## 3 Results and Discussion
### Evaluation of Automated Laser Point Detection Algorithm  
For a quantification of the accomplished advances in the laser point detection algorithm, we process exemplary high-speed video recordings of eight test subjects (four females and four males recorded at 4 kHz). The initial grid detection and the tracking algorithm are assessed separately with regard to their detection success and the resulting detection duration. The initial grid detection is performed on the first frame displaying the glottis in a closed state. A sample frame including all possible detection results and the classifying nomenclature are shown in Figure 13. The algorithm is supposed to detect all \"relevant\" laser points (as indicated by the red enclosing line in Figure 13), i.e., the laser points on the vocal folds but not the ones on the epiglottis, the arytenoid cartilages and the pharynx walls. On average, the best suggestion of the automatic initial grid detection provides 88.7% correctly detected laser points (yellow circles in Figure 13). 9.2% of the initially suggested grid points require an adjustment in their position (pink dots in Figure 13) and only 2.1% of the detected points prove to be erroneous, i.e., specular reflections instead of laser points or not relevant (light blue crosses in Figure 13). The combined number of the initially correct and adjusted laser points constitutes a portion of 84.7% of the desired, objective laser grid on the vocal folds. The remaining 15.3% of the points have to be added manually by the means of the graphical user interface (points within green area in Figure 13). The corresponding quantitative results are shown in Figure 14.  
Figure 13: Classification scheme for the evaluation of initial grid detection algorithm. The laser points from the first frame are then tracked in all frames over the following five oscillation cycles, which corresponds to \(61\) - \(116\) frames in our example files depending on the phonation frequency. The assessment of the tracking algorithm follows the procedure in Section 3.1. The detection results for each frame are categorized according to Table 2.  
The sensitivity \(TPR\) as given in (3) is a measure for the correct tracking and the automatic \"unfreeze\" action, while the specificity \(TNR\) as given in (4) quantifies the success of the automatic \"freeze\" action. The results are depicted in Figure 15, allowing a direct comparison between the present (green) and the previous algorithm (blue) [20]. As before, the sensitivity (top) and specificity (bottom) are calculated for each frame separately and then averaged over all frames within each series. The total average values (on the right) are determined over all frames of all series. The vertical error bars indicate the corresponding standard deviations. The sensitivity of the tracking algorithm has already been very high in the previous implementation and is now slightly decreased within the range of the standard deviation by 0.8%. The specificity, however, is significantly increased by 38.3%. Statistical analysis using IBM SPSS Statistics v21 (i.e., pairwise comparison of video frames over all series, applying Wilcoxon Rank Test - data was not normally distributed) showed a statistically highly significant improvement (\(p\) = 0.000) between the methods of [PERSON] [20] and [PERSON] [22] for both measures. As before, the standard deviation of the specificity is reduced from 37.1% to 25.4%, which indicates a decreased dependence on the quality of the high-speed footage. \begin{table}
\begin{tabular}{l c c} \hline \hline  & **Discernible** & **Indiscernible** \\  & **Laser Points** & **Laser Points** \\ \hline Detected by algorithm (not freezed) & True positive (TP) & False positive (FP) \\ Not detected by algorithm (freezed) & False negative (FN) & True negative (TN) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Confusion matrix for evaluation of the automated laser point tracking algorithm.