spatial vision, it is generally assumed that the retina is comprised of a series of overlapping spatial filter mechanisms and that there is a commensurate increase in spatial scale as a function of retinal eccentricity. If the same holds true for mechanisms sensitive to stereoscopic depth, then stereo-thresholds for low spatial frequency stereoscopic stimuli may remain relatively invariant across the visual field, while rhresholds for relatively high spatial frequency stimuli would increase. To further understand the role of the disparity sensitive mechanisms involved in depth discrimination, increment depth discrimination thresholds for both crossed and uncrossed disparities were measured as a function of eccentricity for retinal locations up to 10.0 deg along the horizontal meridian. We found that stereoscopic depth discrimination thresholds, as a function of distance from the horopter, increased in an exponential manner irrespective of spatial frequency. Stereo-thresholds also increased as a function of retinal eccentricity, however, the rate of increase depended on the spatial frequency composition of the stimuli. Best stereo-thresholds for stimuli composed of low spatial frequencies remained relatively invariant for retinal eccentricities up to 10.0 deg, while thresholds for the high spatial frequency stimuli increased with eccentricity.

Effects of the spatial frequency of test and reference stimuli on stereo-thresholds

The perceived depth of adjacent regions of stereoscopic stimuli may be influenced, in part, by differences in the spatial frequency composition of adjacent stimuli. Consequently, it would be predicted that, if the test and reference stimuli differ in their spatial frequency composition, depth discrimination thresholds should be asymmetric about the retinal disparity of the reference stimulus. We measured depth discrimination thresholds with test and reference stimuli that differed by up to 2 octaves in their spatial frequency composition. Stereothresholds decreased as a function of spatial frequency to about 2–4 c/deg and were then constant. However, in contrast to the predicted effects, our results show that, for the range of spatial frequencies used, differences of up to 2 octaves in spatial frequency, between test and reference stimuli, do not affect depth discrimination thresholds.

Precision of stereoscopic depth perception from double images

The increment depth discrimination function was originally described by Ogle (1953) Journal of the Optical Society of America, 43, 906–913 as a single exponential function. In contrast, recent studies have suggested that a two-component function better describes increment depth discrimination. To determine the relative effects of stereoscopic and non-stereoscopic width cues on the form of the function, we measured increment depth discrimination under conditions where both stereoscopic and dichoptic width cues were available. We found that increment depth discrimination data were well described by two-segment functions if both stereoscopic and dichoptic width cues were available. However, when dichoptic width cues were eliminated, by randomizing the pedestal disparity (crossed or uncrossed disparity) between trials, the increment depth discrimination function was better described by a single exponential function. This result has important implications for models of stereoscopic depth processing because it shows that stereoscopic depth discrimination thresholds progressively increase as a function of distance from the horopter.

Surface segmentation mechanisms and motion perception

Two studies are presented which explore how depth information is determined from conditions of transparency and whether this information combines with other depth information to determine the segmenting of motion information on the basis of likely surface boundaries. The first study explored how binocular disparity combines with monocular depth cues associated with transparency to determine whether subjects see one or multiple surfaces in depth in static displays. When transparency provided a depth cue that was consistent with binocular disparity, depth discrimination thresholds were at normal levels. However, if transparency was inconsistent with the binocular disparity, depth discrimination thresholds were elevated, indicating that subjects had difficulty seeing distinct surfaces lying in separate depth planes. Moreover, threshold elevations were found to correspond to the reductions in contrast between the intersecting contours of the stimulus, suggesting that the strength of perceived depth from transparency is the result of attenuated responses from competing contrast sensitive T-junction mechanisms responsible for the detection of opaque occlusion. A second experiment explored whether the grouping of local motion signals relied on surface interpretations that result from the interaction of transparency and disparity. Surface interpretations were manipulated in moving plaids by combining transparent layering and binocular disparity to show that the motion arising from contours is grouped together (pattern motion) when these cues support the existence of a single surface, and is segregated (component motion) when they support separate surfaces. When these cues were consistent, only small disparity differences were required for the gratings to appear as separately moving surfaces. However, when they were inconsistent, greater disparities were required (about a factor of 2 greater). Taken together, these studies demonstrate that the grouping of local motion information is not resolved within the motion system alone. Information seemingly unrelated to motion processing, namely surface segmentation cues, is used to determine whether or not motion information arising from various contours is pooled together to determine a single motion.

Depth discrimination of a line is improved by adding other nearby lines

Depth discrimination thresholds are shown to be lowered by up to a factor of 10 when a few reference lines are added to a stimulus containing a single isolated test line. Four reference lines are better than two, which are better than one, and the improvement in performance is greater when the test line lies between the two reference lines in depth. Stereoacuity for the relative depth of a target line, relative to other nearby reference lines, is shown to be insensitive to changes of disparity of the whole pattern of up to about ± 5arc min and is only weakly sensitive to larger displacements of up to ±10arc min.

Modulation detection interference: Interference for discriminating a change in the depth of amplitude modulation

Discrimination of a change in the depth of sinusoidal amplitude modulation of a sinusoidal probe carrier was measured in a modulation detection interference (MDI) paradigm (discrimination between [1 + mb cos(2πfmt)] [cos)2πfρt)] and [1 + mρ cos(2πfmt)] × [cos(2πfρt)], where mb = baseline depth of modulation; mρ = probe‐tone modulation depth to be discriminated from mb; fm = amplitude modulation rate; and fc = carrier frequency). Three conditions were tested for each carrier frequency (1000 and 4000 Hz) and baseline depth (0%, 25%, 50%, 75%, and 100%): probe alone conditions depth discrimination was measured for the probe‐tone carrier presented by itself; unmodulated masker condition—depth discrimination was measured for the probe‐tone carrier when an unmodulated masker tone was simultaneously presented at the other tonal carrier frequency; and modulated masker condition—depth discrimination was measured when the masker tone was sinusoidally amplitude modulated at 100% depth and at the same rate (11, 20, or 32 Hz) as the probe tone. The depth of discrimination thresholds averaged over five listeners for both probe‐tone carrier frequencies for all three modulation rates, and for both the probe alone and unmodulated masker conditions, was approximately the same and decreased as the baseline depth increased from 0% to 100%. However, depth discrimination thresholds increased dramatically for all modulated masker conditions that indicated significant modulation detection interference for depth discrimination as has been shown for modulation detection and modulation rate discrimination [Yost et al., J. Acoust. Soc. Am. 86, 2138–2147 (1989)]. The results will be discussed in terms of cross‐spectral modulation interactions. [Work supported by NIDCD and AFOSR.]

Neural model of stereoacuity and depth interpolation based on a distributed representation of stereo disparity [published erratum appears in J Neurosci 1991 Mar;11(3):following Table of Contents

We have developed a model for the representation of stereo disparity by a population of neurons that is based on tuning curves similar in shape to those measured physiologically (Poggio and Fischer, 1977). Signal detection analysis was applied to the model to generate predictions of depth discrimination thresholds. Agreement between the model and human psychophysical data was possible in this model only when the population size representing disparity in a small patch of visual field was in the range of about 20-200 units. Interval encoding and rate encoding were found to be inconsistent with these data. Psychophysical data on stereo interpolation (Westheimer, 1986a) suggest that there are short-range excitatory and long-range inhibitory interactions between disparity-tuned units at nearby spatial locations. We extended our population model of disparity coding at a single spatial location to include such lateral interactions. When there was a small disparity gradient between stimuli at 2 locations, units in the intermediate, unstimulated position developed a pattern of activity corresponding to the average of the 2 lateral disparities. When there was a large disparity gradient, units at the intermediate position developed a pattern of activity corresponding to an independent superposition of the 2 lateral disparities, so that both disparities were represented simultaneously. This mixed population pattern may underlie the perception of depth discontinuities and transparent surfaces. Similar types of distributed representations may be applicable to other parameters, such as orientation, motion, stimulus size, and motor coordinates.

Neural Models of Binocular Depth Perception

We have developed a model for the representation of stereo disparity by using a population of neurons that is based on tuning curves similar in shape to those measured physiologically (Lehky and Sejnowski 1990). The model predicts depth discrimination thresholds that agree with human psychophysical data only when the population size representing disparity in a small patch of visual field was in the range of about 20-200 units. This population model of disparity coding at a single spatial location was extended to include lateral interactions, as suggested by psychophysical data on stereo interpolation (Westheimer 1986a). Disparity is a measure of depth relative to the plane of fixation. Additional sources of information are needed to estimate the distance to the point of fixation, such as that provided by eye vergence, vertical disparity, and accommodation. We have developed a simple model that combines disparity information in a distributed representation and vergence information to compute the absolute depth of objects from the observer (Pouget and Sejnowski 1990). Although these are models of binocular vision, a number of the ideas presented here generalize to the representations of other sensory cues.

Binocular depth perception in the cat following early corpus callosum section.

The role of the corpus callosum in the mediation of binocular depth perception was examined by measuring monocular and binocular depth discrimination thresholds in cats which had undergone section of the corpus callosum shortly after birth. Three kittens had the posterior callosum sectioned at the age of eleven days. A fourth kitten underwent a sham operation and one additional animal served initially as an unoperated control. Monocular and binocular depth thresholds were measured for all kittens when they were between three and five months old. Although there was some individual variability, none of the callosum-sectioned kittens showed any deficits of binocular depth perception relative to normal animals. The initially unoperated kitten had its callosum sectioned at five months and was retested following surgery. Its performance did not change from preoperated levels. Finally, the three neonatal callosum-sectioned kittens underwent section of the optic chiasm when they were six months old, causing a complete breakdown in binocular depth discrimination. The results are interpreted to indicate that although the corpus callosum may be a sufficient pathway for the maintenance of stereopsis in cat, it is not necessary.

The effects of early and late monocular deprivation on binocular depth perception in cats

Binocular and monocular depth discrimination thresholds were obtained from cats which had been monocularly deprived either from the time of natural eye opening or else at the age of 4 months. Among normal cats, binocular depth thresholds typically are very much better than monocular thresholds, allowing the inference that normal cats have good stereopsis. For the early-deprived animals in the present study, only those whose deprived eyes were opened by 30 days of age showed any binocular advantage. Deprivation periods lasting to 35 days or older completely eliminated the binocular superiority, with no sign of any recovery. These results provide behavioral evidence that binocular visual mechanisms are extremely susceptible to disruption and, unlike those underlying visual acuity, do not have the potential for recovery. The effect of deprivation imposed later in life was quite different. Three cats, deprived for 1, 2 or 3 months respectively, beginning at the age of 4 months, showed no deficits in binocular depth perception. This latter finding implies the existence of a sensitive period for stereopsis which is over completely by the age of 4 months.

Variability of depth-discrimination thresholds as a function of observation distance.

Variability of depth-discrimination thresholds as a function of observation distance.

Effect of target-background luminance contrast on binocular depth discrimination at photopic levels of illumination

Data are presented on binocular depth-discrimination thresholds for stationary and oscillating black or self-illuminated targets which are presented against a large illuminated background. The stereoscopic threshold angle, η AD is measured at target-background contrast values ranging from0 to ± 100 per cent at five fixed levels of target or background retinal illuminances (−1.22, −0.57, 1.02, 1.57, and 2.06 log td). The results show that for target-background contrasts greater than some critical near-zero value, the magnitude of η AD is determined by the prevailing retinal illuminance of that component, either target or background, which has the higher illumination level. The data for the target-varied and for the background-varied conditions were essentially identical, suggesting the absence of any areal effects. An analysis of the corresponding constant errors of the equidistance settings, η ΔR is also presented, and the results for η ΔR are similar to those for η AD , but somewhat more variable. A schematic representation which predicts the results of contrast effects greater than near-zero values is presented, based on the relationship between stereoscopic threshold and target or background illumination level under 100 per cent contrast conditions.