The precision of position estimates provided by the Quest 2 is not homogeneous in space
In our first experiment we measured arm kinematics during center-out reaching movements, a widely used task in motor control studies (see, for example48), To this end, we measured the position of the subject’s right hand while he was performing reaching movements from a central hand rest position to three different positions arranged to his left, frontally and to his right (Fig. 2A). On each trial, we computed, both from Oculus and Optitrack data, the movement length defined as the distance traveled by the hand from its starting to its final position. Figure S1 shows the hand trajectory and the average velocity profiles for all trials.
The left panel of Fig. 2B shows the distributions of traveled distances estimated from Oculus (red) and Optitrack (blue) data in the tethered condition. The mean traveled distance (Oculus: leftward = 18.2 ± 0.63; frontal = 19.5 ± 0.9; rightward = 18.8 ± 0.68 – Optitrack: leftward = 18.1 ± 0.47; frontal = 20.4 ± 0.57; rightward = 18.6 ± 0.38) estimated from Oculus data was significantly smaller than that estimated from Optitrack data for frontal movements but not significantly different for leftward and rightward movements (leftward: T = 85, p-value = 0.47; frontal: T = 3, p-value = 9.5 10− 6; rightward: T = 60, p-value = 0.1 – Wilcoxon signed rank test). The mean ratio of the Oculus and Optitrack estimates were 1.0 ± 0.01, 0.96 ± 0.02, and 1.01 ± 0.02 for leftward, frontal, and rightward movements respectively. The scaling factors, that represent the dispersion around the median, of the Oculus and Optitrack distributions of traveled distance were not significantly different across all conditions (leftward: statistics = 179, p-value = 0.1; frontal: statistics = 187, p-value = 0.22; rightward: statistics = 178, p-value = 0.08; Ansari-Bradley test). The right panel of Fig. 2B shows the scatterplot of hand traveled distances estimated from Oculus and Optitrack data. For all three movement directions, the Oculus and Optitrack measurements were significantly correlated (leftward: ρ = 0.98, p-value = 3.7 10 − 14; frontal: ρ = 0.84, p-value = 3.8 10 − 6; rightward: ρ = 0.88, p-value = 2.3 10 − 7 – Spearman’s rank correlation) and they were well fit by a linear model (leftward: slope = 0.72, R2 = 0.97; frontal: slope = 0.57, R2 = 0.9; rightward: slope = 0.49, R2 = 0.88).
The left panel of Fig. 2C shows the distributions of traveled distances derived from Oculus (red) and Optitrack (blue) data in the untethered condition (Oculus: leftward = 17.9 ± 0.48; frontal = 19.7 ± 0.72; rightward = 19.2 ± 0.76 – Optitrack: leftward = 18.3 ± 0.56; frontal = 21.3 ± 0.67; rightward = 18.9 ± 0.43). In this case, the mean distances computed from Oculus and Optitrack data were significantly different for all movement directions (leftward: T = 0, p-value = 1.9·10− 6; frontal: T = 0, p-value = 1.9·10− 6; rightward: T = 50, p-value = 0.04 – Wilcoxon signed rank test). The mean ratio of the Oculus and Optitrack estimates were 0.98 ± 0.007, 0.93 ± 0.01, and 1.01 ± 0.02 for leftward, frontal, and rightward movements respectively. The scaling ratio of their distributions were not significantly different across all three directions of hand motion (leftward: statistics = 216, p-value = 0.77; frontal: statistics = 210, p-value = 1.0; rightward: statistics = 179, p-value = 0.1; Ansari-Bradley test). Also in this case, for all three movement directions, the Oculus and Optitrack measurements were significantly correlated (leftward: ρ = 0.97, p-value = 2.65·10− 12; frontal: ρ = 0.93, p-value = 1.8·10− 9; rightward: ρ = 0.78, p-value = 4.4·10− 5 – Spearman’s rank correlation) and they were well fit by a linear model (leftward: slope = 1.13, R2 = 0.97; frontal: slope = 0.88, R2 = 0.92; slope = 0.49, rightward: R2 = 0.87).
Taken together, the results in Fig. 2B, C show that, in general, the Oculus produces estimates of the hand position (and thus its traveled distance) that, in some cases, might significantly differ from their veridical values both in their mean and standard deviations. However, the average difference is relatively small (in the range of 1–2 cm, see average values above) and, most importantly, in all investigated conditions the trial-by-trial estimates of hand traveled distance were significantly correlated with their ground-truth values. Furthermore, both in the tethered and in the untethered conditions the dispersions of the Oculus estimates were not significantly different from their ground-truth values.
Traveled distance and peak velocity during center-out reaching movements – (A) Experimental paradigm. The subject executed reaching movements from a central position to three different end positions to his left (purple curves) and right (green curves) and in front of him (dark yellow curves). (B) Violin plots (left) and scatterplots (right) of the hand traveled distances during the reaching movements as estimated from Oculus (red) and Optitrack (blue) data in the tethered condition for each of the three endpoint positions. (C) Hand traveled distances measured in the untethered condition. Conventions and symbols are as in panel B. (D) Violin plots (left) and scatterplots (right) of the peak velocities during the reaching movements as estimated from Oculus (red) and Optitrack (blue) data in the tethered condition for each of the three endpoint positions. (E) Peak velocities measured in the untethered condition. Conventions and symbols are as in panel D. Raw position and velocity data are plotted in Figure S1.
The Quest 2 overestimates peak velocity during reaching movements
We next examined the peak velocity during reaching movements estimated from Oculus and Optitrack data. The peak velocity is, for example, an important indicator in clinical assessments6,47,49. The right columns in Figures S1 B, C show the velocity profiles for all trials and experimental conditions. In general, the velocity profiles estimated from Oculus position information were noisier than their ground-truth value and their shape (top panels in the right columns of Figure S1 B, C) differed from its ground-truth bell-shaped profile (bottom panels in the right columns of Figure S1 B, C).
As shown in Fig. 2D, E, the estimates of peak velocity derived from Oculus data (red distributions. Tethered: leftward = 65 ± 7.2; frontal = 71 ± 6; rightward = 61 ± 4.5. Untethered: leftward = 71 ± 5.7; frontal = 64 ± 5; rightward = 63 ± 5.1) were significantly higher than their veridical values (blue distributions. Tethered: leftward = 43 ± 2.8; frontal = 47 ± 2.3; rightward = 45 ± 3.2. Untethered: leftward = 50 ± 3.2; frontal = 49 ± 2.8; rightward = 48 ± 2.2) both in the tethered and untethered condition (Tethered: leftward: T = 0, p-value = 1.9·10− 6; frontal: T = 0, p-value = 1.9·10− 6; rightward: T = 0, p-value = 1.9·10− 6. Untethered: leftward: T = 0, p-value = 1.9·10− 6; frontal: T = 0, p-value = 1.9·10− 6; rightward: T = 0, p-value = 1.9·10− 6 – Wilcoxon signed rank test). with the ratio between Oculus and Optitrack estimates being 1.51 ± 0.12, 1.52 ± 0.12, and 1.36 ± 0.11 for leftward, frontal, and rightward movements respectively in the tethered condition and 1.41 ± 0.12, 1.33 ± 0.1, and 1.3 ± 0.07 for leftward, frontal, and rightward movements respectively in the untethered condition. Furthermore, the scaling ratio of their distributions was significantly different only along the leftward direction in the tethered condition and in the leftward and frontal directions in the untethered condition (Tethered – leftward: statistics = 166, p-value = 0.02; frontal: statistics = 178, p-value = 0.09; rightward: statistics = 195, p-value = 0.44 – Untethered – leftward: statistics = 166, p-value = 0.02; frontal: statistics = 173, p-value = 0.04; rightward: statistics = 179, p-value = 0.1; Ansari-Bradley test).
The right panels in Fig. 2D, E show the scatterplots of the peak velocity estimated from Oculus (x axis) and Optitrack (y axis) data. Contrary to position information, the Oculus and Optitrack measurements of peak velocitiy tended not to be correlated across trials with the only exception of leftward movements in the tethered condition and rightward movements in the untethered condition (Tethered – leftward: ρ = 0.66, p-value = 0.001; frontal: ρ = 0.36, p-value = 0.11; rightward: ρ = 0.33, p-value = 0.15 – Untethered – leftward: ρ = 0.2, p-value = 0.39; frontal: ρ = 0.39, p-value = 0.09; rightward: ρ = 0.78, p-value = 4.4·10− 5 – Spearman’s rank correlation). Consequently, the R2 values of their linear fits were lower compared to those yielded by position information (Tethered – slope = 0.26, leftward: R2 = 0.66; frontal: slope = 0.11, R2 = 0.29; rightward: slope = 0.3, R2 = 0.43 – Untethered: leftward: slope = 0.15, R2 = 0.27; frontal: slope = 0.2, R2 = 0.36; rightward: slope = 0.34, R2 = 0.76).
To gain a better understanding of the results of Fig. 2 we examined Oculus’ trial-by-trial estimates of hand position and velocity along the different axes (Fig. 3). When examined vis-à-vis their ground-truth values they revealed several characteristics of how the Oculus estimates hand kinematics. First, at the onset of the reaching movement, the Oculus exhibits an initial delay in detecting the motion of the hand. The Oculus estimates of hand position initially lag behind their veridical position (see, for example, the time points around t = 0 in the rightmost panel in Fig. 3A) and the Oculus then compensates with a “catch-up” movement (see time points around t = 0.5s in panels A, B and C). The effect of this “catching-up” process is an overshoot in the velocity profile of the hand approximately in the middle of the reaching movement (see time points around t = 0.5s in Fig. 3 panels D, E, and F). This explains the overshoot in the estimation of the peak velocity shown in Fig. 2D, E. This overshoot is potentially related to predictive computations (e.g., Kalman filtering) performed by the Oculus. These predictive computations are likely independent of the specific value of the velocity, which might explain why Oculus and Optitrack estimates of peak velocity tended to be, at least in the sample of 20 trials for each condition examined here, uncorrelated (but see47 for results in a larger sample). Second, it appears that the Oculus exhibits also a delay in detecting that the hand has stopped. As a consequence, it overshoots the hand position when it reaches zero velocity, exhibiting then a correction towards the final veridical position (see, for example, time points around t = 1 in the left panels in Fig. 3A, B,C). This overshoot in the estimate of the hand position produces also an overshoot in the velocity compared to its veridical value toward the end of the reaching movement (see, for example, time points around t = 1 in the left panels in Fig. 3A, B,C). Third, when the movement of the hand along an axis is small (i.e. few centimeters) then the Oculus’ estimates can exhibit substantial errors (see, for example, the central panel in Fig. 3A and B and the leftmost panel in Fig. 3B).
Trial-by-trial position and velocity profiles during center-out reaching movements – Trial-by-trial position (A, B,C) and velocity (D, E,F) of the hand along the x, y and z axes during execution of the leftward (purple), frontal (dark yellow) and rightward (green) reaching movements in the untethered condition shown Fig. 2 (data for the tethered condition are shown in Figure S2).
Taken together, the results of Figs. 2 and 3 suggest that the estimates of peak velocity provided by the Oculus are significantly less accurate than position information and they tend to overestimate their veridical values. This overestimation is lower in the untethered compared to the tethered condition.
Estimates of grip aperture provided by the Quest 2 are noisy but overall reliable
The Oculus does not only provide a measure of the hand trajectory, but it also fits a kinematic model to the instantaneous hand posture to recover the configuration of different joints. To assess the reliability of these joint positions we motion captured the subject while performing reach-to-grasp movement to cylinders of 3 cm and 5 cm diameters. On each trial, we estimated the grip aperture from Oculus data by computing the distance between the position of the two joints r_index_fingernail_marker_pos, r_thumb_fingernail_marker_pos (Table S1) and from Optitrack data by computing the distance between the two markers RIND3, RTMB2 (Fig. 1). In the following, we analyze the distributions of the grip apertures at the end of the reaching movement when the subject was grasping the goal object. Figure S3 shows the temporal unfolding of the grip aperture during trials in which the 3 cm cylinder was grasped.
Figure 4B shows the distributions of the final grip apertures in the tethered conditions. Both Oculus and Optitrack estimates of the grip aperture correlated well with the actual diameter of the goal object (Oculus – 3 cm cylinder: 4.14 ± 0.34; 5 cm cylinder: 6.7 ± 0.27. Optitrack: 3 cm cylinder: 5.2 ± 0.17; 5 cm cylinder: 7.2 ± 0.19). It is not meaningful to compare the averages of the Oculus and Optitrack distributions since the two considered joints of the Oculus hand model and the considered Optitrack markers were not matched to the same physical position on the hand. They thus index two different distances that do not necessarily need to have the same average. It is, however, meaningful to compare the scaling ratio of the two distributions to assess the relative precision of the measurements of grip aperture. In the tethered condition, these ratios were significantly different in the 5 cm but not in the 3 cm condition (3 cm: statistic = 187, p-value = 0.23; 5 cm: statistic = 161, p-value = 0.008). In the untethered condition (Oculus – 3 cm cylinder: 3.9 ± 0.6; 5 cm cylinder: 6.6 ± 0.97. Optitrack: 3 cm cylinder: 5.1 ± 0.13; 5 cm cylinder: 7.1 ± 0.18), however, the scaling ratios were significantly different for both the 3 cm and the 5 cm object (3 cm: statistic = 148, p-value = 0.3.4 10− 5; 5 cm: statistic = 150, p-value = 0.0009;) . As a consequence, in the scatterplot of Oculus vs. Optitrack estimates of grip aperture the dots exhibited a larger “spread” along the horizontal axis compared to the tethered condition (compare the right panels in Fig. 4B and C). A direct comparison of the tethered vs. untethered conditions showed that Oculus measures of grip aperture had significantly higher scaling ratio in the untethered compared to the tethered condition both for 3 cm and 5 cm objects (3 cm: statistic = 271, p-value = 0.003; 5 cm: statistic = 261, p-value = 0.005; Ansari-Bradley test). This was not the case for Optitrack measures of grip aperture for which, as expected, the scaling ratio of the distribution of the grip apertures was not significantly different between the tethered and untethered conditions for both the 3 cm and the 5 cm object (3 cm: statistic = 215, p-value = 1; 5 cm: statistic = 212, p-value = 0.94; Ansari-Bradley test).
The results of Fig. 4B, C suggest that, when the Oculus is tethered (Fig. 4B), the dispersion of its estimates of grip aperture is, at least for bigger objects (i.e. a 5 cm cylinder), not significantly different from that of Optitrack measurements. However, when the Oculus is untethered (Fig. 4C) the dispersion of its estimates of grip aperture are significantly larger than those provided by the Optitrack both for small and bigger objects. When the tethered and untethered conditions are directly compared the dispersion is significantly larger when the Quest moves together with the participant’s head compared to when it rests on a tripod.
Grip aperture during reach-to-grasp movements – (A) Experimental paradigm. The subject executed reach-to-grasp movements from a central position to two a cylinder having a diameter of either 3–5 cm. The curves in the bottom panel represent the position of the wrist during one of the experimental sessions. (B – left panel) Distributions of the grip aperture measured at the end of the movement when the subject’s fingers were grasping the goal object. Grip aperture was computed from Oculus (red) and Optitrack (blue) data in the tethered condition. (B – right panel) Scatterplot of the same data shown in the left panel. Green and purple dots indicate grip apertures measured when the subject was grasping the 3 cm and 5 cm cylinder respectively. (C) Distributions (left) and scatterplot (right) of the grip apertures measured in the tethered condition. Conventions and symbols are as in panel B.
The Quest 2 provides noisy measures of acceleration
So far, we have focused on analyzing relevant events during reaching and grasping movements by considering their kinematic characteristics up to their first derivative (i.e. velocity). In this section, we broaden our analysis in two ways. First, we do not focus only on specific phases of the movement but we, more generally, consider its entire unfolding in time. Second, we do not stop at the first derivative but investigate the consistency between Oculus and Optitrack estimates of kinematic variables up to their second derivative (acceleration).
To address the two points above, we measured hand kinematics during the performance of two types of curvilinear hand movements: an ellipse (Fig. 5A) and a figure-of-eight (Figure S4A), and we assessed the reliability of Oculus-derived measures of acceleration by investigating whether they can be used to reveal the two-thirds power law, a kinematic invariant normally found in healthy human movements. In the following, we will discuss results obtained during performance of elliptical hand movements. Very similar results were obtained for figure-of-eight movements (Figure S4).
Wrist position, velocity and acceleration during curvilinear hand movements – (A) Experimental paradigm. The subject executed elliptical hand movements in the air with his right hand. The curves in the bottom panel represent the position of the wrist during one of the experimental sessions. (B, C, D) Scatterplots of Oculus/Optitrack measures of wrist instantaneous position (B), velocity (C), and acceleration (C) along the x (left/right direction, red), y(close/far away direction, green) and z (top/down direction, blue) in the tethered (top row) and untethered (bottom row) conditions. Plotted data are from one out of five experimental sessions. In all panels, the black lines signify a linear fit of the data. The slope and R2 of this fit are shown in the insert. (E) Scatterplot of the instantaneous curvature (x axis) against velocity (y axis) of the wrist measured from Oculus (left column) and Optitrack (right column) data in the tethered (top row) and untethered (bottom row) conditions. Results for the figure-of-eight trajectory are shown in Figure S4.
Figure 5B, C,D show the scatterplot of the instantaneous position, velocity, and acceleration of the wrist for one of the five repetitions. In all panels, the inset shows the slope of the linear fit and the R2 value of this fit.
Estimates of hand position along the x and z axes provided by the Oculus were in virtually perfect agreement with their Optitrack ground-truth values throughout the movement both in the tethered and untethered conditions (Fig. 5B). Indeed, both the slope and R2 of their linear fits were very close to 1 (Tethered – x: slope = 0.88, R2 = 0.99; z: slope = 0.99, R2 = 0.98 – Untethered: x: slope = 0.95, R2 = 0.99; z: slope = 0.94, R2 = 0.97 – average across all repetitions). However, in agreement with results in Fig. 2B, C, estimates of hand position along the y axis (the frontal direction in Fig. 2B, C) were noisier and, as a consequence, both the slope of the linear fit and the R2 strongly deviated from 1 (Tethered – y: slope = 0.77, R2 = 0.90 – Untethered: y: slope = 0.36, R2 = 0.8 – average across all repetitions). These results indicate that the Oculus provides fairly accurate measures of position (i.e., R2 > 0.80 and slope close to 1) in the left/right and up/down directions and it tends, however, to overestimate/underestimate the position along the close/far away direction during curvilinear hand movements. Indeed, in this direction, the Oculus underestimates the position of the hand when it is closer to the body, and it overestimates the position of the hand when it is far away from the body. The overall effect is a distortion of the veridical trajectory along the close/far away as shown in the bottom panel in Fig. 5A.
Oculus measures of velocity (Fig. 5C) followed the same pattern and they thus exhibited a closer match to their Optitrack ground-truth values along the x and z compared to the y axis both in the tethered and in the untethered conditions (Tethered – x: slope = 0.87, R2 = 0.99; y: slope = 0.66, R2 = 0.8; z: slope = 0.95, R2 = 0.95 – Untethered: x: slope = 0.93, R2 = 0.96; y: slope = 0.33, R2 = 0.66; z: slope = 0.87, R2 = 0.9 – average across all repetitions). Oculus estimates of velocity were thus still reliable (R2 > 0.8 and slope close to 1), albeit noisy, along the left/right and up/down directions, although they tended to overestimate their Optitrack ground-truth values along the close/far away direction.
The accuracy of Oculus measures of acceleration (Fig. 5D) was also axis-dependent, with measures along the left/right axis being less noisy than along the up/down direction, which was, in turn, less noisy than along the close/far direction both in the tethered and untethered conditions (Fig. 5D). The average slope and R2 of the linear fit between Oculus and Optitrack data, averaged across all 5 repetitions were: Tethered – x: slope = 0.78, R2 = 0.87; y: slope = 0.3, R2 = 0.37; z: slope = 0.63, R2 = 0.62 – Untethered: x: slope = 0.71, R2 = 0.72; y: slope = 0.17, R2 = 0.26; z: slope = 0.44, R2 = 0.45. To assess whether second derivatives estimated from Oculus position information could be used in kinematics assessments we computed the slope and the R2 of the power-law that relates the radius of curvature (which depends on the second derivative) and instantaneous velocity (Fig. 5E). Log-log curvature-velocity plots derived from Oculus measures differred from those obtained from ground-truth Optitrack measures (compare left and right columns in Fig. 5E) and estimates of the slope and R2 of their linear fits were slightly different in the two cases both in the tethered (Oculus: – slope=-0.21, R2 = 0.57 – Optitrack: slope=-0.26, R2 = 0.7) and untethered (Oculus: – slope=-0.22, R2 = 0.59 – Optitrack: slope=-0.27, R2 = 0.87) conditions.
To further characterize how the Oculus estimates the hand kinematics characteristics during curvilinear movements we sampled the position, velocity and acceleration of the hand at points where the velocity was maximal (black dots in Fig. 6A) and minimal (black dots in Fig. 6B). These points were chosen because velocity (and acceleration) maxima and minima are often used to segment human movements50,51 and, given the temporal periodicity of the performed movements, they were appropriately spaced in time not to be correlated by any of our necessary filtering procedures.
Distance, velocity and acceleration measured at two different points along a curvilinear elliptical path – (A, E) Points of velocity maxima (black dots in panel A) and minima (black dots in panel E) where distance, velocity and acceleration were sampled. The dashed lines indicate the distance between consecutive pairs of points. (B) Distributions (top panels) and scatterplots (bottom panels) of the x, y and z components of distances measured between consecutive pairs of points of velocity maxima from Oculus and Optitrack data. (C, D) Distributions (top panels) and scatterplots (bottom panels) of the x, y and z components of the velocities and accelerations measured at points of velocity maxima from Oculus and Optitrack data. (E, F, G, H) Same as (A, B, C, D) for points at velocity minima.
Results for points at velocity minima (Fig. 6A) in untethered condition are shown in Fig. 6B-D. The x component of the distances between pairs of consecutive points at local velocity maxima estimated from Oculus data was significantly higher compared to Optitrack data (Top panels in Fig. 6B. x: Oculus = 4.13 ± 2.9, Optitrack = 2.26 ± 1.7; y: Oculus = 2.1 ± 1.4, Optitrack = 2.1 ± 1.1; z: Oculus = 16.6 ± 2.8, Optitrack = 16.1 ± 1.8) and its scaling ratio significantly higher (x: statistic = 2380, p-value = 6.8 10− 6; y: statistic = 2789, p-value = 0.12; z: statistic = 2789, p-value = 0.12; Ansari-Bradley test). Optitrack and Oculus measures were correlated along the x and z, but not the y axis (bottom panels in Fig. 6B. x: ρ = 0.49, p-value = 6.2 10− 6, slope = 0.3, R2 = 0.51; y: ρ=-0.03, p-value = 0.78, slope=-0.02, R2=-0.02; z: ρ = 0.87, p-value = 3.5 10− 25, slope = 0.59, R2 = 0.91 – p-values refer to Spearman’s rank correlation).
In agreement with results in Figs. 2, 3, 4 and 5, Oculus-derived measurements of velocity (Fig. 6C) overestimated their Optitrack ground-truth values along all axes, with the overestimation along the y axis being the largest in percentage (x: Oculus = 81 ± 13, Optitrack = 79 ± 9.8; y: Oculus = 42 ± 16, Optitrack = 14 ± 3.7; z: Oculus = 15.2 ± 10, Optitrack = 7.3 ± 5.2). The scaling ratio across all axes was significantly larger for Oculus- compared to Optitrack-derived estimates (x: statistic = 3062, p-value = 0.02; y: statistic = 2581, p-vaue = 6.4 10− 8; z: statistic = 2791, p-value = 5.6 10− 5; Ansari-Bradley test). Optitrack and Oculus estimates of velocity were correlated along all three axes (bottom panels in Fig. 6B. x: ρ = 0.74, p-value = 1.4 10− 15, slope = 0.56, R2 = 0.75; y: ρ = 0.39, p-value = 0.003, slope = 0.05, R2 = 0.24; z: ρ = 0.53, p-value = 3.6 10− 7, slope = 0.21, R2 = 0.39 – p-values refer to Spearman’s rank correlation).
Similar to measurements of velocity, also Oculus-derived measurements of absolute acceleration overestimated their Optitrack ground-truth values along all axes (x: Oculus = 173 ± 189, Optitrack = 30.2 ± 21.3; y: Oculus = 164 ± 255, Optitrack = 109 ± 44; z: Oculus = 235 ± 193, Optitrack = 194 ± 60). The scaling ratio across all axes was significantly larger for Oculus- compared to Optitrack-derived estimates (x: statistic = 2157, p-value = 2.5 10–16; y: statistic = 2771, p-vaue = 3.2 10− 5; z: statistic = 2258, p-value = 5 10–14; Ansari-Bradley test) and Optitrack and Oculus estimates of acceleration were not correlated along any of the axes (x: ρ = 0.21, p-value = 0.06, slope = 0.002, R2 = 0.02; y: ρ=-0.2, p-value = 0.08, slope=-0.02, R2=-0.13; z: ρ = 0.21, p-value = 0.06, slope = 0.1, R2 = 0.32 – p-values refer to Spearman’s rank correlation). The lack of correlation between Oculus and Optitrack measurements of acceleration is likely due to the fact that, in human hand movements, acceleration has a minimum at points of maximal velocity and, as also noted above, when the measured quantities are small Oculus’ errors can be substantial.
Results for points at velocity minima (Fig. 6E) in untethered condition are shown in Fig. 6F-H. The y component of the distances between pairs of consecutive points at local velocity minima estimated from Oculus data was significantly higher compared to Optitrack data (Fig. 6F. x: Oculus = 32 ± 2.6, Optitrack = 31.1 ± 1.96; y: Oculus = 17 ± 2, Optitrack = 6.2 ± 1.5; z: Oculus = 4.2 ± 2, Optitrack = 3.3 ± 1.5). The scaling ratio across all axes was significantly larger for Oculus- compared to Optitrack-derived only for estimates along the z axis (x: statistic = 2883, p-value = 0.16; y: statistic = 2837, p-value = 0.08; z: statistic = 2747, p-value = 0.02; Ansari-Bradley test). Optitrack and Oculus measures of distance were correlated across all axes (bottom panels in Fig. 6F. x: ρ = 0.89, p-value = 5.5 10− 28, slope = 0.7, R2 = 0.92; y: ρ=-0.81, p-value = 2.4 10− 19, slope=-0.63, R2=-0.85; z: ρ = 0.79, p-value = 3.3 10− 18, slope = 0.49, R2 = 0.81 – p-values refer to Spearman’s rank correlation).
Oculus-derived measurements of velocity (Fig. 6G) overestimated their Optitrack veridical values across all axes, with the overestimation along the y axis being the largest in percentage (x: Oculus = 9.7 ± 7.8, Optitrack = 8 ± 5.1; y: Oculus = 9 ± 8.1, Optitrack = 4.7 ± 2.8; z: Oculus = 47 ± 11, Optitrack = 46 ± 7.2). The scaling ratio across all aces was significantly larger for Oculus- compared to Optitrack-derived estimates (x: statistic = 3105, p-value = 0.01; y: statistic = 2688, p-value = 2.6 10− 7; z: statistic = 3011, p-value = 0.002; Ansari-Bradley test) and Optitrack and Oculus estimates of velocity were correlated along the y and z but not the x axis (bottom panels in Fig. 6G. x: ρ = 0.08, p-value = 0.44, slope = 0.16, R2 = 0.25; y: ρ=-0.22, p-value = 0.04, slope=-0.07, R2=-0.19; z: ρ = 0.69, p-value = 8.4 10− 13, slope = 0.48, R2 = 0.74 – p-values refer to Spearman’s rank correlation).
Oculus-derived measurements of absolute acceleration overestimated their Optitrack veridical values along all axes (x: Oculus = 469 ± 200, Optitrack = 457 ± 69; y: Oculus = 350 ± 284, Optitrack = 121 ± 108; z: Oculus = 161 ± 153, Optitrack = 59 ± 39). The scaling ratio all axes was significantly larger for Oculus- compared to Optitrack-derived estimates (x: statistic = 2585, p-value = 6 10− 9; y: statistic = 2896, p-value = 0.0001; z: statistic = 2402, p-value = 2.6 10–12; Ansari-Bradley test) and Optitrack and Oculus estimates of acceleration were correlated along all axes (x: ρ = 0.51, p-value = 1.1 10− 6, slope = 0.15, R2 = 0.44; y: ρ=-0.69, p-value = 4 10− 13, slope = 0.19, R2 = 0.51; z: ρ = 0.23, p-value = 0.03, slope = 0.09, R2 = 0.35 – p-values refer to Spearman’s rank correlation).
Results in Figs. 5 and 6 confirm, in agreement with Figs. 2, 3 and 4, that Oculus estimates of distances, velocity and acceleration are noisy and their variance is larger than that of their ground-truth values in almost all investigated conditions and along all axes (panels highlighted in red in Fig. 6). That said, Oculus estimates of both distance and velocity correlated (panels highlighted in green in Fig. 6), with very few exceptions, with their ground-truth values. Oculus estimates of acceleration, instead, correlated with their ground-truth values only at points of acceleration maxima (i.e. at velocity minima). Furthermore, the accuracy of Oculus estimates of distance appears to be axis-dependent (Fig. 5). Estimates along the left/right direction are the most accurate, followed by estimates along the top/down axis. Estimates along the near/far axis appear to be the noisiest. This measurement noise along the y axis was more pronounced in the untethered condition, where the R2 of the linear fits of data was smaller than in the tethered condition.
