Fig 1.
Block diagram of the proposed method.
The overall process can be divided in five steps: 1) Extraction of marker trajectories parameters. 2) Individual recovery models. 3) Time constraint: trajectory continuity. 4) Distance-probability weighted averaging. 5) Spacing constraint: reference marker distance likelihoods.
Table 1.
Motion sequences used in the methods comparison.
Fig 2.
Trajectory continuity correction.
The yellow curve shows incomplete data of a marker trajectory (m) on which a gap was introduced between frames 1130 and 1190 (only z-axis is shown). The blue curve represents the recovered data (), and the red curve shows the corrected data using trajectory continuity constraint (
) (see Eqs 16–19).
Fig 3.
Reference distance soft constraints.
The green intensity colormap indicates the probability of presence for the recovered frame. If the recovered frame is outside the confidence zone (delimited by spheres of radii r1 and R1), it is projected onto the closest point in this confidence zone (
).
Fig 4.
Mean recovery error for different gap sizes and gap recovery methods.
Top: CMU1. Bottom: CMU3. Left: results including BoLeRo method. Right: results without BoLeRo method. Each point represents the mean of recovery errors, computed with 20 iterations, of three randomly created gaps of the same length (0.5, 1, 2 or 5 seconds). Solid lines show results for each individual method. Dashed lines show results for distance-probability averages of various combinations of individual methods.
Fig 5.
Mean recovery error for different sequence durations and gap recovery methods.
To illustrate the influence of sequence duration on performance of gap recovery methods, fragments of different durations were extracted from each motion file. Each point represents the mean of the recovery errors computed on 20 iterations of three randomly created gaps of 1 second. Continuous lines show results for each individual method. Dashed lines show results for PMA with various methods combinations.
Fig 6.
Mean recovery error for different numbers of missing markers and gap recovery methods.
Each point represents the mean of recovery errors computed over 20 iterations of a number of randomly created gaps of 1 second (1, 3, 6, 10 or 20 gaps). Solid lines show results for each individual method. Dashed lines show results for distance-probability averages of various methods combinations.
Table 2.
Effect of constraints on mean recovery error (t-test, n = 200; conditions: 3 gaps of 1 seconds).
Table 3.
Effect of constraints on the mean recovery error (t-test, n = 200; conditions: 10 gaps of 5 seconds).
Fig 7.
Mean recovery error for different recovery methods, for all test motion sequences.
Left: different gap lengths (3 concomitant gaps, total sequence duration); Center: different motion durations (3 concomitant gaps of 1 second); Right: different numbers of concomitant gaps (gaps of 1 second, total sequence duration). Each point represents the mean of recovery errors computed over 20 iterations of a number of randomly created gaps. Solid lines show results for each individual method. Dashed lines show results for PMA with various individual methods combinations.