Eight human subjects (3 female) participated in this study. Informed consent was obtained from all participants and all procedures were reviewed and approved by the human subjects committee of Washington University.
Subjects were seated in a padded racing seat mounted on a 6-degree-of-freedom Moog© motion platform. A 3-chip DLP projector (Galaxy 6; Barco, Kortrijk, Belgium) was also mounted on the motion platform behind the subject and front-projected images onto a large (149×127 cm) projection screen via a mirror mounted above the subject’s head. The projection screen was located ~70 cm in front of the eyes, thus allowing for a visual angle of ~94°×84°. A 5-point harness held subjects’ bodies securely in place and a custom-fitted plastic mask secured the head against a cushioned head mount thereby holding head position fixed relative to the chair. Subjects were enclosed in a black aluminum superstructure, such that only the display screen was visible in the darkened room. Subjects also wore active stereo shutter glasses (CrystalEyes 3; RealD, Beverly Hills, CA), thereby restricting the field of view to ~90°×70°. Eye position was recorded for both eyes at 600 Hz via a video-based eye-tracking system (ISCAN©) attached to the stereo glasses and subjects were instructed to look at a centrally-located, head-fixed target throughout each trial. Sounds from the platform were masked by playing white noise through headphones. Behavioral tasks and data acquisition were controlled by Matlab and responses were collected using a button box. Additional details specific to the human apparatus can be found in recent publications 
Experimental Protocol: Main Experiment
The visual scene consisted of a 3-dimensional (3D) starfield composed of randomly placed triangles with base and height of 1 cm. The triangles filled a volume 170 cm wide ×170 cm tall× 100 cm deep and the 3D density of triangles was 0.001 triangles/cm3
. With this density and viewing frustum, ~1000 triangles were rendered on a given frame. The nearest and farthest rendered triangles subtended ~3° and ~0.6°, respectively. A spherical object (diameter of 10 cm, i.e., ~8°) was rendered at the same depth as the screen, and located to the left of the fixation point, ~27 cm (~21°) away. The object was also composed of random triangles and the density of triangles within the volume of the object was the same as for the starfield, such that the object was distinguished only by its velocity relative to the background motion. Given the volume of the sphere and its density, ~4 triangles were rendered within the sphere on a given video frame. Motion coherence of the starfield and object was set to 70% and the elements of the scene were limited-lifetime (1 sec). Note, reduced motion coherence was used to make the relative reliabilities of the visual and vestibular self-motion cues more equal 
, and to allow comparison with heading discrimination data collected under the same conditions with a range of heading eccentricities 
. To prevent pop-out of the object relative to the background, object motion coherence matched coherence of the background star field.
Each trial simulated a 13cm, 1s translation of the subject relative to the starfield and object. The object was simultaneously displaced either upward or downward relative to the starfield and the subject’s task was to indicate whether the object moved upward or downward relative to the world (). Note that we did not attempt to evaluate whether subjects made their judgments in world or screen coordinates. However, regardless of the coordinate frame of the judgment, subjects had to parse the optic flow field to perform the task. Thus, for this task, we do not suspect that the basic conclusions of the present study would change depending on the strategy used by the subjects.
Schematic of the experimental design.
The simulated self-motion and object motion followed synchronized Gaussian velocity profiles, such that the object could not be distinguished simply by having a different temporal profile of motion than the background. Given this velocity profile, the peak simulated visual and vestibular speed of self-motion was 30 cm/s and peak acceleration/deceleration was 1.13 m/s2
. This dynamic stimulus was chosen because: (1) it is a smooth, transient, natural stimulus, (2) it evokes robust visual and vestibular responses in cortical multisensory neurons (e.g., areas MSTd and VIP; both visual and vestibular responses tend to reflect stimulus velocity more than acceleration 
), (3) it results in near-optimal multisensory integration, both at the level of behavior 
and at the level of single neurons 
Due to the independent object motion in the scene, the retinal image motion associated with the object deviated from that of the surrounding optic flow (). Deviation angle was varied from trial to trial according to a staircase procedure. The staircase began at the largest deviation angle and possible deviation angles were +/− [80° 64° 48° 32° 16° 8° 4° 2° 1° 0.5° 0.25°]. The deviation angle was reduced 30% of the time after correct responses and was increased 80% of the time after incorrect responses. This staircase rule converges to the 73% point of the psychometric function. The deviation angle was positive (upward) on 50% of trials and negative (downward) on the other 50%.
The angle of deviation is given by
, respectively, are the independent velocity components (in screen coordinates) associated with self-motion and object motion, respectively (). The self-motion component (vs
) depended on heading angle but was constant for a given heading (peak velocity of 10.2°/s, 20.7°/s, 24.0°/s, and 20.8°/s for headings of 0°, 30°, 60°, and 90°, respectively). Deviation angle (d) for a given trial was specified by the staircase procedure. Object speed on the screen (vo
) was therefore constrained to satisfy the above equation.
Four different heading directions were examined (0°, 30°, 60°, and 90° from straight ahead, ), with data for each heading angle collected in a separate block of trials. Trials for visual-only and combined (visual/vestibular) conditions were interleaved within a given block (200 trials/block, lasting ~25 min). This made for a total of 8 stimulus conditions in the Main Experiment. At least 800 trials per condition per subject (6 subjects, S1-S6) were collected.
Experimental Protocol: Eye-movement Control
Because no eye movement data were recorded initially, we repeated the visual-only and combined protocols in a second experiment for the lateral (90°) heading only, while recording eye movements. This was necessary to verify that subjects maintained fixation equally well during both visual-only and combined visual-vestibular trials. At least 500 trials per subject per condition were collected in 5 subjects (S4-S8) for the second experiment.
Experimental Protocol: Retinal-speed Control
Finally, in a third experiment, observers were presented with visual-only trials, as described above, except that the simulated distance of translation was reduced to <13cm (6.75, 5.56, and 6.13 cm for heading directions of 30°, 60° and 90°, respectively) in order to achieve the same retinal image speed (vs in ) at the eccentric location where the moving object was presented (vs equal to 10.2°/s for all headings). This control experiment was necessary to examine to what extent the observed dependence of object motion discrimination thresholds on heading direction was simply a result of changes in retinal speed. Because translation distance was fixed in the first experiment, vs increases with eccentricity, such that effects of heading eccentricity (i.e. flow-field geometry) and retinal speed are confounded. At least 600 trials per subject per condition were collected in 5 subjects (S4-S8) for the third experiment.
For each subject and each condition we plotted the proportion of ‘upward’ responses as a function of object deviation angle and a cumulative Gaussian function was fit to these data using psignifit software 
. Threshold is given by the standard deviation of the fitted function. A two-factor repeated measures ANOVA was performed on threshold data from the Main Experiment to examine the effect of heading eccentricity (0°, 30°, 60°, 90°), the effect of condition (visual-only, combined), and their interaction. Data were further examined using paired t-tests. Threshold data from the Retinal-speed Control experiment were analyzed with a one-factor repeated measures ANOVA to examine the effect of heading eccentricity (0°, 30°, 60°, 90°) when retinal speed at the object location was matched across headings.
To analyze eye movement data, horizontal eye position traces were first smoothed by applying a boxcar filter and then differentiated to obtain eye velocity traces for both eyes. From these traces we calculated mean eye velocity during the stimulus presentation (1s) on each trial and then examined how psychophysical threshold changed as a function of mean eye velocity for each subject. Over the entire range of mean eye velocities, we used a sliding window 1°/s wide, and fit a psychometric function to all trials within that window, provided that a minimum of 150 trials were available in a given velocity window. Window position was increased from the minimum to the maximum mean velocity at 0.1°/s intervals, so that a different threshold was calculated for each window position (i.e., each mean eye velocity). A regression line was fit to the resulting data and the slope and significance of the regression were used to evaluate the influence of mean eye velocity on discrimination performance.