Factors Affecting Stimulus Duration Threshold for Depth Discrimination of Asynchronous Targets in the Intermediate Distance Range

Abstract

Purpose: Binocular depth discrimination in the near distance range (< 2 m) improves with stimulus duration. However, whether the same response-pattern holds in the intermediate distance range (approximately 2–25 m) remains unknown because the spatial coding mechanisms are thought to be different.

Methods: We used the two-interval forced choice procedure to measure absolute depth discrimination of paired asynchronous targets (3, 6, or 16 arc min). The paired targets (0.2 degrees) were located over a distance and height range, respectively, of 4.5 to 7.0 m and 0.15 to 0.7 m. Experiment 1 estimated duration thresholds for binocular depth discrimination at varying target durations (40–1610 ms), in the presence of a 2 × 6 array of parallel texture-elements spanning 1.5 × 5.83 m on the floor. The texture-elements provided a visible background in the light-tight room (9 × 3 m). Experiment 2 used a similar setup to control for viewing conditions: binocular versus monocular and with versus without texture background. Experiment 3 compared binocular depth discrimination between brief (40, 80, and 125 ms) and continuous texture background presentation.

Results: Stimulus duration threshold for depth discrimination decreased with increasing disparity in experiment 1. Experiment 2 revealed depth discrimination performance with texture background was near chance level with monocular viewing. Performance with binocular viewing degraded without texture background. Experiment 3 showed continuous texture background presentation enhances binocular depth discrimination.

Conclusions: Absolute depth discrimination improves with target duration, binocular viewing, and texture background. Performance further improved with longer background duration underscoring the role of ground surface representation in spatial coding.

Absolute distance judgments of consecutive objects in the intermediate distance visual space play an important role during navigation, such as when walking, running, or driving. There is evidence showing our visual system uses the prevalent ground surface, where terrestrial creatures populate, as a reference frame for coding spatial locations for distance judgments in the intermediate distance range.^1–4 Empirical findings have revealed the ground-based spatial coding scheme accurately localizes objects on the ground when the horizontal ground surface is continuous and carries rich depth cues (e.g. Loomis et al.,⁵ Loomis et al.,⁶ Ooi et al.,⁷ Philbeck et al.,⁸ Rieser et al.,⁹ Sinai et al.,¹⁰ Thomson,¹¹ and Wu et al.¹²). Absolute distance judgment of an object on the rich ground surface is accurate regardless of whether the observer viewed with one or both eyes, or if the observer had strabismus with reduced stereopsis.¹³ However, when the ground surface is interrupted by a gap, a partially occluding obstacle, or texture boundary, or is limited in its visible extent due to having a small field of view, observers can no longer make accurate distance judgments.^{3,7,10,12,14–20} 

The visual system also uses the ground surface as a reference frame to localize objects that have no physical contact with the ground. It uses the relative depth information between the objects in midair and the ground, such as relative binocular disparity, nested contact relations among surfaces, and relative motion parallax.^{13,18,21–27} Of these, the relative binocular disparity information is the most precise one. For example, in the same study mentioned above, Ooi and He¹³ found observers with normal binocular vision could accurately judge the location of an object suspended above the ground in midair with both eyes viewing, but not when they were only viewing with their dominant eyes. Furthermore, they found that strabismic observers with poor stereoacuity failed to accurately judge the location of the suspended object even with both eyes viewing, attesting to the significant role of relative binocular disparity for judging object location suspended above the ground. 

Along with the need for stereo vision, Wu et al.²⁷ revealed the important role of the ground surface reference frame for localizing an object suspended above the ground surface. They measured the judged location of a dimly lit target above the ground in a reduced cue environment, where the configuration of the ground surface in a totally dark room was only made visible by several sparse texture elements on the floor. Three pairs of texture elements (2 × 3 array) were arranged in two rows along the sagittal depth plane from the observer (Fig. 1A). In the first, parallel-texture condition, the texture elements were parallel to provide linear perspective. In the second, convergent-texture condition, the lateral separations of the paired texture elements were made successively smaller to provide a false convergence perspective (Fig. 1B), which caused the target distance on the ground to be relatively overestimated.^20,27 Confirming the influence of the ground surface configuration, they found observers judged the target suspended above the ground to be farther, and the relative binocular depth between two targets to be larger in the convergent texture condition. This indicates that to localize an object suspended in midair, the visual system first represents the ground surface, and then localizes the target in midair with respect to the ground surface based on its relative binocular disparity to the ground surface (Fig. 1C). 

Figure 1.

 

An illustration of the Wu et al.²⁷ study. (A) Parallel-texture condition. Three pairs of texture elements (2 × 3 array) were arranged in two parallel rows along the sagittal depth plane from the observer to provide linear perspective. (B) Convergent-texture condition. The lateral separations of three pairs of texture elements (2 × 3 array) were made successively smaller to provide a false convergence perspective. (C) Localization of an object suspended in midair. The visual system first represents the ground surface, and then localizes the target in midair with respect to the represented ground surface based on its relative binocular disparity to the ground surface.

Stimulus duration could be another factor affecting the accuracy of judging absolute distance of a suspended target in the intermediate distance range. In the same study by Wu et al.,²⁷ they found that observers showed an advantage for judging target locations with binocular viewing rather than monocular viewing when the stimulus duration was 5 seconds. Interestingly, a shorter stimulus duration of 0.15 seconds did not confer a significant binocular advantage (fig. 5b in the Wu et al. paper). But unlike the Wu et al. paper, most previous empirical studies have mainly focused on determining the effect of stimulus duration on targets viewed within the near distance range (<2 m). Generally, it was found that as stimulus duration increases, relative binocular depth discrimination between two targets improves and eventually reaches an asymptotic level.^28–32 However, it is unknown whether this knowledge obtained with targets in the near distance range could be applied to binocular depth perception in the intermediate distance range as different visual processes/mechanisms are involved (e.g. Ooi and He¹³ and Wu et al.²⁷). 

Human observers can make absolute distance judgment in the near distance range by using external depth information, including accommodation/blur, absolute motion parallax, and absolute binocular disparity.^33–46 However, the effectiveness of these cues are limited to the near distance range (e.g. Beall et al.,³⁷ Fisher and Ciuffreda,³⁸ Campbell,⁴⁷ and Sprague et al.⁴⁸). For instance, let us consider the utility of the convergence state of the eyes (absolute binocular disparity) for judging absolute distance^33–36 (although, see Linton³⁴ for a different perspective on vergence as a cue). As shown in Figure 2A, the visual system can use the vergence angle information (α) to estimate the absolute distance (d) of the fixated object. For a target not on the fixation point, the visual system can in theory use the procedure depicted in Figure 2B to obtain the absolute binocular disparity of the target with respect to fixation (α − α′). This is done by obtaining the vergence angle information at fixation (α) and computing the target's absolute distance (d) based on angle α − α′ and the inter-pupil distance.⁴⁹ However, this computational procedure becomes less reliable for a target located in the intermediate distance range beyond 2.0 m (Fig. 2C). This is because, it has been suggested,³⁵ the magnitude of the absolute binocular disparity of a target (β − β′) beyond 2 m becomes too small to be precise.^35,50,51 One can visually note that the difference in vergence angles (β − β′) in Figure 2C is much smaller than the difference (α − α′) in Figure 2B. Instead, the visual system relies on large continuous surfaces, such as the ground surface, to reliably judge absolute distance in the intermediate distance range (Fig. 1C). Thus, given that the visual system uses different processes for the near and intermediate distance ranges, it is unknown whether stimulus duration influences absolute depth perception in the same manner. The current study further investigated the influence of stimulus duration and binocular disparity on absolute depth perception of a target suspended above the ground. The outcomes of the study will reveal the role of stimulus duration on binocular depth perception in the intermediate distance range. 

Figure 2.

 

Using vergence angle information to judge absolute distance. (A) The vergence angle information (α), obtained by converging the eyes on the target, can be used to estimate the target's absolute distance in the near distance range (<2 m). (B) For a target not being fixated, the visual system can in theory obtain the absolute binocular disparity of the target with respect to fixation (α − α′). This is done by obtaining the vergence angle information at fixation (α) and computing the target's absolute distance (d) based on angle α’ and the inter-pupil distance. (C) For a target in the intermediate distance range > 2 m, vergence angle can no longer serve as an effective cue for absolute distance judgment. This is because the absolute binocular disparity of the target (β − β′) is too small to be meaningful.

Here, we tested the observers’ ability to perceive the difference in absolute distance (i.e. absolute distance discrimination) between two targets suspended above the ground surface in the intermediate distance range, which we presented one after another in a two-interval forced choice (2IFC) protocol. Notably, unlike the typical relative depth discrimination studies where the two targets are viewed at the same time, our protocol had an asynchronous target presentation. This likely induced the observer to estimate each target's absolute depth (distance) and then determine their relative depth. The targets were suspended above the floor and we varied their relative binocular disparity (disparity interval) as well as presentation duration. Figure 3 illustrates an example of the main experimental design. In a dark room, the observer first saw a dimly lit target above an array of texture elements on the floor (see Fig. 3A). After a dark interval (inter-stimulus-interval [ISI] = 500 ms; see Fig. 3B), the observer saw a second dimly lit target of the same angular size and stimulus duration at a different location (see Fig. 3C). The observer was asked to report which of the two targets appeared nearer. We obtained their performance, that is, percentage correct of distance discrimination, as a function of presentation duration, and from which we estimated the duration threshold using the Weibull function that defined the threshold at the 81.6% of the percentage correct performance. (Please refer to the Data Analysis and Statistical Testing section for details.) Overall, our first experiment showed that the duration threshold increased as the depth separation (disparity interval) between the two targets decreased. In our second experiment, we tested a monocular control condition where the observer viewed with only their motor dominant eye,^52,53 and we found they failed to discriminate the target distance (chance level), supporting the advantage of binocular vision. Furthermore, we tested a texture control condition with binocular viewing and found observers showed superior performance when there was a texture array on the floor to serve as the background, than when the texture was absent. This supports the notion that the ground surface acts as a reference frame for localizing a target suspended above the ground. Further emphasizing the significant role of the surface reference frame, experiment 3 showed that continuous presentation of the texture background spanning both 2IFC intervals led to a superior depth discrimination performance. To the best of our knowledge, these findings are the first to reveal the stimulus duration thresholds for binocular depth discrimination in the intermediate distance range. Consequently, they also lay the foundation for future investigations of stimulus duration thresholds for depth judgments in the intermediate distance range in the clinical population, a little researched topic in contrast to the abundant studies conducted in the near distance range. In addition, please refer to the Discussion section on the potential implication for future clinical research. 

Figure 3.

 

An illustration of the main experimental design. (A) In a dark room, the observer first saw a dimly lit target above an array of texture elements on the floor. After a dark interval (B), the observer saw a second dimly lit target of the same angular size and stimulus duration at a different location (C). The observer reported which of the two targets appeared nearer.

Method

Observers

Nine observers (mean age = 24.22 ± 1.47 years) who were naïve to the purposes of the study participated in experiments 1 and 2, and 6 of the 9 observers in experiment 3. They all had normal or corrected-to-normal visual acuity of at least 20/20 (measured with the revised Early Treatment Diabetic Retinopathy Study [ETDRS] chart [Precision Vision, Woodstock, IL, USA] at 3 m) and stereo acuity ≤ 40 arc sec (measured with Frisby Stereotest [Stereotest Ltd., Sheffield, UK]). Informed consent was obtained from the naïve observers after explanation of the nature and possible consequences of the study at the beginning of the study. The research conducted followed the tenets of the Sixth revision of the Declaration of Helsinki and was approved by the Institutional Review Board (IRB). 

Stimulus and Design

Test Environment

All experiments were conducted in an approximately 9 × 3 m rectangular testing room. The room's walls were painted black, with black ceiling tiles and black carpet on the floor to ensure that it was light tight. The layout and dimensions of the room were unknown to the naïve observers. One end of the room (approximately 1 × 3 m), just before the testing area, served as the resting area for the observer. The testing and resting areas were separated by a black curtain. A white LED light on the ceiling in the resting area provided ambient illumination while the observer took breaks. All room lights were switched off during the experiment. 

The resting area also served to prepare the observer for the experiment. It had an adjustable platform on the floor for the observers to stand to maintain their eye height at 170 cm during the experiment. Four fluorescent elements were taped on the platform for the observer to align themselves in the correct position facing the test area. This was done by having the observer step on the fluorescent elements to completely cover the elements, with the front end of their shoes just covering the front pair of fluorescent elements. 

Target and Texture Stimuli

The test target was constructed by housing a red colored LED inside a ping-pong ball to produce an internally illuminated stimulus. The ping-pong ball was then placed in a small box (5 × 5 × 5 cm) that was opaque on all surfaces except one. An adjustable iris diaphragm, serving as the aperture, was attached to the open surface of the box, allowing for the stimulus size to be adjusted to the same angular size (0.2 degrees in diameter). The LED was controlled by an Arduino board (Uno R3) via a Windows 10 computer running on Python that maintained the stimulus luminance at the desired intensity (0.16 cd m⁻² and 0.23 cd m⁻², respectively, for binocular and monocular viewing). (Higher stimulus luminance for monocular viewing, to compensate for binocular summation, was designed to make the subjective brightness similar in the two viewing conditions.) 

The dimly-lit LED target-elements were located in a configuration that achieved the desired relative depth and angular declination (Figs. 4A front view; 4B top view; 4C, 4D side view). Calculated relative to target C₁, targets R₁ and L₁ each had 3 arc min relative binocular disparity, targets R₂ and L₂ each had 6 arc min relative binocular disparity, and targets C₂ and C₃ each had 16 arc min relative binocular disparity. All targets, except C₂ and C₃, had the same angular declination (12.5 degrees) from the eye level. To achieve this, paired targets R₁ and L₁ and R₂ and L₂ were shifted laterally, with a center-to-center angular separations between the pairs of, respectively, 1 degree and 2 degrees. Targets C₂ and C₃ were located, respectively, slightly above (11.9 degrees) and below (13.1 degrees) the angular declination of other targets (12.5 degrees). In linear dimensions, the target locations (x = distance from observer; y = height from floor; and z = lateral shift) were as follows: C₁ = (7.00 m, 0.15 m, and 0 m), R₁ = (6.31 m, 0.30 m, and +0.055 m), L₁ = (6.31 m, 0.30 m, and −0.055 m), R₂ = (5.75 m, 0.43 m, and +0.10 m), L₂ = (5.75 m, 0.43 m, and −0.10 m), C₂ = (4.50 m, 0.70 m, and 0 m), and C₃ = (4.50 m, 0.65 m, and 0 m). 

Figure 4.

 

Schematized views of the experimental design (not-to-scale). (A) Front view of the dimly lit LED target-elements. Paired targets R₁ and L₁ and R₂ and & L₂ had the same angular declination as C₁ (12.5 degrees) and were shifted laterally, with a center-to-center angular separations between the pairs of, respectively, 1 degree and 2 degrees. Targets C₂ and C₃ were located, respectively, slighted above (11.9 degrees) and below (13.1 degrees) the angular declination of other targets. (B) Top view of the dimly lit LED target-elements. Calculated relative to target C₁, targets R₁ and L₁ each had 3 arc min relative binocular disparity, targets R₂ and L₂ each had 6 arc min relative binocular disparity, and targets C₂ and C₃ each had 16 arc min relative binocular disparity. (C, D) Side view of the arrangements of all the dimly-lit LED target-elements and texture-elements. The target-elements were located over a horizontal viewing distance of 4.5 to 7 m from the observer. The difference between C and D were a relative change in the distances of the texture-elements on the floor from the observer: texture A in C was distributed over 1.17 to 7.00 m and texture B in D was distributed over 1.75 to 7.58 m.

During the experiments, target pairs L₁ and R₁, L₁ and R₂, and L₂ and R₁ were used as the catch trial targets. The purpose of having the catch trials was to prevent observers from learning that all the targets were always presented in a set manner. 

The texture stimulus used similarly constructed LED elements as the test target-elements. The luminance of the red texture LED was set at 0.04 cd m⁻² and 0.06 cd m⁻², respectively, for binocular and monocular viewing. For experiments utilizing the texture stimulus, two sets of texture elements spanning the same area on the floor (5.83 × 1.5 m), texture A and texture B, were used (see Figs. 4C, 4D). Each set comprised a 2 × 6 parallel array of the dimly lit LED elements. Elements in the two sets were arranged in an interdigitated manner, 0.58 m apart. The two sets were distributed from the observer over a viewing distance of 1.17 to 7.00 m and 1.75 to 7.58 m, respectively. These two sets of texture arrays were used to help ensure observers based their judgments of absolute distances on perceived depth, rather than on comparison of local 2D geometrical patterns from each 2IFC interval. This is because, in principle, observers could perform the discrimination task based on the relative locations between the target and texture elements. Thus, we reduced the likelihood of observers being dependent on local geometrical patterns by testing with varying combinations of the two different texture patterns during the experiments (please refer to the test procedures below). 

All texture elements had a fixed aperture of 3 cm in diameter. During the experiments, either of the two sets of texture arrays could be presented (in a predetermined manner). 

Test Procedure

We tested observers in an absolute depth discrimination task using the 2IFC psychophysical procedure in all three experiments. Each trial comprised the presentation of paired targets in consecutive intervals and required the observer to judge whether the target in the first or second interval was nearer to them. The paired test targets were elements C₁ and C₂, C₁ and C₃, C₁ and R₁, C₁ and L₁, C₁ and R₂ and C₁ and L₂ (see Figs. 4A & 4B). The catch trial target pairs were L₁ & R₁, L₁ & R₂, and L₂ & R₁. 

The observer stood at the starting point in total darkness to ready for a test trial. A 1000 ms beep sound generated by the computer alerted the observer of the upcoming trial. One thousand milliseconds after the beep, the first of the paired target (e.g. C₁) was presented. A 500 ms ISI followed and the second target (e.g. C₂) was presented. A 25 ms tone accompanied the start of the target presentation at each interval. The target duration was the same for each interval. 

For experiments requiring the texture elements to serve as the background, and depending on the specific experimental condition, the texture stimuli were presented either together with, or before, the target. More details regarding the texture presentation and target durations will be provided along with descriptions of each experiment below. 

The observer was instructed not to make body and head movements during the trial. No feedback regarding their performance was given. Music was played aloud during the experiments to mask possible acoustic cues about the locations of the targets and the experimenter. 

Data Analysis and Statistical Testing

The percentage correct of judging the absolute depth order of the paired targets was calculated. For experiment 1, we fitted the data with the Weibull function to estimate the duration threshold for seeing depth. To do so, the psychometric function at each disparity was fitted using Palamedes 1.11.9⁵⁴ based on the following equation:  

\begin{eqnarray*} \psi \left( {{\rm{x}};\,\alpha ,\,\beta ,\,\gamma ,\,\lambda } \right) &=& \gamma + \left( {1 - \gamma - \lambda } \right){\rm{F}}\,\left( {{\rm{x}};\,\alpha ,\,\beta } \right)\\ &=& \gamma + \left( {1 - \gamma - \lambda } \right)\left[ {1 - {\rm{exp}}\left( { - {{\left( {{\rm{ x }}/{\rm{\alpha }}} \right)}^\beta }} \right)} \right], \end{eqnarray*}

where, F (x; α, β) is the Weibull function; x is the target duration; α is the threshold; β is a free parameter related to the slope of the function; γ is the guessed rate (0.5); and λ is the lapse rate (0). A maximum likelihood method was used to derive the threshold and slope of the psychometric function for each disparity of each subject. We then ran the F-test to determine if the outcomes from the full model (with different slopes across different disparities) and the reduced model (with the same slopes across different disparities) was statistically different. Doing so reveals whether the psychometric slopes were significantly different across the three disparities for each observer. In addition, as can be seen from the equation, when x = α, γ = 0.5, and λ = 0, the threshold level ψ can be calculated as 1–0.5/e = 0.816. Therefore, we determined 81.6% to be the relevant percentage to define the duration threshold. 

The duration threshold data obtained from the Weibull fitting in experiment 1 were analyzed using the linear mixed-effects model analysis. Data from experiments 2 and 3 were analyzed using 2-way ANOVA with repeated measures. The Mauchly's test was applied to verify the assumption of sphericity. 

Experiment 1: Binocular Viewing With Texture Background (in the Dark)

As mentioned above, six paired test targets (C₁ and C₂, C₁ and C₃, C₁ and R₁, C₁ and L₁, C₁ and R₂, and C₁ and L₂ see Fig. 4) were designed to provide relative binocular disparities of 3 arc min, 6 arc min, and 16 arc min. Each trial presented the paired target in a 2IFC manner, accompanied by one of four texture background combinations that were presented along with the two targets. For instance, the first target interval would be presented along with texture A and the second target interval presented along with texture B. The remaining three texture combinations for the first and second intervals were: texture B and texture A, texture A and texture A, and texture B and texture B. Doing so prevented the observers from relying on the set 2D pattern of the texture locations relative to the target between the two intervals, rather than using the perceived absolute target depth in 3D space, to judge which of the two asynchronous targets was nearer to them. The texture background was presented along with the target presentation, and not during the interval between the two targets. We also switched the order of the paired target being presented, for example, paired target C₁ and C₂ would be presented as C₁-first interval and C₂-second interval in one trial and C₂-first interval and C₁-second interval in another trial. Altogether, and before considering target duration as a variable, we had a combination of: 6 (paired test targets with 3 binocular disparities) × 2 (target presentation orders) × 4 (texture A and texture B patterns) = 48 test trial settings. Furthermore, each test trial setting was repeated twice. 

We also intermingled catch trials with the test trials during the experiment. These comprised: 3 (target pairs [L₁ and R₁, L₁ and R₂, and L₂ and R₁]) × 2 (target presented order) × 4 (texture A and texture B patterns) = 24 catch trial settings. These 24 catch trial settings were distributed over 2 experimental sessions with 12 catch trials being included in each session. Therefore, there were 60 trial settings (48 test trials + 12 catch trials) applied to each target duration tested during one experimental session. 

Each observer was tested over 4 or 5 target durations, which ranged from 40 to 1610 ms. Prior to the two formal experimental sessions, the observer was tested in a preliminary session to familiarize them with the experiment and stabilize their responses. This session was also required to determine the range of test durations most suited to obtain a psychometric function for threshold determination. We found most observers could be tested with target durations of 80, 125, 165, and 1610 ms. However, for those observers with a correct rate for judging depth order higher than 81.6% (threshold level) when the target duration was 80 ms, a 40 ms test target duration was added. In addition, for one observer whose correct rate was already at chance level with a target duration of 125 ms at all relative binocular disparities, target durations of 125 ms, 165 ms, 805 ms, and 1610 ms were used for formal testing. Stimuli with longer durations (805 and 1610 ms), in this and the following experiments, were flickered at a rate of 3 Hz to reduce the likelihood of observers experiencing the illusory drifting motion of the target (autokinetic effect).^55,56 

The observers were then tested in two formal experimental sessions on different days. The first session tested from the longest target duration to the shortest duration, and the second session tested in the reverse order. Each target duration was tested over three blocks with 20 trials/block, separated by a 3-minute break. A 5-minute break, in a lighted room outside the testing room, was provided after testing 2 target durations. The order of trials performed within an experimental session of one test duration was randomized, with the second experimental session having the reverse trial order. Each observer used a different randomized test sequence. In this and the following experiments, observers were dark adapted for 5 minutes in the testing room whenever they entered from the lighted room outside. Dark adaptation was done to increase visual sensitivity so that the dimly lit stimuli used in our study were fully visible. Five minutes of dark adaptation ensured the human cone's sensitivity was near optimal.⁵⁷ 

Experiment 2: Roles of Binocularity and Texture Surface as the Ground Reference

We tested all nine observers from experiment 1 in two control conditions (mono-texture and bino-dark) using the stimulus duration of 1610 ms and 3 levels of binocular disparity settings (3, 6, and 16 arc min). The results from these two control conditions were compared with the results from the first experiment (bino-texture) that used the stimulus duration of 1610 ms. 

Control Condition 1 (Mono-Texture): Monocular Viewing With Texture Background

During the experiment, observers were tested with only their motor dominant eyes viewing, while the fellow eye was occluded. Motor eye dominance was determined using the hole-in-the-hand method. We also tested with the longest target duration used to test the observers in experiment 1, which was 1610 ms, to provide for ample viewing time. 

Otherwise, the stimulus design and procedures were the same as that in experiment 1. Namely, the six pairs of test targets (C₁ and C₂, C₁ and C₃, C₁ and R₁, C₁ and L₁, C₁ and R₂, and C₁ and L₂) carrying three relative binocular disparities (3, 6, and 16 arc min) were tested with the four possible texture background combinations (AA, BB, AB, and BA). As such, the total test target trials were: 6 (paired test targets with 3 binocular disparities) × 2 (target presentation orders) × 4 (texture A and texture B patterns) × 2 (repeats) = 96 test trials. Catch trials were included in the experiment. These comprised 3 (target pairs [L₁ and R₁, L₁ and R₂, and L₂ and R₁]) × 2 (target presented orders) × 4 (texture A and texture B patterns) × 1 (repeat) = 24 catch trials. The test and catch trials were intermingled and altogether there were 120 trials, which were broken into 20-trial blocks. Observers received a 3-minute break after the first, second, fifth, and sixth blocks, and a 10-minute break between the third and fourth blocks. Each observer used a different randomized test sequence. 

Control Condition 2 (Bino-Dark): Binocular Viewing Without Texture Background (in the Dark)

Observers were tested with binocular viewing in the absence of the texture array to delineate the floor. The target duration was the same as in the control condition 1 (monocular texture) above, which used the longest stimulus duration that was previously tested on each observer in the experiment 1 (i.e. 1610 ms). The test target trials comprised 6 (paired test targets with three binocular disparities) × 2 (target presentation orders) × 4 (repeats) = 48 test trials. Catch trials were included in the experiment. These comprised 3 (target pairs [L₁ and R₁, L₁ and R₂, and L₂ and R₁]) × 2 (target presented order) × 1 (repeat) = 6 catch trials. The test and catch trials were intermingled and altogether there were 54 trials, which was broken into 3 blocks of 18-trials/block. Observers received a 3-minute break after each block. Each observer used a different randomized test sequence. 

Experiment 3: Binocular Viewing With Prolonged Texture Background

We investigated whether the temporal threshold for depth discrimination would be reduced if the texture background was continuously presented during the 2IFC trial. Our previous works led us to predict having a continuous presence of texture information would allow the visual system to form a more stable representation of the ground surface.^27,58 Here, we tested observers in two new conditions, a “brief texture” condition and a “continuous texture” condition for comparison. The brief texture condition was essentially the same as in experiment 1, where the texture was only presented together with the target and not during the interval between the two targets. The continuous texture condition had the texture visible 1 second before the first target presentation (of the 2IFC protocol), as well as during and in between target presentations. In both conditions, we set the relative binocular disparity of the two paired targets tested (C₁ and R₂ and C₁ and L₂) at 6 arc min. The catch trials used paired stimuli L₁ and R₂ and R₁ and L₂. 

For the brief texture condition, the four texture pattern combinations (AA, BB, AB, and BA), as in experiment 1, were used. This yielded a total stimulus setting of: 2 (paired test targets with 6′ binocular disparity) × 2 (target presentation orders) × 4 (texture A and texture B patterns) = 16 test trial settings. Each test trial setting was repeated twice during the experiment. The catch trials comprised: 2 (target pairs) × 2 (target presented orders) × 4 (texture A and texture B patterns) = 16 catch trial settings. Altogether, there was 48 trial settings (32 test trials + 16 catch trials). These trial settings were applied to the 3 target durations being tested (more on duration below), effectively, bringing the total trials to 144 trials. These 144 trials were blocked into 6 blocks of 24 trials/block over the 2-hour testing session. 

For the continuous texture condition, two texture patterns (AA and BB) were used. This yielded a total stimulus setting of: 2 (paired test targets with 6’ binocular disparity) × 2 (target presentation orders) × 2 (texture A and texture B patterns) = 8 test trial settings. Furthermore, each test trial setting was repeated four times. The catch trials comprised: 2 (target pairs) × 2 (target presented orders) × 2 (texture A and texture B patterns) = 8 catch trial settings. Altogether, there was total of 40 trial settings (32 test trials + 8 catch trials). These trial settings were applied to the 3 target durations being tested (more on duration below), effectively, bringing the total trials to 120 trials. These 120 trials were blocked into 6 blocks of 20 trials/block over the 2-hour testing session. 

The 3 target durations tested in each condition were 40 ms, 80 ms, and 125 ms. The order of test durations tested was from the longest to shortest and then from the shortest to longest. During the experiment, both the brief texture and continuous texture conditions’ blocks were intermingled, with the testing order counterbalanced between observers. 

Results

Experiment 1: Binocular Viewing With Texture Background (in the Dark)

As mentioned in the Methods section, observers were tested over 4 to 5 stimulus durations for each binocular disparity interval between pairs of targets to obtain a percentage correct depth discrimination that straddled the 81.6% threshold level. This was done to fit the data with the Weibull function to derive the duration threshold for depth discrimination (see individual psychometric function fits in Supplementary Fig. S1). Figure 5 plots the average duration threshold as a function of binocular disparity. 

Figure 5.

 

Duration threshold for depth discrimination. The graph plots the average duration threshold as a function of binocular disparity. The average duration thresholds of eight of nine observers are plotted for the 3 and 6 arc min binocular disparity intervals. For the 16 arc min binocular disparity interval, the average duration threshold of 5 of the 9 observers is plotted. The error bars represent the standard errors of the means among observers at each binocular disparity.

Overall, the results reveal a clear trend where the duration threshold decreased with binocular disparity interval. For the 3 and 6 arc min binocular disparity intervals, we were able to obtain the duration threshold for 8 of the 9 observers. The exceptional observer did not reach a performance level above the percentage correct (81.6% threshold criterion) that defines duration threshold at the longest duration (1610 msec) used in our experiment, indicating this observer's duration thresholds at 3 and 6 arc min were longer than that at 16 arc min. For the 16 arc min binocular disparity interval, 4 out of 9 observers’ performance levels were never lower than 81.6% (threshold criterion) for the shortest duration (40 msec) tested, indicating that their duration thresholds at the 16 arc min binocular disparity were shorter than that at 3 and 6 arc min binocular disparities. A linear mixed-effects model analysis showed the duration threshold was significantly associated with binocular disparity (F(2, 2.778) = 295.102, P < 0.001). Post hoc test with Bonferroni correction revealed the duration threshold at 3 arc min was significantly higher than that at 6 arc min (P < 0.001), the duration threshold at 6 arc min was significantly higher than that at 16 arc min (P = 0.023), and the duration threshold at 3 arc min was significantly higher than that at 16 arc min (P < 0.001). 

Experiment 2: Roles of Binocularity and Texture Surface as the Ground Reference

We suggest the finding in Figure 5 above reveals a ground-based binocular depth mechanism, perhaps operating according to a Quasi-2D coding strategy.^27,59 In adopting the strategy, the visual system first represents the ground surface and then defines the coordinates of each individual target with respect to the ground surface that serves as a reference frame (also see Glennerster and McKee,⁶⁰ Mitchison and McKee,⁶¹ and Gillam et al.²² on near stereopsis). This allows the relative disparities between the targets to be transformed into metric depth representations. To investigate this ground-based binocular depth hypothesis, we needed to rule out two potentially confounding factors. The first was that monocular depth cues alone could contribute to depth discrimination. This was because various monocular depth cues, which were beyond our control in a naturalistic viewing protocol such as very small head movements, could not be fully eliminated. Accordingly, we tested a first control condition (mono-texture) where observers viewed the same stimuli as in experiment 1 with their motor dominant eye alone. Thus, if the performance in experiment 1 mainly relied on binocular depth information, depth judgment in this monocular viewing condition was predicted to be at the chance level (approximately 50%). 

The second potentially confounding factor was that the visual system could still make absolute distance discrimination in the dark using vergence angle. Thus, we tested a second control condition (bino-dark) in which observers viewed targets without the texture background in the dark. If the depth discrimination performance in Experiment 1 with the texture background reflected the Quasi-2D coding strategy, performance in the bino-dark control condition was expected to be reduced in the dark without a visible ground surface than that in experiment 1. 

Figure 6 compares the average percentage correct in depth discrimination for all 9 observers as a function of binocular disparity for the data from experiment 1 (bino-texture: red square symbols) against the two control conditions (mono-texture = blue triangle symbols and bino-dark = green circle symbols). Data from all 3 conditions were obtained with a stimulus duration of 1610 ms. Overall, performance in the bino-texture condition was superior to the two control conditions. This suggests that the decrease in duration threshold with binocular disparity reported in Figure 5 reflects the temporal characteristics of a ground-based binocular depth mechanism. The data further highlight the importance of the ground surface in binocular depth perception in the intermediate distance range. Specifically, the average performance in the mono-texture condition (blue triangles) was around the 50% chance level for all binocular disparity intervals, indicating binocular depth information is required for absolute depth discrimination between two targets suspended above the ground. This finding is remarkable because it underscores the preeminence of binocular vision and provides strong empirical evidence that monocular depth cues, such as blur/accommodation, are not effective over the distance range tested. Similarly, the monocular motion parallax depth cue was also likely to be less effective because our observers were standing stationary with little head movements. 

Figure 6.

 

The depth discrimination performance in the Bino-texture, mono-texture, and bino-dark conditions. The average percentage correct in depth discrimination of all nine observers is plotted as a function of binocular disparity for the data from experiment 1 (bino-texture = red square symbols) and the two control conditions (mono-texture = blue triangle symbols and bino-dark = green circle symbols). The stimulus duration was 1610 ms. The error bars represent the standard errors of the means among nine observers at each binocular disparity.

In addition, as predicted, the performance in the bino-dark condition (green circles) where the ground surface was not visible was much lower than in the bino-texture (red squares) condition, especially with target binocular disparities of 3 and 6 arc min (also revealing the vergence signal as a weak cue). Performance in the bino-dark condition was higher for the 16 arc min target. This is possibly due to the substantial depth magnitude of this target (16 arc min) making its absolute binocular depth cue more salient than the 3 and 6 arc min targets when there was no explicit surface representation. The superior performance in the bino-texture condition, compared to the bino-dark condition, supports the notion that a representation of the visible ground surface perhaps according to the Quasi-2D coding strategy improves depth discrimination performance. 

A 2-way ANOVA with repeated-measures showed significant differences among the three different conditions (main effect of condition: F(1.184, 9.476) = 62.910, P < 0.001; main effect of binocular disparity: F(2, 16) = 15.991, P < 0.001; and interaction effect: F(4, 32) = 7.288, P < 0.001). Further planned analysis revealed significant differences when the three conditions were compared in pairs, bino-texture versus bino-dark (main effect of condition: F(1, 8) = 73.411, P < 0.001; main effect of disparity: F(2, 16) = 34.432, P < 0.001; and interaction effect: F(2, 16) = 4.272, P = 0.033); bino-texture versus mono-texture (main effect of condition: F(1, 8) = 291.255, P < 0.001; main effect of disparity: F(2, 16) = 4.280, P =0.032; and interaction effect: F(2, 16) = 3.677, P = 0.049]; bino-dark versus mono-texture (Main effect of condition: F(1, 8) = 6.179, P =0.038; main effect of disparity: F(2, 16) = 8.008, P =0.004; and interaction effect: F(2, 16) = 13.046, P < 0.001; 2-way ANOVA with repeated measures). 

Experiment 3: Binocular Viewing With Prolonged Texture Background

In experiment 1, the target and texture background were presented in synchrony during each test interval of the 2IFC protocol. The texture background was not visible (presented) in between the two (IFC) intervals. Here, we tested a condition (continuous presentation of texture) where the texture was visible for 1 second before the first target presentation (of the 2IFC protocol), as well as during and in between target presentations. We reasoned that should the texture surface act as a reference frame for coding target location, the visual system could be more efficient in extracting target location with a longer texture presentation duration, which would provide for a more stable texture surface representation. This then would lead to a better depth discrimination performance than that in experiment 1 with a brief texture presentation. 

Figure 7 plots the average percentage correct in depth discrimination of the 6 arc min paired targets as a function of stimulus duration for the continuous texture condition and the brief texture condition. Superior performance was found when the texture background was presented continuously rather than briefly (main effect of condition: F(1, 5) = 104.752, P < 0.001; main effect of duration: F(2, 10) = 51.566, P < 0.001; and interaction effect: F(2, 10) = 16.113, P < 0.001, 2-way ANOVA with repeated-measures). This supports our hypothesis that the continuous presence of texture information would allow the visual system to form a more stable representation of the ground surface, benefitting depth discrimination. 

Figure 7.

 

Depth discrimination performance in the continuous texture condition and the brief texture condition. The average percentage correct in depth discrimination (6 arc min binocular disparity) of six observers is plotted as a function of stimulus duration for the continuous texture condition (cyan diamond symbols) and the brief texture condition (red square symbols). The error bars represent the standard errors of the means among the six observers at each duration.

Discussion

Our first experiment revealed that, in the presence of a texture surface background, the stimulus duration threshold for absolute distance discrimination increased as the binocular disparity interval between two asynchronously viewed targets decreased (see Fig. 5). Subsequent control conditions in experiment 2 revealed that with binocular viewing, absolute distance discrimination was better when there was a visible texture surface background than in the dark (see Fig. 6). Thus, experiment 1 revealed the significant dependence on a surface based binocular depth mechanism in the intermediate distance range. Previous studies investigating relative depth detection at the near distance had reported that longer stimulus duration led to lower stereo threshold.^28–32 Although findings from those previous studies at the near distance range resemble those reported here in that both involve temporal integration, the underlying mechanisms are not exactly the same. 

For the surface based binocular depth mechanism, a particular factor determining the stimulus duration threshold could be the integration time needed for constructing the surface reference.^3,12 This notion receives support from experiment 3, which revealed the advantage of a stable background surface for depth discrimination. In contrast, the predominant information supporting relative depth discrimination in the near distance range is vergence angle information, as schematized in Figure 2.^35,50,51 

We recognize, however, that the vergence angle based binocular depth mechanism could work in the intermediate distance range. One way would be to fixate at the first target, maintain the first target's vergence angle during the 2IFC interval in the dark, so that the second target's relative disparity to the previously presented first target could be derived. However, this strategy was less effective than the surface-based mechanism as demonstrated by our control experiment in the dark (see Fig. 6). The inability to maintain a stable vergence angle during the dark interval of the 2IFC test protocol, thus creating vergence noise, could be a significant factor limiting depth discrimination between the two targets in our experiment when the texture surface was not visible in the dark. Indeed, our observers failed to perform above the chance level at the 3 arc min disparity interval, which was smaller than the estimated vergence noise level for inexperienced/naïve psychophysical observers (e.g. Chopin et al.⁶²). 

To the best of our knowledge, the current study is the first to investigate the stimulus duration thresholds for binocular depth discrimination in the intermediate distance range. The findings provide theoretical insights into the surface based binocular depth mechanism. Furthermore, the outcomes of our study highlighting the important role of binocular depth relative to the ground surface has practical implication that will stimulate further clinical science research on space perception in the intermediate distance range. Absolute distance judgments of consecutive objects are frequently performed in the natural 3D environment, especially during navigation (e.g. walking, running, or driving) where observers need to attend to either objects (goals) or obstacles beyond the near distance range for quick decision making and planning of upcoming actions.^63–67 Thus, having a short stimulus duration threshold would allow one to make quick judgments about the 3D depth of objects and obstacles ahead, particularly when one moves at a fast speed. 

Compared to other distance cues, such as motion parallax and shading, binocular disparity cue can lead to a quicker response time to 3D stimuli in both monkeys and humans.⁶⁸ Taken together, it is tempting to speculate that observers with binocular visual deficits would have longer stimulus duration thresholds for discriminating depth in the intermediate distance range. One consequence would be delayed actions/reactions during walking and driving in the natural 3D environment. Grant and Moseley⁶⁴ reviewed studies of functional performance in tasks ranging from eye-hand coordination to walking and driving in people with strabismus and/or amblyopia. Overall, they reported that deficits in stereopsis negatively impacted the various task performance. Maag et al.⁶⁹ found taxi drivers with binocular vision problems stemming from reduced stereopsis or visual acuity less than 20/40 had greater number of crashes per year. Clearly, binocular visual deficits related to failure to utilize binocular disparity information impair not only near, but intermediate visual space perception and action as well. What is less clear is the mechanistic constraints imposed on the visual system that cause a failure to optimally utilize the binocular disparity information especially in the intermediate visual space. Therefore, our findings obtained from observers with clinically normal vision are foundational as both basic and clinical studies of binocular depth perception seldom explore visual performance in the intermediate distance visual space. 

Acknowledgments

Supported by the National Institutes of Health (EY033190 and P30EY032857). 

Disclosure: Y. Chen, None: Z.J. He, None; T.L. Ooi, None