**Purpose**:
We developed a stereo task that is based on a motion direction discrimination to examine the role that depth can play in disambiguating motion direction.

**Methods**:
In this study, we quantified normal adults’ static and dynamic (i.e., laterally moving) stereoscopic performance using a psychophysical task, where we dichoptically presented randomly arranged, limited lifetime Gabor elements at two depth planes (one plane was at the fixation plane and the other at an uncrossed disparity relative to the fixation plane). Each plane contained half of the elements. For the dynamic condition, all elements were vertically oriented and moved to the left in one plane and to the right in another plane; for the static condition, the elements were horizontally oriented in one plane and vertically oriented in another plane.

**Results**:
For the range of motion speed that we measured (from 0.17°/s to 5.33°/s), we observed clear speed tuning of the stereo sensitivity (*P* = 3.0 × 10^{−5}). The shape of this tuning did not significantly change with different spatial frequencies. We also found a significant difference in stereo sensitivity between stereopsis with static and laterally moving stimuli (speed = 0.67°/s; *P* = 0.004). Such difference was not evident when we matched the task between the static and moving stimuli.

**Conclusions**:
We report that lateral motion modulates human global depth perception. This motion/stereo constraint is related to motion velocity not stimulus temporal frequency. We speculate that the processing of motion-based stereopsis of the kind reported here occurs in dorsal extrastriate cortex.

^{1}

^{–}

^{4}Stereopsis exhibits lowpass temporal properties

^{5}in that the faster the disparity is modulated in time, generally the worse the stereo sensitivity (also see Hadani and Vardi

^{6}). The filtering properties of the underlying mechanisms are thought to be spatiotemporally separable and consistent with a spatiotemporal gradient limit.

^{5}These results are pertinent to the early stages of cortical processing involving nondirectionally selective detectors.

^{7}Separate from the temporal modulation of disparity is the dependence of stereopsis on lateral stimulus motion, a property that involves directionally selective detectors in early regions of the cortical pathway.

^{8}In general, the faster the lateral motion, above about 2°/s, the worse the stereopsis.

^{1}For extended grating stimuli, Morgan and Castet

^{9}argued for a fixed spatial phase limit for different spatial frequencies, consistent with a temporal frequency rather than velocity dependence. Hadani and Vardi

^{6}found a very different dependence for a multielement stimulus where all the elements moved in a fixed direction across an abrupt disparity-defined trajectory. Stereopsis was impaired at low velocities (1°/s to 3°/s) and improved at higher velocities (11°/s) where it was equivalent to that for stationary elements. The findings of these two studies appear to be at odds but the stimuli and methods are so fundamentally different that it is likely they reflect very different neural limits.

^{10}

^{–}

^{12}We examined this issue using a limited lifetime, multielements display but with control over spatial frequency. The display consisted of two fields of spatial Gabors moving in opposite directions and distributed in one of two depth planes, one being the fixation plane that was arranged to not coincide with the screen plane. The subject was asked to identify the motion direction of the stimulus in depth (uncrossed disparity). We confined our task to one polarity of disparity to avoid any processing/sensitivity differences that might occur between uncrossed and crossed disparities.

^{13}

^{–}

^{15}We wanted to know how disparity processing and lateral motion processing were related when both kinds of information were required to solve the task. Our intent was to use a task that would access processing at a higher stage in the pathway (i.e., extrastriate cortex) than involved in the simple depth detection of moving stimuli (i.e., striate cortex). Therefore an additional question, concerning the possible site of this stereo/motion interaction, was whether this was a velocity or temporal frequency dependence.

^{16}All stimuli were presented on a gamma-corrected LG D2792PB 3D LED screen (LG Life Science, Seoul, Korea), which had a resolution of 1920 × 1080 pixels and a refresh rate of 60 Hz. We used Bits# Stimulus Processor (Cambridge Research Systems Ltd., Rochester, UK) to generate contrast resolution of 14-bit. Throughout the psychophysical experiments, we dichoptically displayed the stimuli using polarized glasses to the observers in a dark room at a viewing distance of 171 cm. The mean luminance through polarized glasses was 36.5 cd/m

^{2}.

_{min}) of the Gabor elements. We varied the disparity in each trial based on observer's performance with an initial relative step-size of 50% before the first reversal and 20% in all subsequent trials. We used subpixel interpolation for the stimuli by Gaussian windowing each Gabor element and recomputing the peak of the Gaussian function. At the sixth reversal point, the staircase was terminated. To more accurately measure the threshold for stereopsis, we repeated each staircase three times. We averaged the last five reversals of each repetition to compute the threshold and variance; there were 15 reversal points for each condition. Before completing each staircase, subjects performed the alignment task (see Fig. 1A) to ensure correct fusion between their two eyes. During the alignment task, subjects were asked to align four dots so that the distance between the neighboring dots was equal.

_{min}) in arc seconds. Then, we analyzed the difference of stereo sensitivity across different speeds using a one-way repeated-measures analysis of variance (ANOVA) and that across different local Gabor spatial frequencies using a 2-way repeated-measures ANOVA, with their effect size calculated as partial eta squared. We also performed post-hoc pairwise

*t*-tests (with Bonferroni correction) for comparing the stereo sensitivity between each two local Gabor spatial frequencies. Linear mixed-effects models were applied to explore associations of local Gabor spatial frequency with the parameters of the speed tuning function. Furthermore, we compared the values of stereo sensitivity among the conditions shown with static and dynamic (i.e., laterally moving and randomly moving) stimuli at four different local Gabor spatial frequencies using a two-way repeated-measures ANOVA, and conducted a Pearson correlation test to find the relationship between them.

^{17}

^{,}

^{18}:

*φ*is the stereo sensitivity and

*s*corresponds to the stimulus speed in degrees per second. The function has four free parameters.

*φ*represents a general amplitude,

_{0}*A*is the peak amplitude,

*σ*determines the (logarithmic) tuning width,

*s*represents the preferred speed.

_{p}*F*-test for nested models was used to compare the preferred speed and tuning width among the speed tunings of 0.75, 1.5, 3, and 6 cyc/deg local Gabor spatial frequencies for each observer. In particular, we compare the full model where the speed tunings of four local Gabor spatial frequencies have different preferred speeds and tuning widths with the reduced model where the speed tunings of four local Gabor spatial frequencies have identical preferred speeds and tuning widths. For two nested models with

*k*and

_{full}*k*parameters, the

_{reduced}*F*statistic is defined as:

*df*, and

_{1}= k_{full}− k_{reduced}*df*, for

_{2}= N − k_{full}*N*data points. If these two models generate significantly different fits (i.e.,

*P*< 0.05), we choose the full model; otherwise, we take the prediction of the reduced model.

*P*= 3.0 × 10

^{−5}, partial eta squared = 0.497. Note that this tuning for speed occurs at relatively slow speeds.

^{17}

^{,}

^{18}We successfully fitted the individual data (the median R

^{2}value is 0.90) and the averaged data (see Fig. 3, R

^{2}= 0.87) using the model.

^{2}= 0.86, 0.91, 0.84, 0.87 separately). A two-way repeated-measure ANOVA revealed a significant difference in stereo sensitivity among different speeds (F(2.740, 19.181) = 15.459,

*P*= 3.3 × 10

^{−5}, partial eta squared = 0.688) and different local Gabor spatial frequencies (F(3, 21) = 5.957,

*P*= 0.004, partial eta squared = 0.460). No significant interaction was found between speed and local Gabor spatial frequency, F(6.258, 43.808) = 1.727,

*P*= 0.135, partial eta squared = 0.198. Post-hoc pairwise

*t*-test (with Bonferroni correction) showed significant difference between 0.75 cyc/deg and 1.5 cyc/deg, 0.75 cyc/deg and 3 cyc/deg spatial frequencies of Gabors (

*P*= 0.011, 0.001). The results suggested that spatial frequency of Gabors also could affect absolute stereoscopic performance.

*P*= 0.084, partial eta squared = 0.234), but a significant difference among different local Gabor spatial frequencies (F(3, 21) = 3.526,

*P*= 0.033, partial eta squared = 0.335). No significant interaction was found between speed and local Gabor spatial frequency, F(15, 105) = 1.197,

*P*= 0.286, partial eta squared = 0.146. The results indicated that such speed tuning function could not be accounted for by reaction times.

*P*= 0.232, partial eta squared = 0.195) or bandwidth (F(3, 21) = 0.668,

*P*= 0.581, partial eta squared = 0.087). Linear mixed-effects models also showed that the preferred speed and bandwidth were not significantly associated with spatial frequency (

*P*= 0.091 for preferred speed;

*P*= 0.283 for bandwidth).

*F*-test for nested models to statistically compare the difference in preferred speeds and tuning widths among the speed tunings of different local Gabor spatial frequencies. These fits are drawn in Figure 6. According to the

*F*-test for nested models, the full model (with different preferred speeds and tuning widths among speed tunings of four local Gabor spatial frequencies) failed to generate better fits (all

*P*> 0.05) than the reduced model (with the same preferred speeds and tuning widths among speed tunings of four local Gabor spatial frequencies), and the latter successfully accounted for 81.3% to 91.0% of the variance for all observers except S6, and the average observer. These results indicated that the preferred speeds and tuning widths among four speed tunings of different local Gabor spatial frequencies were not significantly different in these observers. For S6, the

*F*-test for nested models showed that the full model generated better fitting (F = 5.407,

*P*= 0.016) than the reduced model and the former successfully accounted for 90.4% of the variance. Applying full model fitting for S6 generated the same conclusions with the present version. These results indicated that different spatial frequencies of Gabors did not make a significant change to the shape of the speed tuning function.

*P*= 0.004, partial eta squared = 0.708; local Gabor spatial frequency: F(1.219,8.532) = 3.031,

*P*= 0.114, partial eta squared = 0.302; Speed × Local Gabor spatial frequency: F(3,21) = 0.426,

*P*= 0.737, partial eta squared = 0.057). Moreover, a two-tailed Pearson correlation test revealed a strong correlation between dynamic and static stereo sensitivities (r = 0.761,

*P*= 4.36 × 10

^{−7}), suggesting that there might be partial common mechanism in stereopsis for static and dynamic stimuli.

*P*= 4.70 × 10

^{−5}). However, no significant difference was found between them for all local Gabor spatial frequencies (two-way repeated measure ANOVA: Speed: F(1,5) = 0.004,

*P*= 0.955, partial eta squared = 0.001; local Gabor spatial frequency: F(3,15) = 9.033,

*P*= 0.001, partial eta squared = 0.644; Speed × Local Gabor spatial frequency: F(3,15) = 1.912,

*P*= 0.171, partial eta squared = 0.277), which indicated that the difference of stereopsis we found in Experiment 3 was not evident when we matched the task between the static and moving stimuli.

*P*= 0.014, partial eta squared = 0.417).

*P*= 0.003, partial eta squared = 0.492; Presentation duration: F(1, 5) = 9.042,

*P*= 0.030, partial eta squared = 0.644; Speed × Presentation duration: F(5, 25) = 1.861,

*P*= 0.137, partial eta squared = 0.271). An

*F*-test for nested models revealed that the reduced model (assuming the tuning curves of 1000 ms and 200 ms presentation durations have same preferred speeds and tuning widths) could generate as good fit as the full model (assuming the tuning curves of 1000 ms and 200 ms presentation durations have different preferred speeds and tuning widths): F = 1.518,

*P*= 0.323. The reduced model successfully accounted for 92.2% for the average result (Fig. 9). These results indicated that the speed tuning function that we reported above could not be accounted for by the potential effects of eye movement.

^{1}

^{,}

^{4}

^{,}

^{9}

^{,}

^{19}Some previous studies

^{1}

^{,}

^{19}have argued that stereo acuities for laterally moving line targets appeared no difference from the static stereopsis if the lateral motion is less than 2°/s motion speed, and increase monotonically at higher velocities. Others

^{4}have argued that there is no difference between the static stereo acuity and stereo acuity at 2°/s motion speed, using random dot stimulus. Our results suggest that there is a bell-shaped dependence with a peak at around 0.67°/s (Fig. 6). Our stimuli (as well as our task) differed from those of previous studies in being locally spatial frequency narrowband and globally distributed in space.

^{17}

^{,}

^{20}Snowden and Kavanagh

^{21}reported that the mean lower threshold of motion for the younger observers was 0.087°/s, which was much slower as the minimum speed we chose for our experiment. What's more, if our slowest stimulus was below the lower threshold of motion, the task (of recognizing which motion direction was in front and which behind) would be rendered impossible since motion would not be perceived. This verifies that the stimulus motion that we measured (from 0.17°/s to 5.33°/s) was well above the lower threshold for motion for our subjects.

^{9}and global

^{5}stereopsis reported in previous studies was the evidence for velocity tuning in the current study. It is likely that the use of random Gabor stimuli may necessitate a more global process that would occur at a later site in the pathway where the outputs of earlier spatiotemporally separable filter have been combined to extract motion velocity (e.g., Priebe, Lisberger and Movshon

^{8}). Consistent with this, the log Gaussian form of the tuning response we measure psychophysically is similar to that found for speed tuning dependence of MT neurons for random-dot stimuli,

^{17}which in turn may suggest the involvement of area MT in process of stereopsis for spatially distributed stimuli of the sort used here. Studies for the speed tuning of macaque MT neurons also suggest that different units of MT neurons prefer different speeds, containing both slow and high speed within the range that we investigated.

^{17}

^{,}

^{20}Because the tuning for speed we found occurs at relatively slow speeds with a preferred speed at around 0.67°/s, MT neurons tuned to very slow speeds may contribute to the stereo judgements in our study.

^{22}

**Y. Chen,**None;

**Z. Yao,**None;

**Z. He,**None;

**Z. Cheng,**None;

**P.-C. Huang,**None;

**S.H. Min,**None;

**F. Lu,**None;

**R.F. Hess,**None;

**J. Zhou,**None

*J Opt Soc Am*. 1978; 68: 450–455. [CrossRef] [PubMed]

*J Am Optom Assoc*. 1985; 56: 712–715. [PubMed]

*Proc SPIE*. 2013; 8648: 86480O.

*Invest Ophthalmol Vis Sci*. 2016; 57: 3545–3553. [CrossRef] [PubMed]

*J Neurosci*. 2014; 34: 1397–1408. [CrossRef] [PubMed]

*Percept Psychophysiol*. 1987; 42: 158–165. [CrossRef]

*J Neurosci*. 2004; 24: 2065–2076. [CrossRef] [PubMed]

*J Neurosci*. 2006; 26: 2941–2950. [CrossRef] [PubMed]

*Nature*. 1995; 378: 380–383. [CrossRef] [PubMed]

*J Neurophysiol*. 1983; 49: 1148–1167. [CrossRef] [PubMed]

*Neural Comput*. 1996; 8: 1449–1461. [CrossRef] [PubMed]

*Neuron*. 2003; 37: 525–535. [CrossRef] [PubMed]

*Vis Res*. 1999; 39: 331–339. [CrossRef] [PubMed]

*J Neurosci*. 2008; 28: 11315–11327. [CrossRef] [PubMed]

*Neuroimage*. 2018; 168: 358–365. [CrossRef] [PubMed]

*J Neurosci*. 2005; 25: 10049–10060. [CrossRef] [PubMed]

*Cereb Cortex*. 2009; 19: 1957–1967. [CrossRef] [PubMed]

*Vis Res*. 2005; 45: 789–799. [CrossRef] [PubMed]

*J Neurosci*. 2003; 23: 7647–7658. [CrossRef] [PubMed]

*Perception*. 2006; 35: 9–24. [CrossRef] [PubMed]

*Annu Rev Neurosci*. 2004; 27: 649–677. [CrossRef] [PubMed]