# A Fully-Automatic Gap Filling Approach for Motion Capture Trajectories
## 5 Results

Table 5: Summary of the performance per activity. Mean (standard deviation) of RMSE are presented, in cm. Figure 5A evidences an increase in error with the size of the gap on the rigid body fill method, but the same steady increase cannot be observed on the other methods (ours and pattern fill). In terms of number of missing markers (Figure 5B), we can observe that the increase in the number of missing markers affects mostly the pattern fill method, with errors increasing as the number of missing markers increase. Although our method and the rigid body fill present slightly higher errors when a higher number of markers is missing, the errors are much more consistent throughout the tested conditions. Table 7 shows the detailed performance of our algorithm when applied to the reconstruction of the 512 samples with gaps located in the initial or final frames of the trajectories. In these experiments, only the performance of our algorithm could be reported, as the three methods used for the comparison--spline interpolation, rigid body fill and pattern fill--cannot fill gaps occurring at these positions [5, 17]. The average error obtained in these samples is slightly above the error reported for our algorithm when reconstructing gaps in the middle, but it is considerably below the errors reported for Vicon Nexus' methods (for gaps in the middle). The errors (average values) increase both with the number of missing markers and the length of the generated gaps. The dispersion of the errors (standard deviation) remains consistent throughout all tested conditions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(I\) & **Method** & \(n=1\) & \(n=2\) & \(n=4\) & \(n=6\) & \(n=8\) & \(n=10\) & \(n=12\) & \(n=14\) \\ \hline \multirow{4}{*}{60} & Ours & 3.1 (0.7) & 3.0 (0.6) & 3.4 (0.5) & 3.4 (0.6) & 3.3 (0.7) & 3.5 (1.0) & 3.3 (0.7) & 4.3 (2.3) \\  & Pattern & 1.5 (1.0) & 1.4 (0.8) & 5.2 (9.8) & 4.5 (8.2) & 12.9 (11.2) & 9.4 (10.7) & 13.6 (13.1) & 13.8 (15.0) \\  & Rigid body & 4.5 (5.0) & 3.9 (2.6) & 4.9 (4.0) & 4.8 (3.1) & 5.0 (3.6) & 4.9 (3.2) & 5.4 (3.5) & 5.3 (3.3) \\  & Spline & 4.5 (4.7) & 4.8 (3.8) & 4.3 (3.8) & 4.3 (3.5) & 5.1 (3.7) & 4.9 (3.9) & 5.1 (3.5) & 4.8 (3.2) \\ \hline \multirow{4}{*}{120} & Ours & 2.5 (1.2) & 2.5 (0.9) & 2.6 (0.6) & 2.5 (0.5) & 2.7 (0.6) & 2.7 (0.6) & 3.0 (0.8) & 2.9 (0.8) \\  & Pattern & 2.7 (1.5) & 2.4 (0.8) & 2.5 (0.8) & 5.9 (8.9) & 12.2 (13.2) & 6.6 (7.4) & 13.1 (9.9) & 14.0 (11.6) \\  & Rigid body & 7.7 (5.3) & 6.6 (3.8) & 7.6 (4.2) & 7.4 (3.8) & 8.0 (4.1) & 8.0 (3.7) & 7.9 (3.7) & 7.8 (3.6) \\  & Spline & 13.2 (11.6) & 13.7 (9.3) & 15.4 (11.4) & 16.4 (11.7) & 17.8 (11.4) & 18.2 (12.2) & 17.0 (10.3) & 16.6 (10.9) \\ \hline \multirow{4}{*}{240} & Ours & 2.3 (1.4) & 3.0 (1.5) & 2.7 (1.0) & 3.4 (1.1) & 2.8 (1.1) & 3.4 (1.2) & 4.2 (1.5) & 4.6 (17.7) \\  & Pattern & 3.1 (1.5) & 7.0 (11.9) & 7.9 (11.0) & 8.7 (9.6) & 11.2 (11.1) & 15.7 (11.8) & 16.0 (12.1) & 18.1 (13.4) \\ \cline{1-1}  & Rigid body & 7.8 (5.4) & 13.6 (6.8) & 10.7 (3.9) & 10.8 (4.5) & 10.2 (4.0) & 10.6 (3.8) & 10.6 (3.9) & 10.6 (3.8) \\ \cline{1-1}  & Spline & 53.9 (51.8) & 72.3 (48.0) & 70.3 (46.6) & 90.9 (76.2) & 78.2 (61.4) & 59.7 (35.4) & 65.8 (39.7) & 65.3 (37.8) \\ \hline \multirow{4}{*}{600} & Ours & 3.0 (2.8) & 4.8 (3.1) & 3.5 (1.3) & 5.2 (2.5) & 5.5 (2.3) & 5.0 (2.5) & 5.9 (3.0) & 6.4 (2.8) \\ \cline{1-1}  & Pattern & 5.4 (3.4) & 6.9 (3.2) & 5.4 (2.2) & 8.3 (5.7) & 13.2 (11.1) & 11.8 (9.8) & 13.9 (10.9) & 14.2 (10.0) \\ \cline{1-1}  & Rigid body & 11.5 (6.9) & 14.5 (7.6) & 14.9 (5.9) & 16.3 (5.8) & 15.9 (6.0) & 15.9 (5.6) & 15.0 (5.0) & 15.8 (5.0) \\ \cline{1-1}  & Spline & 545.1 (1033.7) & 477.8 (427.0) & 532.4 (578.0) & 578.7 (484.0) & 512.3 (376.1) & 581.0 (430.7) & 559.7 (477.7) & 560.2 (410.7) \\ \hline \hline \end{tabular} \(l\)– gap length; \(n\)—number of missing markers.  
\end{table} 
Table 6: Performance of the four gap filling methods (ours, pattern fill, rigid body fill and spline fill) in each tested condition. Mean (standard deviation) of RMSE is presented in cm.