# A New Approach to Fall Detection Based on the Human Torso Motion Model
## 4 Experiment and Results
### Result and Evaluation  
The human skeleton is used to track the monitored person and to discriminate human objects and other objects. Figure 8 shows that the Kinect-provided skeleton is an effective way to recognize the human object correctly, even when the joints are covered by a skirt or gown or there are other objects in the scene. Additionally, walking devices, such as a walking stick, can also be recognized and excluded from skeleton information by the embedded program of Kinect. Although the joints of the lower part of the skeleton may have a slight deviation where they are covered, the effect on the accuracy of HTMM can be ignored because of the consideration of only the shoulder center and hip center joints. The four typical falls in Figure 9 show the common torso angle and centroid height changes. Before a fall is detected, the torso angle increases rapidly while the centroid height declines sharply. In HTMM, the changing rate of the torso angle, the changing rate of the centroid height and the tracking time are the three parameters that have a strong effect on the accuracy. In [37], the range of the decay rate of the centroid height is from 1.21-2.05 m/s. We set 1.21 m/s as its threshold value in our  
Figure 8: The detected skeletons with different postures, clothes or walking devices. model. Through the experiments, our approach received the best accuracy rate when the parameters were set as follows:  
\[T_{vn}=12\text{ degree}/100\text{ ms}\]  
\[T_{vth}=1.21\text{ m}/\text{s}\]  
\[T=1300\text{ ms}\]  
where \(T_{vn}\) is the threshold value of the torso angle increase rate, \(T_{vth}\) is the centroid height decay rate and \(T\) is the tracking time. As shown in Figure 10, most falls of our self-collected dataset happened in 1.1-1.6 s. Therefore, the values from 1100-1600 ms are all suitable for \(T_{a}\). The max changing rates of the torso angle and  
Figure 9: Detected frames of different falls and two features’ curves. The left picture of each group is the depth image of the frame when our method detected the fall. The dotted line in the depth image stands for the torso line, while the solid line stands for the gravity line. Shoulder center joint and hip center joint were marked in red. (**a**) Fall left; (**b**) fall right; (**c**) fall forward; (**d**) fall backward. the centroid height in this period are used in HTMM to check whether there is a fall. In the program, we took 1300 ms as the default value. Eleven groups of experiments were tested on the self-collected dataset with different \(T_{\text{vu}}\) to find out its best default value. According to the results, when \(T_{\text{vu}}\) was set 12 degree/100 ms, a fall can be detected in the middle of the activity; while a fall may not be detected if \(T_{\text{vu}}\) was set too large, and false alarm rate increases when \(T_{\text{vu}}\) was set too small. Table 1 shows the test results on our self-collected dataset with different values of \(T_{\text{vu}}\). Figures 11 and 12 record the changing curves of the torso angle and centroid height of the five wrongly judged samples. By reviewing the data, we found that there are two major factors that affect the accuracy of our method. First and foremost, in rare situations, joint positions may be improperly provided by the embedded program of the Kinect sensor. For example, in Figure 11, from Frame 22-Frame 24 of the \"lay\" curve, the torso angle increased from 20-69.8 degrees. This abnormal transformation let our method make false judgments in two fall samples and one lay sample. Secondly, some samples were too quick to be detected correctly. For examples, \"crouch\" and \"bend\" curves show that the actions were accompanied with a quick