# Computational Analysis of Deep Visual Data for Quantifying Facial Expression Production
## 5 Experimental Results
### Assessment on ASD Children  
In the second experimental phase, the proposed algorithmic pipeline was exploited to gather scores for facial expression production on the group of ASD diagnosed children. The numeric outcomes are graphically reported in Figures 8-11.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**TD Children** & **Th** & **F1** & **P** & **R** & **TP** & **FP** & **FN** & **TN** \\ \hline H & 63 & 0.87 & 0.84 & 0.91 & 32/35 & 6/15 & 3/35 & 9/15 \\  & & & & & 91\% & 40\% & 9\% & 60\% \\ S & 78 & 0.80 & 1 & 0.68 & 17/25 & 0/25 & 8/25 & 25/25 \\  & & & & & 68\% & 1\% & 32\% & 100\% \\ F & 45 & 0.79 & 0.71 & 0.88 & 23/26 & 9/24 & 3/26 & 15/24 \\  & & & & & 88\% & 38\% & 12\% & 62\% \\ A & 108 & 0.86 & 1 & 0.76 & 13/17 & 0/33 & 4/17 & 33/33 \\  & & & & & 76\% & 0\% & 24\% & 100\% \\ Overall rating & & 0.84 & 0.85 & 0.83 & 83\% & 15\% & 17\% & 85\% \\ \hline \end{tabular}
\end{table}
Table 8: Accuracy of the automatic system with respect to manual annotations for TD children when the best decision threshold (in terms of F1-score) for each expression was used.  
Figure 7: Expressions by TD children: classification accordance between system and experts while varying decision threshold.  
Figure 8: Scores computed for the production of Happy expressions by ASD children.  
Figure 10: Scores computed for the production of Fear expressions by ASD children.  
Figure 9: Scores computed for the production of Sad expressions by ASD children.  
In this case, the correlation between the scores provided by the system and the psychologists' manual annotations is even more evident than in the case of TD children. This results by the fact that ASD children were used to not occlude their face while producing facial expression. In the worst cases, the children moved the head or the whole body (even in a stereotyped fashion) but those behaviors were handled by the algorithms that kept a correct positioning and tracking of facial landmarks even in those critical circumstances. What stated above, better emerges by quantitatively comparing the system's outcomes with the annotations provided by psychologists. Similarly to what reported for TD children, Figure 12 reports, in the topmost graphs, the precision and recall curves for classification of expressions of ASD children while varying decision threshold whereas, in each figure, bottom graphs represent the corresponding curves for the F1-score. The best value for the decision threshold, i.e., the value that maximized the related F1-score, is indicated on the \(x\)-axis.  
Figure 11: Scores computed for the production of Anger expressions by ASD children.  
Figure 12: Expressions by ASD children: Classification accordance between system and experts while varying decision threshold.  
Table 9 reports classification performance for ASD children when using the best decision threshold (in terms of F1-score) for each expression as pointed out in previous figures.  
Values in Table 9 demonstrate that, for ASD children, the proposed pipeline provides even more robust outcomes than for TD children, since computed scores showed even higher correlated with annotation provided by psychologists. In particular, the excellent F1-score (0.87), precision (0.90) and recall 0.85) values stand out. Although in this experimental phase subtle executions of facial expressions frequently occurred, from values in the table, it emerged that they were handled by the system in a very robust way.