# A Fully-Automatic Gap Filling Approach for Motion Capture Trajectories
## 5 Results  
The comparison of the initialization strategies--i.e., using the sequences with artificially generated gaps and the original sequences without gaps--is shown in Table 3, where reconstruction performance results are presented per activity (i.e., boxing, reaching, walking and dancing). The performance obtained with both initialization strategies is very similar for all activities considered. The summary statistics of the performance of the four gap filling methods--i.e., ours, pattern fill, rigid body fill and spline fill achieved in samples with gaps in the middle--is shown in Table 4, along with a boxplot representation that omitted spline fill results since its error can be up to three orders of magnitude superior to that of the remaining approaches. Our method achieved the lowest mean RMSE and the lowest dispersion of the errors, as evidenced by standard deviation (SD) and interquartile range (IQR) values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Calibration Trajectory** & **Boxing** & **Reaching** & **Walking** & **Dancing** \\ \hline Sequences with gaps & 3.2 (1.7) & 3.9 (1.7) & 2.8 (1.2) & 4.6 (2.8) \\ Sequence without gaps & 3.1 (1.2) & 3.9 (1.7) & 2.9 (1.2) & 4.5 (2.7) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the performance of our method per activity using the sequences with gaps and the original sequences (without gaps) as calibration trajectories during initialization. Mean (standard deviation) of RMSE are presented in centimeters. The minimum error was obtained with the pattern fill method, whereas the maximum error was obtained with spline. The summary of the performance per activity (i.e., boxing, reaching, walking and dancing) is shown in Table 5, again, considering only the samples with gaps in the middle. The results show that our method is associated with lower errors than the remaining approaches for all activities under analysis. One can also observe more consistency of overall error across all activities for our method by verifying that the differences between average errors of each activity were no greater than 1.6 cm and that it systematically achieved the lowest standard deviation per activity when compared to the remaining methods. Table 6 shows the detailed performance of the four gap filling methods applied to the samples with gaps in the middle, where results are presented for each condition tested under the scope of this work--i.e., the four gap lengths and the eight numbers of missing markers. In this table, we can observe that our algorithm presents the most consistent performance (with regards to gap length and number of missing markers), with differences in errors no higher than 3 cm. In contrast, spline fill presents consistent results with regards to the number of missing markers, but errors tend to increase with the length of the gap, with errors approaching values in the order of meters for larger gaps. For this reason, spline fill was omitted from Figure 5, which shows a summary of the results achieved with each method in terms of gap length and number of missing markers, respectively. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Statistic** & **Ours** & **Pattern** & **Rigid Body** & **Spline** \\ \hline Mean & 3.6 & 9.0 & 9.5 & 158.4 \\ Median & 3.1 & 3.9 & 9.5 & 23.4 \\ SD & 1.9 & 10.5 & 6.1 & 361.2 \\ IQR & 1.6 & 10.7 & 8.3 & 108.7 \\ Min & 0.8 & 0.1 & 0.4 & 0.2 \\ Max & 13.5 & 52.9 & 31.2 & 4485.5 \\ \hline \hline \end{tabular} SD—Standard deviation; IQR—Interquartile range.  
\end{table} 
Table 4: Summary of the performance per method (RMSE values in cm). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Boxing** & **Reaching** & **Walking** & **Dancing** \\ \hline Ours & 3.1 (1.2) & 3.9 (1.7) & 2.9 (1.2) & 4.5 (2.7) \\ Pattern & 3.2 (1.3) & 4.9 (4.1) & 12.1 (12.2) & 15.8 (12.9) \\ Rigid body & 12.5 (4.5) & 12.0 (6.9) & 4.3 (4.1) & 9.3 (4.6) \\ Spline & 213.8 (313.3) & 315.5 (599.8) & 35.5 (56.0) & 69.0 (100.0) \\ \hline \hline \end{tabular}
\end{table}