## 3 Experimental Results and Discussion
### State Analysis
Figure 9: The upper image represents the height difference between the top and bottom positions and the bottom image indicates the ratio of minor axis to major axis that can be used to detect the start of the fall state. depth value. Therefore, fall detection can be improved by additionally using the depth information. Table 1 lists the 3D mean error of scenes that include walking, side fall, front fall, and back fall. The error is the difference between a 3D value estimated by our tracking algorithm and a real 3D value measured with a ruler. This was possible since we found that there is a linear relationship between the physical and estimated distance with a depth map generated from a single RGB image. More specifically, the human's bottom position is estimated through human tracking and the corresponding depth value is obtained using the depth map, which is derived through the background image as described in the preceding section. The real distance value is calculated through the depth versus real distance graph. Calculating the error between algorithm output and the real value yields the error rate shown in Table 1, which shows that our algorithm can provide reliable real distance values from a single camera. The error interval is approximately 12 frames because we acquire 12 frames per second. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Case 1** & **Error Rate (\%)** & **Case 2** & **Error Rate (\%)** & **Case 3** & **Error Rate (\%)** \\ \hline Frame 1 & 12.6 & Frame 1 & 5.6 & Frame 1 & 8.9 \\ Frame 13 & 6.9 & Frame 13 & 16.5 & Frame 13 & 0.1 \\ Frame 25 & 12.1 & Frame 25 & 12.5 & Frame 25 & 18.2 \\ Frame 37 & 3.8 & Frame 37 & 3.1 & Frame 37 & 11.6 \\ Frame 49 & 2.1 & Frame 49 & 3.9 & Frame 49 & 5.3 \\ Frame 61 & 10.5 & Frame 61 & 3.1 & Frame 61 & 6 \\ Frame 73 & 7.6 & Frame 73 & 4.4 & Frame 73 & 6 \\ Frame 85 & 5.4 & Frame 85 & 4.4 & Frame 85 & 5.8 \\ Frame 97 & 10.3 & Frame 97 & 4.4 & Frame 97 & 5.8 \\ Frame 109 & 18.4 & Frame 109 & 6.3 & Frame 109 & 5 \\
**Average** & 8.97 & **Average** & 6.42 & **Average** & 7.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: 3D mean error obtained from walking (Case 1), side fall (Case 2), front/back fall (Case 3). Figure 13: Top and Bottom depth values (upper line) and Ratio of Top to Bottom depth value (middle line) and 3D trajectories (bottom line): (**a**) normal walking; (**b**) sideway fall; (**c**) optical fall. Figure 14a shows the result of state classification based on the features obtained earlier, which is similar to [44] in terms of fall severity levels from the normal to the emergency. The overall fall process is divided into five states and, as mentioned previously, the prior state requirements have to be met for moving onto the next state. When a person's vertical velocity changes suddenly, the indicator of the potential fall is turned on and the normal indicator is turned off. From this moment, the algorithm observes whether the condition for going to the fall state is satisfied or not. If a fall does not occur for a certain period, the normal indicator is turned on. If the fall indicator is turned on, we need to observe if the fall is temporary or permanent. If there is no human motion for a prolonged period, the no-motion indicator is turned on. The duration of the no-motion phase is monitored to raise the emergency signal and the criteria for this duration may vary. When no incident of fall is detected, the state from fall to recovery must remain zero. Figure 14b,c show the normal and fall indicators when confounding motion occurs, such as sitting and squatting motion respectively. If the potential fall indicator is not turned on, both the no-motion indicator and the recovery indicator are not turned on. The proposed algorithm accurately judges these confounding motions as normal motion. Figure 15 shows the state transition diagram for the fall detection process proposed in this paper. It shows how the change among normal state, potential fall state, fall state, emergency state, and recovery state occurs under certain conditions.