Fig 1.
Search algorithm and algorithm outputs.
(A) Flowchart describing stages of search algorithm used to find segments of videos containing pairs of walkers. We (i) extracted frames from subsampled videos, (ii) fit pose to the frames using OpenPose, (iii) detected pairs from pose estimates, then (iv) identified sequences of frames that contained pairs of people, resulting in a set of pose estimates from frame sequences. (B) Example video frame containing a walking pair with overlaid pose estimates. A bounding box highlights the persons identified as a pair. (C) Examples of walking pairs with overlaid pose estimates.
Fig 2.
Analysis of relative phase illustrated.
(A) Main stages of data analysis performed on pose estimates from videos of walking pairs. (i) We tracked the pose of Walker 1 and Walker 2 from each video clip. For details, see Fig 1A. (ii) We detrended key point coordinates for each walker within frames by subtracting a reference point on the same skeleton (yref, the neck) from the ankle coordinates (ya) and dividing by the length of the skeleton (l). (iii) This resulted in a time-series of y-coordinates for the left and right ankles for Walker 1 and Walker 2. (iv) For each walker, we subtracted right from left ankle coordinates to give a time series of the left-right displacement between ankles. (v) We used the Hilbert phase of the displacement signal to approximate walking angle for each walker. (vi) Finally, we computed the difference between the phase of Walker 1 and Walker 2 to obtain a time series of the relative phase of the walkers (upper panel) from which we computed the distribution of relative phase on the circular axis (lower panel). For a similar analysis, see [17] (B) Pair walking in phase. The ankle displacement signal overlaps for Walker 1 and Walker 2, as the pair walks perfectly in phase. There is therefore a constant relative phase of 0. (C) Pair walking in anti-phase. The displacement signals are in antiphase with each other. There is a constant absolute phase difference of π between the signals in the Hilbert phase time series, leading to a relative phase distribution with a peak at π.
Fig 3.
Descriptive analysis of videos.
(A) Distribution of duration of video segments in seconds. (B) Number of video segments for each city we searched for. (C) Distribution of estimated age of walkers averaged across the pair in years.
Fig 4.
Extracting relative phase from the image y-coordinates of the left and right ankles.
Walker 1 and Walker 2 from the same pair are presented on the same panel (video #13, see S1 File). The strong overlap between the signals shows that the pair is walking in phase. (A, B) Raw y-coordinates of the left ankles (A) and right ankles (B) with Walker 1 and Walker 2 shown in different colors. (C, D) We then detrended the signal by subtracting the y-coordinate of a reference body part, the neck, and dividing by the height of the walker. This gave a signal that was invariant to the position of the walkers in the frame and their size. (E, F) We removed outliers, normalized and low-pass filtered the signal. (G) Using the normalized y-coordinate signal, we subtracted right ankle coordinate from the left ankle coordinate to give a displacement signal for each walker. (H) We computed the phase angle by taking the Hilbert transform of the displacement. (I) We examined the distribution of the relative phase between walkers by computing the mean of the distribution (red).
Fig 5.
Comparison of relative phase and walking frequency computed from pose estimates and signals extracted from human labels of foot strike timings from 43 5-second long videos.
(A) Mean relative phase from pose estimates as a function of mean relative phase from human-labelled data with overlaid linear fit (shaded area = 95% confidence interval). (B) Walker frequency from pose estimates as a function of walker frequency from human-labelled data with overlaid linear fit (shaded area = 95% confidence interval).
Fig 6.
Group results on relative phase and walking frequency.
(A) We fitted mixture of von Mises distribution models to the distribution of mean relative phase, varying the number of peaks of the distribution. The best-fitting model contains three peaks. (B) The distribution of the mean relative phase across pairs of walkers and means of the best-fitting mixture of von Mises distributions (red). (C) Histogram of the variance of the relative phase signal extracted for each walking pair. Vertical lines show relative phase variance of.25,.5, and.75, with the proportion of the data that was in these intervals (D) Scatter plot of the relative phase variance on the radial axis as a function of the mean relative phase for each pair. Pairs are strongly synchronized with mean relative phase near 0 or ±π radians when variance is low. (E) The distribution of the mean relative phase across pairs of walkers where there was no hand contact (N = 288). (F) The distribution of the mean relative phase across pairs of walkers where there was hand contact (N = 60). (G) Distribution of walking frequency, quantified using ankle displacement (Mean = 1.85 Hz, SD = .32). (H) Scatterplot of walking frequencies of walkers within each pair.