# A New Approach to Fall Detection Based on the Human Torso Motion Model
## 4 Experiment and Results
### Result and Evaluation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{\(T_{\text{vu}}\)} & \multicolumn{2}{c}{**Fall**} & \multicolumn{2}{c}{**Non-Fall**} \\ \cline{2-5}  & **TP** & **FN** & **FP** & **TN** \\ \hline
**0** & 98 & 2 & 4 & 96 \\
**3** & 98 & 2 & 4 & 96 \\
**6** & 98 & 2 & 4 & 96 \\
**9** & 98 & 2 & 4 & 96 \\
**12** & **98** & **2** & **3** & **97** \\ \hline
**15** & 93 & 7 & 2 & 98 \\
**18** & 92 & 8 & 1 & 99 \\
**21** & 89 & 11 & 1 & 99 \\
**24** & 86 & 14 & 1 & 99 \\
**27** & 80 & 20 & 1 & 99 \\
**30** & 70 & 30 & 1 & 99 \\
**33** & 67 & 33 & 1 & 99 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The test results on the self-collected dataset with different \(T_{\text{vu}}\). TP: true positive; FN: false negative; FP: false positive; TN: true negative. Figure 10: The duration of each fall in the self-collected dataset. There are in total 100 fall videos in the dataset. In Table 2, TP (true positive) denotes the fall samples that are judged as falls. FP (false positive) means the non-fall samples that are judged as falls. TN (true negative) denotes the non-fall samples that are judged as non-falls. FN (false negative) means the fall samples judged as non-falls. Then, we have \(\text{TPR}=\frac{\text{TP}}{\text{TP}+\text{FN}}\), \(\text{TNR}=\frac{\text{TN}}{\text{TN}+\text{FP}}\) and \(\text{Accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{IN}+\text{FP}+ \text{FN}}\). We compared our proposed method with other Kinect sensor-based approaches [22; 24; 26; 28]. All of these approaches were tested on our self-collected dataset. The results are recorded in Table 3.  
As shown in Table 3, all of the approaches worked well in discriminating fall and walk. However, the height-based approaches [24; 26] were unable to differentiate fall and other fall-like activities. Especially in terms of controlled lying down, all of the lay samples were wrongly judged as falls by the above two methods. The vertical height velocity-based approach [22] performed much better than height-based approaches [24; 26] in discriminating fall and controlled lying down, but it performed poorly in differentiating fall, crouch and bend. The main reason is that both height-based \begin{table}
\begin{tabular}{c c c} \hline \hline
**Activity Type** & \
\begin{tabular}{c} **The Number of** \\ **Sample Videos** \\ \end{tabular} &
\begin{tabular}{c} **The Number of** \\ **Detected as Fall Videos** \\ \end{tabular} \\ \hline Fall & 100 & 98 \\ Lay & 25 & 1 \\ Crouch & 25 & 1 \\ Bend & 25 & 1 \\ Walk & 25 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results and evaluation of our approach. Figure 13: The time consumptions of each frame in walk and fall. The two test videos of this graph were selected randomly from the self-collected dataset. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Approach**} & \multicolumn{4}{c}{**Fall**} & \multirow{2}{*}{**Crouch**} & \multirow{2}{*}{**Bend**} & \multirow{2}{*}{**Walk**} & \multirow{2}{*}{**Lay**} \\ \cline{2-2} \cline{6-9}  & **Forward** & & & & & & & & \\ \hline [PERSON], [PERSON] et al. [22] & 25 & 25 & 25 & 11 & 20 & 0 & 1 \\ [PERSON] et al. [24] & 10 & 15 & 23 & 18 & 2 & 8 & 0 & 25 \\ [PERSON], [PERSON] et al. [26] & 23 & 22 & 25 & 25 & 12 & 25 & 0 & 25 \\ [PERSON], [PERSON] et al. [28] & 8 & 22 & 21 & 25 & 0 & 0 & 0 & 0 \\ Our proposed method & 25 & 23 & 25 & 25 & 1 & 1 & 0 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the fall detection capability on our self-collected dataset with other Kinect-based fall detection approaches. and vertical velocity-based approaches did not lay a clear line between balance and unbalance. Hence, the fall-like activities are difficult or even impossible to detect correctly. As for the bounding box-based approach [28], it performed well in differentiating fall and fall-like activities. However, it performed badly in terms of detecting falling forward.