A New Approach to Fall Detection Based on the Human Torso Motion Model

Featured Application: In our proposed method, a new feature named torso angle is firstly proposed and imported in the human torso motion model (HTMM) for fall detection. By tracking the changing rate of torso angle and centroid height, our fall detection model has a strong capability of differentiating falls from other fall-like activities, such as controlled lying down, quickly crouching and bending, which may be big obstacles for other existing computer vision-based approaches to discriminate. Abstract: This paper presents a new approach for fall detection based on two features and their motion characteristics extracted from the human torso. The 3D positions of the hip center joint and the shoulder center joint in depth images are used to build a fall detection model named the human torso motion model (HTMM). Person’s torso angle and centroid height are imported as key features in HTMM. Once a person comes into the scene, the positions of these two joints are fetched to calculate the person’s torso angle. Whenever the angle is larger than a given threshold, the changing rates of the torso angle and the centroid height are recorded frame by frame in a given period of time. A fall can be identiﬁed when the above two changing rates reach the thresholds. By using the new feature, falls can be accurately and effectively distinguished from other fall-like activities, which are very difﬁcult for other computer vision-based approaches to differentiate. Experiment results show that our approach achieved a detection accuracy of 97.5%, 98% true positive rate (TPR) and 97% true negative rate (TNR). Furthermore, the approach is time efﬁcient and robust because of only calculating the changing rate of gravity and


Introduction
Falls are one of the major health hazards among the aging population aged over 60.According to the report of the World Health Organization, approximately 28~35% of people aged 65 and over fall each year and 32~42% for those over 70 years of age.In fact, falls exponentially increase due to age-related biological changes, which lead to a high incidence of falls and fall-related injuries in ageing societies [1].Nowadays, falls are not only life threatening, but also one of the major issues in elderly health.A fall can cause severe consequences, including broken bones, superficial cuts and abrasions to the skin soft tissue [2,3].If a falling person cannot get help in a short period of time, the situation will be even worse.As many people in this ageing group live alone, it is difficult for them to seek help immediately.For these and many other reasons, the number of research works on fall detection has increased dramatically over recent years.Automatic detection of human falls provides help to reduce the time between the fall and the arrival of medical attention [4,5].
Appl.Sci.2017, 7, 993 3 of 17 a single camera covering the full view of the room environment is used for the video recording of an elderly person's daily activities for a certain time period.Fall detection is realized by analyzing the postures that are extracted from video clips.Rougier et al. [22] proposed a new way to track 3D head trajectory by only one calibrated camera.The vertical velocity of the 3D head is used to judge whether a fall happens.Olivieri et al. [23] used optical flow to detect falls and recognize other human activities.
Recently, depth images have been widely used for action recognition and classification, because of the particular advantages in privacy protection and the availability of being easily collected by Kinect or other sensors.Lei Yang et al. [24] proposed a fall detection method based on spatio-temporal context tracking over three-dimensional (3D) depth images captured by the Kinect sensor.Rougier, C. et al. [25] used several cameras to create 3D vision.A measure of the vertical distribution along the vertical axis is calculated, and a fall event is detected when this distribution is abnormally near the ground for a certain length of time.Gasparrini et al. [26] proposed a fall detection method for indoor environments, based on the usage of the Kinect depth sensor in an "on-ceiling" configuration and on the analysis of depth frames.Rodrigo Ibañez et al. [27] proposed a lightweight approach to recognize gestures with Kinect by utilizing approximate string matching.Georgios Mastorakis et al. [28] fetch data from the depth image and detect falls by measuring the velocity based on the contraction or expansion of the width, height and depth of the 3D bounding box.Aguilar et al. [29] presented a 3D path planning system that uses a point cloud obtained from the robot workspace, with a Kinect V2 sensor to identify the interest regions and the obstacles of the environment.Alazrai R. [30] built a view-invariant descriptor for human activity representation by 3D skeleton joint positions to detect falls and other activities.
However, all of these methods have shortcomings.For example, in [31], the ratio of the height and width of the rectangle extracted from a person was used to determine whether a person falls.This method uses three features, i.e., human aspect ratio, effective area ratio and center variation rate.However, the human aspect ratio changes greatly when the relative positions of the camera and the target change, which results in a high false alarm rate and low accuracy of the detection system.Multi-cameras [32] and wide-angle camera-based [33] methods are effective ways to detect falls.However, the pre-works, i.e., camera installation, image calibration and 3D human identification, are difficult and complex.As for the deep learning method [34], the need for a huge number of labeled data makes it complicated in adjustment and poor in flexibility.

Our Approach for Fall Detection
In our proposed method, a new feature named torso angle is adopted.This feature together with the centroid height and their motion characteristics form a descriptor for human fall representation, called the human torso motion model (HTMM).Different from machine learning and deep learning methods, HTMM is a threshold-based approach for fall detection with high time efficiency because of the calculation of only the changing rates of the torso angle and centroid height.Before we elaborate the model, some technical terms will be detailed first in the following.

Torso Line and Torso Vector
There are in total 20 points of a person's skeleton that can be tracked by the Kinect sensor when the person is standing, while 10 points when sitting if used in front view.Additionally, the untracked joints can be estimated by the embedded program in Kinect.Especially when the part of the body that contains the joints can be detected, the positions of these untracked joints can be exactly estimated.Figure 1 shows the details of the joints in standing and sitting postures.A line connecting the shoulder center and the hip center is a key concept in our algorithm to calculate torso angle.This line is named as the torso line and marked in red as shown in Figure 1.In a red, green, blue (RGB) image, each pixel only contains 2D position information.However, the depth image provides each pixel's 3D position information.Figure 2 shows the joints in 3D depth image space.These joints of a person's skeleton can be considered as pixels in the depth image.With these 3D joint points of the skeleton, the computer can understand the meaning of human gestures when a set of complex activities is made by human beings in front of the Kinect.As the main purpose of our system is to alarm as soon as a fall happens, we only take the shoulder center and hip center joints into consideration.In other words, our method only pays attention to the human torso.
The torso line can be represented as a vector and calculated by: where is the vector of the torso line.H(Xh, Yh, Zh) is the position of the hip-center joint in 3D coordinates, and S(Xs, Ys, Zs) indicates the position of the shoulder-center joint.We call the vector the torso vector in our approach.

Gravity Vector and Torso Angle
As we all know, the gravity line is always vertical to the ground.Therefore, all lines parallel with the y-axis can be seen as the gravity lines.Every two points on the gravity line can form a vector, which is called the gravity vector in our approach.
According to vector translation theory in solid geometry, the start point of the gravity vector and the start point of the torso vector can be moved to origin coordinates.We take a middle frame of a fall video for example.Figure 3 shows the process of forming the torso angle.In a red, green, blue (RGB) image, each pixel only contains 2D position information.However, the depth image provides each pixel's 3D position information.Figure 2 shows the joints in 3D depth image space.These joints of a person's skeleton can be considered as pixels in the depth image.With these 3D joint points of the skeleton, the computer can understand the meaning of human gestures when a set of complex activities is made by human beings in front of the Kinect.As the main purpose of our system is to alarm as soon as a fall happens, we only take the shoulder center and hip center joints into consideration.In other words, our method only pays attention to the human torso.
The torso line can be represented as a vector and calculated by: where −→ HS is the vector of the torso line.H(X h , Y h , Z h ) is the position of the hip-center joint in 3D coordinates, and S(X s , Y s , Z s ) indicates the position of the shoulder-center joint.We call the vector the torso vector in our approach.In a red, green, blue (RGB) image, each pixel only contains 2D position information.However, the depth image provides each pixel's 3D position information.Figure 2 shows the joints in 3D depth image space.These joints of a person's skeleton can be considered as pixels in the depth image.With these 3D joint points of the skeleton, the computer can understand the meaning of human gestures when a set of complex activities is made by human beings in front of the Kinect.As the main purpose of our system is to alarm as soon as a fall happens, we only take the shoulder center and hip center joints into consideration.In other words, our method only pays attention to the human torso.
The torso line can be represented as a vector and calculated by: where is the vector of the torso line.H(Xh, Yh, Zh) is the position of the hip-center joint in 3D coordinates, and S(Xs, Ys, Zs) indicates the position of the shoulder-center joint.We call the vector the torso vector in our approach.

Gravity Vector and Torso Angle
As we all know, the gravity line is always vertical to the ground.Therefore, all lines parallel with the y-axis can be seen as the gravity lines.Every two points on the gravity line can form a vector, which is called the gravity vector in our approach.
According to vector translation theory in solid geometry, the start point of the gravity vector and the start point of the torso vector can be moved to origin coordinates.We take a middle frame of a fall video for example.Figure 3 shows the process of forming the torso angle.

Gravity Vector and Torso Angle
As we all know, the gravity line is always vertical to the ground.Therefore, all lines parallel with the y-axis can be seen as the gravity lines.Every two points on the gravity line can form a vector, which is called the gravity vector in our approach.
According to vector translation theory in solid geometry, the start point of the gravity vector and the start point of the torso vector can be moved to origin coordinates.We take a middle frame of a fall video for example.Figure 3 shows the process of forming the torso angle.According to the cosine law, the angle between these two vectors, named the torso angle, can be calculated by: where means the vector from any point on the y-axis to the hip center joint.Since the point on the gravity line is self-defined and the hip center is moved to the origin coordinates, so = (0, − , 0).Equation ( 2) can be also represented by: Figure 4 shows the torso angles in three common daily activities, standing, walking and sitting.Figure 4a-c shows the RGB images of each video and Figure 4d-f are their depth images marked with the torso line and the gravity line.According to the cosine law, the angle between these two vectors, named the torso angle, can be calculated by: where −→ GH means the vector from any point on the y-axis to the hip center joint.Since the point on the gravity line is self-defined and the hip center is moved to the origin coordinates, so −→ GH = (0, −Y h , 0).Equation ( 2) can be also represented by: Figure 4 shows the torso angles in three common daily activities, standing, walking and sitting.Figure 4a-c shows the RGB images of each video and Figure 4d-f are their depth images marked with the torso line and the gravity line.According to the cosine law, the angle between these two vectors, named the torso angle, can be calculated by: where means the vector from any point on the y-axis to the hip center joint.Since the point on the gravity line is self-defined and the hip center is moved to the origin coordinates, so = (0, − , 0).Equation ( 2) can be also represented by: Figure 4 shows the torso angles in three common daily activities, standing, walking and sitting.Figure 4a-c shows the RGB images of each video and Figure 4d-f are their depth images marked with the torso line and the gravity line.Centroid height means the distance from the centroid point of a person to the ground.In our approach, we adopt the hip center joint as the rough centroid of a person.There are three reasons for using the hip center joint as the centroid, rather than calculating the human shape pixels and finding out the centric position.First, the exact centroid of the human shape is not necessary for our method.The approximated point is also a good choice because of the consideration of only the descending rate of its height.Secondly, the hip touching the ground is a common scene in nearly all kinds of falls.Therefore, although the position of the hip center joint is not the exact position of the centroid of the human shape, it is more representative for fall detection.Thirdly, the Kinect software development kit (SDK) provides a set of user-friendly and effective functions to track or estimate the position of the hip center.
Before calculating the centroid height, ground plane should be found out first.Although finding out the ground plane is a complex work, Kinect SDK provides four parameters for us, which can be used to exactly calculate the height from any points in the depth image to the ground plane.Equation (4) shows the four parameters.
where A, B, C and D are the ground parameters that can be used to calculate point height.
The height from the hip center to the ground Hc is calculated using Equation (5).
where C(X c , Y c , Z c ) is the hip center joint in the depth image.
Through our experiments, we found that the centroid height can be exactly calculated by Equation (5) only when the ground is in the scene.When the Kinect sensor is installed too high to detect the ground, parameters cannot be accurately provided.All four parameters will be set to zero as their default values.Obviously, it will be a big obstacle to estimate one's centroid height.To address this issue, we use the right foot point to estimate the height of centroid when the ground parameters are zero.Therefore, Equation ( 5) is enhanced as: ground can be detected where f (X f , Y f , Z f ) is the position of the right foot joint in the 3D coordinate.
Figure 5 shows the value of centroid height in two typical daily activities, crouching and walking.From the experiment data, it can be concluded that the deviation caused by calculating based on the right foot joint is acceptable.

Human Torso Motion Model
Fall activity is the balance loss of a person.When a fall happens, it is always accompanied with sharp changes in the torso angle and the centroid height.In the proposed method, we take the torso angle and the centroid height as two key features.There are our thresholds in our fall detection model, where T α is the threshold for the start key frame detection, T vα is the threshold of the changing rate of the torso angle, T vh is the threshold of the velocity of the centroid height and Appl.Sci.2017, 7, 993 7 of 17

Human Torso Motion Model
Fall activity is the balance loss of a person.When a fall happens, it is always accompanied with sharp changes in the torso angle and the centroid height.In the proposed method, we take the torso angle and the centroid height as two key features.There are our thresholds in our fall detection model, where Tα is the threshold for the start key frame detection, Tvα is the threshold of the changing rate of the torso angle, Tvh is the threshold of the velocity of the centroid height and Ŧ is the tracking time after the torso angle exceeded Tα.In HTMM.The changing rates of the torso angle and centroid height are calculated frame by frame after the torso angle exceeded Tα.The max values of these two features in the given period of time, Ŧ, are compared to their thresholds, respectively.When both rates exceed their corresponding thresholds Tvα and Tvh, a fall is detected.
For the result shown in the limit of stability test (LOST), an adult person can keep his/her balance with the body leaning forward/backward no more than 12.5 degrees and leaning left/right no more than 16 degrees [35].In LOST, the person is asked to keep the whole body in a line.However, there is always an angle between the lower body and the upper body in daily activities.However, the person's torso always keeps parallel with the gravity line.Therefore, we take the torso line rather than the body line to form the torso angle with the gravity line.In our experiments, the is the tracking time after the torso angle exceeded T α .In HTMM.The changing rates of the torso angle and centroid height are calculated frame by frame after the torso angle exceeded T α .The max values of these two features in the given period of time, 7 of 17 hen a fall happens, it is always accompanied with height.In the proposed method, we take the torso res.There are our thresholds in our fall detection key frame detection, Tvα is the threshold of the ld of the velocity of the centroid height and Ŧ is the HTMM.The changing rates of the torso angle and ter the torso angle exceeded Tα.
The max values of Ŧ, are compared to their thresholds, respectively.
sholds Tvα and Tvh, a fall is detected.ity test (LOST), an adult person can keep his/her d no more than 12.5 degrees and leaning left/right erson is asked to keep the whole body in a line.
, are compared to their thresholds, respectively.When both rates exceed their corresponding thresholds T vα and T vh , a fall is detected.
where f(Xf, Yf, Zf) is the position of the right foot joint in the 3D coordinate.
Figure 5 shows the value of centroid height in two typical daily activities, crouching and walking.From the experiment data, it can be concluded that the deviation caused by calculating based on the right foot joint is acceptable.For the result shown in the limit of stability test (LOST), an adult person can keep his/her balance with the body leaning forward/backward no more than 12.5 degrees and leaning left/right no more than 16 degrees [35].In LOST, the person is asked to keep the whole body in a line.However, there is always an angle between the lower body and the upper body in daily activities.However, the person's torso always keeps parallel with the gravity line.Therefore, we take the torso line rather than the body line to form the torso angle with the gravity line.In our experiments, the torso angle exceeding 13 degree is the start of our detection model.The usage of only the torso angle to detect falls is insufficient and will result in low accuracy and a high false alarm rate.For example, bending or controlled lying down will be judged as a fall.To address this issue, the centroid height is imported in our model as the second feature.
Since a fall is an activity that usually happens in a short period of time (in our experiments, most of the fall samples last 1.1~1.6 s), for a video captured with 30 frames per second, there are 33-48 images during a fall.Thus, we built a motion model called HTMM for fall detection.In this model, we pay special attention to the changing rate of torso angle and centroid height in a given period of time.
Assume that the given period of time is represented as otion Model s the balance loss of a person.When a fall happens, it is always accompanied with the torso angle and the centroid height.In the proposed method, we take the torso troid height as two key features.There are our thresholds in our fall detection is the threshold for the start key frame detection, Tvα is the threshold of the he torso angle, Tvh is the threshold of the velocity of the centroid height and Ŧ is the r the torso angle exceeded Tα.In HTMM.The changing rates of the torso angle and e calculated frame by frame after the torso angle exceeded Tα.The max values of s in the given period of time, Ŧ, are compared to their thresholds, respectively.xceed their corresponding thresholds Tvα and Tvh, a fall is detected.lt shown in the limit of stability test (LOST), an adult person can keep his/her body leaning forward/backward no more than 12.5 degrees and leaning left/right degrees [35].In LOST, the person is asked to keep the whole body in a line.always an angle between the lower body and the upper body in daily activities.son's torso always keeps parallel with the gravity line.Therefore, we take the torso e body line to form the torso angle with the gravity line.In our experiments, the ing 13 degree is the start of our detection model.The usage of only the torso angle sufficient and will result in low accuracy and a high false alarm rate.For example, lled lying down will be judged as a fall.To address this issue, the centroid height is odel as the second feature.s an activity that usually happens in a short period of time (in our experiments, amples last 1.1~1.6 s), for a video captured with 30 frames per second, there are ing a fall.Thus, we built a motion model called HTMM for fall detection.In this ecial attention to the changing rate of torso angle and centroid height in a given the given period of time is represented as Ŧ, and rson's torso angle (α), centroid height (H) and recorded time (T) in each frame can rates of α and H in Ŧ of each frame are calculated using Equations ( 7) and ( 8).

Human Torso Motion Model
Fall activity is the balance loss of a person.When a fall happens, it is always accompanied with sharp changes in the torso angle and the centroid height.In the proposed method, we take the torso angle and the centroid height as two key features.There are our thresholds in our fall detection model, where Tα is the threshold for the start key frame detection, Tvα is the threshold of the changing rate of the torso angle, Tvh is the threshold of the velocity of the centroid height and Ŧ is the tracking time after the torso angle exceeded Tα.
In HTMM.The changing rates of the torso angle and centroid height are calculated frame by frame after the torso angle exceeded Tα.
The max values of these two features in the given period of time, Ŧ, are compared to their thresholds, respectively.When both rates exceed their corresponding thresholds Tvα and Tvh, a fall is detected.For the result shown in the limit of stability test (LOST), an adult person can keep his/her balance with the body leaning forward/backward no more than 12.5 degrees and leaning left/right no more than 16 degrees [35].In LOST, the person is asked to keep the whole body in a line.However, there is always an angle between the lower body and the upper body in daily activities.However, the person's torso always keeps parallel with the gravity line.Therefore, we take the torso line rather than the body line to form the torso angle with the gravity line.In our experiments, the torso angle exceeding 13 degree is the start of our detection model.The usage of only the torso angle to detect falls is insufficient and will result in low accuracy and a high false alarm rate.For example, bending or controlled lying down will be judged as a fall.To address this issue, the centroid height is imported in our model as the second feature.
Since a fall is an activity that usually happens in a short period of time (in our experiments, most of the fall samples last 1.1~1.6 s), for a video captured with 30 frames per second, there are 33-48 images during a fall.Thus, we built a motion model called HTMM for fall detection.In this model, we pay special attention to the changing rate of torso angle and centroid height in a given period of time.
Assume that the given period of time is represented as Ŧ, and N (n | n∈ Z ∧ n ≤ Ŧ × 30) denotes the frames' order in Ŧ.
Then, the person's torso angle (α), centroid height (H) and recorded time (T) in each frame can be represented as: The changing rates of α and H in Ŧ of each frame are calculated using Equations ( 7) and ( 8).
× 30) denotes the frames' order in 7 of 17 fall happens, it is always accompanied with t.In the proposed method, we take the torso ere are our thresholds in our fall detection ame detection, Tvα is the threshold of the e velocity of the centroid height and Ŧ is the M. The changing rates of the torso angle and torso angle exceeded Tα.
The max values of compared to their thresholds, respectively.Tvα and Tvh, a fall is detected.(LOST), an adult person can keep his/her ore than 12.5 degrees and leaning left/right s asked to keep the whole body in a line.ody and the upper body in daily activities.the gravity line.Therefore, we take the torso ith the gravity line.In our experiments, the ion model.The usage of only the torso angle cy and a high false alarm rate.For example, l.To address this issue, the centroid height is a short period of time (in our experiments, tured with 30 frames per second, there are del called HTMM for fall detection.In this f torso angle and centroid height in a given d as Ŧ, and (H) and recorded time (T) in each frame can = {t1, t2, …, tn}.e calculated using Equations ( 7) and ( 8).
The changing rates of α and H in 7 of 17 a person.When a fall happens, it is always accompanied with he centroid height.In the proposed method, we take the torso key features.There are our thresholds in our fall detection r the start key frame detection, Tvα is the threshold of the the threshold of the velocity of the centroid height and Ŧ is the eded Tα.
In HTMM.The changing rates of the torso angle and y frame after the torso angle exceeded Tα.
The max values of d of time, Ŧ, are compared to their thresholds, respectively.nding thresholds Tvα and Tvh, a fall is detected.it of stability test (LOST), an adult person can keep his/her d/backward no more than 12.5 degrees and leaning left/right ST, the person is asked to keep the whole body in a line.tween the lower body and the upper body in daily activities.eps parallel with the gravity line.Therefore, we take the torso the torso angle with the gravity line.In our experiments, the start of our detection model.The usage of only the torso angle sult in low accuracy and a high false alarm rate.For example, be judged as a fall.To address this issue, the centroid height is eature.ually happens in a short period of time (in our experiments, ), for a video captured with 30 frames per second, there are built a motion model called HTMM for fall detection.In this e changing rate of torso angle and centroid height in a given time is represented as Ŧ, and of each frame are calculated using Equations ( 7) and (8).
In HTMM, the max changing rates of torso angle and centroid height in the given period of time are used to compare with their thresholds, T vα and T vh .When both of them exceed their thresholds, HTMM outputs 1one to indicate that the activity is judged as a fall; else HTMM outputs zero to indicate that it is not.Our model can be represented as: Figure 6 shows the general block diagram of our approach.The general block can be divided into two main steps.The first step is calculating the torso angle of every frame and comparing it with the threshold value.When the torso angle reaches the threshold value, the program turns to Step 2. The second step is tracking the changing rate of torso angle and centroid height frame by frame in a given period of time.Once both rates exceed the threshold value, the activity is judged as a fall, and the system starts alarming; or the activity is considered as a normal activity when the given period of time is over, and the program turns back to Step 1 to start another loop.The pseudocode of our fall detection method is described in the following Algorithm 1.The general block can be divided into two main steps.The first step is calculating the torso angle of every frame and comparing it with the threshold value.When the torso angle reaches the threshold value, the program turns to Step 2. The second step is tracking the changing rate of torso angle and centroid height frame by frame in a given period of time.Once both rates exceed the threshold value, the activity is judged as a fall, and the system starts alarming; or the activity is considered as a normal activity when the given period of time is over, and the program turns back to Step 1 to start another loop.The pseudocode of our fall detection method is described in the following Algorithm 1.
In HTMM, we introduced the torso angle to clearly judge whether the supervised person is in balance or not.Furthermore, the centroid height is used to find out whether the person is falling.These two features make HTMM have high accuracy in fall detection and work well in differentiating fall and fall-like activities.Figure 7 lists three typical fall-like activities that cause a high false alarm rate in previous approaches.
In the bounding box ratio analysis approach, the ellipse shape analysis approach or even deep learning approach, the biggest shortcoming of these methods is that there is not a clear line between balance and unbalance.Therefore, when fall-like activity appears, the system will consider it as a fall.However, the torso angle together with the centroid height make it easy for HTMM to distinguish fall-like activities.Take the activities in Figure 7 as examples; each activity reaches only one threshold of two features.For controlled lying down and bending, although the torso angle changes greatly in a short period of time, the centroid height has no changes or changes little during this activity; while for crouching, the centroid height changes dramatically in a short period time, but the torso angle keeps at 12.5 degrees, which is lower than the threshold.Section 4 elaborates detailed statistics of our experiments.a fall happens, it is always accompanied with ht.In the proposed method, we take the torso here are our thresholds in our fall detection frame detection, Tvα is the threshold of the the velocity of the centroid height and Ŧ is the M. The changing rates of the torso angle and e torso angle exceeded Tα.The max values of e compared to their thresholds, respectively.s Tvα and Tvh, a fall is detected.st (LOST), an adult person can keep his/her more than 12.5 degrees and leaning left/right is asked to keep the whole body in a line.r body and the upper body in daily activities.h the gravity line.Therefore, we take the torso with the gravity line.In our experiments, the ction model.The usage of only the torso angle racy and a high false alarm rate.For example, all.To address this issue, the centroid height is n a short period of time (in our experiments, ptured with 30 frames per second, there are odel called HTMM for fall detection.In this of torso angle and centroid height in a given ted as Ŧ, and N (n | n∈ Z ∧ n ≤ Ŧ × 30) denotes t (H) and recorded time (T) in each frame can T = {t1, t2, …, tn}.are calculated using Equations ( 7) and (8).
nd centroid height in the given period of time h.When both of them exceed their thresholds, judged as a fall; else HTMM outputs zero to : approach.In HTMM, we introduced the torso angle to clearly judge whether the supervised person is in balance or not.Furthermore, the centroid height is used to find out whether the person is falling.These two features make HTMM have high accuracy in fall detection and work well in differentiating fall and fall-like activities.In the bounding box ratio analysis approach, the ellipse shape analysis approach or even deep learning approach, the biggest shortcoming of these methods is that there is not a clear line between balance and unbalance.Therefore, when fall-like activity appears, the system will consider it as a fall.However, the torso angle together with the centroid height make it easy for HTMM to distinguish fall-like activities.Take the activities in Figure 7 as examples; each activity reaches only one threshold of two features.For controlled lying down and bending, although the torso angle changes greatly in a short period of time, the centroid height has no changes or changes little during this activity; while for crouching, the centroid height changes dramatically in a short period time, but the torso angle keeps at 12.5 degrees, which is lower than the threshold.Section 4 elaborates detailed statistics of our experiments.

Experimental Setup and Dataset
Our method was implemented using Microsoft Visual Studio 2013 Ultimate 2013 (Redmond,

Experimental Setup and Dataset
Our method was implemented using Microsoft Visual Studio 2013 Ultimate 2013 (Redmond, WA, USA) + emgu.cv3.1 (SourceForge, San Francisco, CA, USA)+ Microsoft Kinect sensor v1.0 2013 (Redmond, WA, USA)on a PC using an Intel Core i7-4790 3.60-GHz processor, 8 GB RAM clocked at 1333 MHz.Since Kinect is a newly emerging sensor and the feature, the torso angle, is first raised and imported for fall detection, the existing depth action datasets cannot provide the necessary information we need.For example, Cornell Activity Datasets CAD-60/120 [36], the most commonly-used RGB-D dataset for action recognition, contains 12 activities, such as rinsing mouth, brushing teeth, wearing contact lens, etc., which do not provide falling action samples.Therefore, we built a dataset by ourselves for experiments.
This dataset was collected using Microsoft Kinect sensor v1.0, which was installed 1.4 m high from the ground.The people involved in the self-collected dataset are aged between 20 and 36, with different heights (1.70~1.81m) and genders (four male and one female volunteers).The distance from the monitored person to the Kinect sensor is between 3 and 4.5 m.The actions performed by the single volunteer were separated into two categories: ADL (activity of daily living, including walking, controlled lying down, bending and crouching) and fall (four directions of falls, including forward, backward, left and right).For safety and realistic performance considerations, subjects performed the fall actions on a 15 cm-thick cushion.Each activity is repeated five times by each subject involved.There are in total 100 fall videos (each fall direction contains 25 videos) and 100 ADL videos (each ADL contains 25 videos).In these experiments, the five volunteers were asked to perform in slow motion to imitate the behavior of an elderly person at least one time in different kinds of activities.The joints positions in the 3D coordinates and joint heights were recorded frame by frame in an XML file.The fall samples contain 55~290 frames, and the ADL samples contain 65~317 frames in each video.All of the samples start by standing postures, which last 1~8 s, containing 30~240 frames.

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.This dataset was collected using Microsoft Kinect sensor v1.0, which was installed 1.4 m high from the ground.The people involved in the self-collected dataset are aged between 20 and 36, with different heights (1.70~1.81m) and genders (four male and one female volunteers).The distance from the monitored person to the Kinect sensor is between 3 and 4.5 m.The actions performed by the single volunteer were separated into two categories: ADL (activity of daily living, including walking, controlled lying down, bending and crouching) and fall (four directions of falls, including forward, backward, left and right).For safety and realistic performance considerations, subjects performed the fall actions on a 15 cm-thick cushion.Each activity is repeated five times by each subject involved.There are in total 100 fall videos (each fall direction contains 25 videos) and 100 ADL videos (each ADL contains 25 videos).In these experiments, the five volunteers were asked to perform in slow motion to imitate the behavior of an elderly person at least one time in different kinds of activities.The joints positions in the 3D coordinates and joint heights were recorded frame by frame in an XML file.The fall samples contain 55~290 frames, and the ADL samples contain 65~317 frames in each video.All of the samples start by standing postures, which last 1~8 s, containing 30~240 frames.

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 [Error!Reference source not found.7],the range of the decay rate of the centroid height is from 1.21~2.05m/s.We set 1.21 m/s as its threshold value in our model.Through the experiments, our approach received the best accuracy rate when the parameters were set as follows: Tvα = 12 degree/100 ms 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 1.21~2.05m/s.We set 1.21 m/s as its threshold value in our model.Through the experiments, our approach received the best accuracy rate when the parameters were set as follows: T vα = 12 degree/100 ms T vh = 1.21 m/s 7 of 17 a person.When a fall happens, it is always accompanied with he centroid height.In the proposed method, we take the torso key features.There are our thresholds in our fall detection r the start key frame detection, Tvα is the threshold of the the threshold of the velocity of the centroid height and Ŧ is the eeded Tα.In HTMM.The changing rates of the torso angle and y frame after the torso angle exceeded Tα.The max values of d of time, Ŧ, are compared to their thresholds, respectively.nding thresholds Tvα and Tvh, a fall is detected.it of stability test (LOST), an adult person can keep his/her d/backward no more than 12.5 degrees and leaning left/right ST, the person is asked to keep the whole body in a line.tween the lower body and the upper body in daily activities.eeps parallel with the gravity line.Therefore, we take the torso the torso angle with the gravity line.In our experiments, the start of our detection model.The usage of only the torso angle esult in low accuracy and a high false alarm rate.For example, be judged as a fall.To address this issue, the centroid height is eature.ually happens in a short period of time (in our experiments, ), for a video captured with 30 frames per second, there are built a motion model called HTMM for fall detection.In this e changing rate of torso angle and centroid height in a given time is represented as Ŧ, and N (n | n∈ Z ∧ n ≤ Ŧ × 30) denotes ), centroid height (H) and recorded time (T) in each frame can = {h1, h2, …, hn}, T = {t1, t2, …, tn}.Ŧ of each frame are calculated using Equations ( 7) and ( 8).
s of torso angle and centroid height in the given period of time olds, Tvα and Tvh.When both of them exceed their thresholds, t the activity is judged as a fall; else HTMM outputs zero to e represented as: diagram of our approach.
= 1300 ms where T vα is the threshold value of the torso angle increase rate, T vh is the centroid height decay rate and is always accompanied with d method, we take the torso sholds in our fall detection Tvα is the threshold of the centroid height and Ŧ is the rates of the torso angle and eded Tα.The max values of eir thresholds, respectively.l is detected.ult person can keep his/her egrees and leaning left/right the whole body in a line.per body in daily activities.Therefore, we take the torso line.In our experiments, the usage of only the torso angle lse alarm rate.For example, s issue, the centroid height is ng Equations ( 7) and ( 8).
t in the given period of time em exceed their thresholds, lse HTMM outputs zero to 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 Tα.The max changing rates of the torso angle and 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.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 α .The max changing rates of the torso angle and 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 Tvα to find out its best default value.According to the results, when Tvα 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 Tvα was set too large, and false alarm rate increases when Tvα was set too small.Table 1 shows the test results on our self-collected dataset with different values of Tvα.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 lean of the upper body.For the first factor, the average filter or other filters can be employed to address the issue.For the second factor, the centroid height can be employed as the third feature to improve the accuracy of our method.These two improvements are under further investigation for our future work.Eleven groups of experiments were tested on the self-collected dataset with different T vα to find out its best default value.According to the results, when T vα 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 vα was set too large, and false alarm rate increases when T vα was set too small.Table 1 shows the test results on our self-collected dataset with different values of T vα .Eleven groups of experiments were tested on the self-collected dataset with different Tvα to find out its best default value.According to the results, when Tvα 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 Tvα was set too large, and false alarm rate increases when Tvα was set too small.Table 1 shows the test results on our self-collected dataset with different values of Tvα.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 lean of the upper body.For the first factor, the average filter or other filters can be employed to address the issue.For the second factor, the centroid height can be employed as the third feature to improve the accuracy of our method.These two improvements are under further investigation for our future work.

Detected fall number
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 lean of the upper body.
For the first factor, the average filter or other filters can be employed to address the issue.For the second factor, the centroid height can be employed as the third feature to improve the accuracy of our method.These two improvements are under further investigation for our future work.Fall detection systems are expected to detect falls as soon as possible, so that the most severe consequences of falls will be avoided if the falling person can be assisted immediately.Our method has advantages in time efficiency because of the calculation of only two features.Figure 13 records the time consumptions of each frame in walk and fall.Fall detection systems are expected to detect falls as soon as possible, so that the most severe consequences of falls will be avoided if the falling person can be assisted immediately.Our method has advantages in time efficiency because of the calculation of only two features.Figure 13 records the time consumptions of each frame in walk and fall.Fall detection systems are expected to detect falls as soon as possible, so that the most severe consequences of falls will be avoided if the falling person can be assisted immediately.Our method has advantages in time efficiency because of the calculation of only two features.Figure 13 records the time consumptions of each frame in walk and fall.
As shown in Figure 13, most frames were processed in 0.1~0.8ms.Although a few frames needed 1.6~1.8ms, the processing time of each frame can be ignored because the time interval between two frames (33.33 ms in our 30 fps videos) is far larger than it.
False alarms comprise one of the biggest obstacles that prevent the computer vision-based fall detection method from being commercialized.Our approach works well in reducing the false alarm rate in fall-like activities' detection.Table 2 records the detailed results.Fall detection systems are expected to detect falls as soon as possible, so that the most severe consequences of falls will be avoided if the falling person can be assisted immediately.Our method has advantages in time efficiency because of the calculation of only two features.Figure 13 records the time consumptions of each frame in walk and fall.As shown in Figure 13, most frames were processed in 0.1~0.8ms.Although a few frames needed 1.6~1.8ms, the processing time of each frame can be ignored because the time interval between two frames (33.33 ms in our 30 fps videos) is far larger than it.
False alarms comprise one of the biggest obstacles that prevent the computer vision-based fall detection method from being commercialized.Our approach works well in reducing the false alarm rate in fall-like activities' detection.Table 2 records the detailed results.

Activity Type
The Number of Sample 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 FN (false negative) means the fall samples judged as non-falls.Then, we TPR = TNR = and Accuracy = .

The of Detected as Fall Videos
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 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 As shown in Figure 13, most frames were processed in 0.1~0.8ms.Although a few frames needed 1.6~1.8ms, the processing time of each frame can be ignored because the time interval between two frames (33.33 ms in our 30 fps videos) is far larger than it.
False alarms comprise one of the biggest obstacles that prevent the computer vision-based fall detection method from being commercialized.Our approach works well in reducing the false alarm rate in fall-like activities' detection.Table 2 records the detailed results.

Activity Type
The 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 TPR = , TNR = and Accuracy = .
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 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 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 TPR = TP TP + FN , TNR = TN TN + FP and Accuracy = TP + TN TP + TN + FP + 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

Figure 1 .
Figure 1.Joints of a person's skeleton provided by Kinect.(a) Twenty joints of the skeleton that can be tracked when the person is standing; (b) 10 joints and two estimated joints of the skeleton when the person is sitting, where spin and hip center joints marked with two circles of dotted lines are estimated.

Figure 2 .
Figure 2. Depth image space created by the Kinect sensor.

Figure 1 .
Figure 1.Joints of a person's skeleton provided by Kinect.(a) Twenty joints of the skeleton that can be tracked when the person is standing; (b) 10 joints and two estimated joints of the skeleton when the person is sitting, where spin and hip center joints marked with two circles of dotted lines are estimated.

Figure 1 .
Figure 1.Joints of a person's skeleton provided by Kinect.(a) Twenty joints of the skeleton that can be tracked when the person is standing; (b) 10 joints and two estimated joints of the skeleton when the person is sitting, where spin and hip center joints marked with two circles of dotted lines are estimated.

Figure 2 .
Figure 2. Depth image space created by the Kinect sensor.

Figure 2 .
Figure 2. Depth image space created by the Kinect sensor.

Figure 3 .
Figure 3.The process of extracting torso angle from a depth image.(a) A depth image fetched from a middle frame in a fall video; (b) torso vector represented in 3D coordinates; (c) torso angle represented in a 2D plane after vector translation.

Figure 4 .
Figure 4.The torso angles in three common daily activities.(a-c) the RGB images of standing, walking and sitting; (d-f) their depth images, where the solid line is the gravity line and the dotted line is the torso line.

Figure 3 .
Figure 3.The process of extracting torso angle from a depth image.(a) A depth image fetched from a middle frame in a fall video; (b) torso vector represented in 3D coordinates; (c) torso angle represented in a 2D plane after vector translation.

Figure 3 .
Figure 3.The process of extracting torso angle from a depth image.(a) A depth image fetched from a middle frame in a fall video; (b) torso vector represented in 3D coordinates; (c) torso angle represented in a 2D plane after vector translation.

Figure 4 .
Figure 4.The torso angles in three common daily activities.(a-c) the RGB images of standing, walking and sitting; (d-f) their depth images, where the solid line is the gravity line and the dotted line is the torso line.

Figure 4 .
Figure 4.The torso angles in three common daily activities.(a-c) the RGB images of standing, walking and sitting; (d-f) their depth images, where the solid line is the gravity line and the dotted line is the torso line.

Figure 5 .
Figure 5.The values of centroid height recorded in two daily activities videos: crouching and walking.(a) Centroid height in crouching activity video; (b) centroid height in walking activity video.

Figure 5 .
Figure 5.The values of centroid height recorded in two daily activities videos: crouching and walking.(a) Centroid height in crouching activity video; (b) centroid height in walking activity video.

Figure 6 .
Figure 6.General block diagram of our approach; where ( ) is the max changing rate of the centroid height in the given period of time and ( ) the max changing rate of the torso angle in the given period of time.The definitions of the given threshold values are elaborated in Section 4.

Algorithm 1 :
Pseudocode of our proposed method for fall detection.Input: Sequence of the skeleton frames captured by Kinect sensor Output: bool bFallIsDetected Loop 1: while (torsoAngle < Tα) { joint_shoulderCenter ← fetch shoulder center 3D position from current skeleton frame; joint_hipCenter ← fetch hip center 3D position from current skeleton frame; torsoAngle ← calculate torso angle of current skeleton frame; } Loop 2: While (trackingTime < Ŧ) { V_torsoAngle ← calculate the current torso angle changing rate by current frame; MaxV_torsoAngle ← update its value if V_torsoAngle is larger

Figure 6 .
Figure 6.General block diagram of our approach; where Max(V h t ) is the max changing rate of the centroid height in the given period of time and Max(V α t ) the max changing rate of the torso angle in the given period of time.The definitions of the given threshold values are elaborated in Section 4.

Algorithm 1 :
Pseudocode of our proposed method for fall detection.Input: Sequence of the skeleton frames captured by Kinect sensor Output: bool bFallIsDetected Loop 1: while (torsoAngle < T α ) { joint_shoulderCenter ← fetch shoulder center 3D position from current skeleton frame; joint_hipCenter ← fetch hip center 3D position from current skeleton frame; torsoAngle ← calculate torso angle of current skeleton frame;

Figure 7 Figure 7 .
Figure 7.The data changing curve of the torso angle and centroid height.(a) The torso angle data changing curve; (b) the centroid height data changing curve.

Figure 7 .
Figure 7.The data changing curve of the torso angle and centroid height.(a) The torso angle data changing curve; (b) the centroid height data changing curve.

Figure 8 .
Figure 8.The detected skeletons with different postures, clothes or walking devices.

Figure 8 .
Figure 8.The detected skeletons with different postures, clothes or walking devices.
f time (in our experiments, rames per second, there are M for fall detection.In this d centroid height in a given | n∈ Z ∧ n ≤ Ŧ × 30) denotes d time (T) in each frame can

Appl. Sci. 2017, 7 , 993 11 of 17 Tvh = 1 .Figure 9 .
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.

FramesFigure 9 .
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.

Figure 10 .
Figure 10.The duration of each fall in the self-collected dataset.There are in total 100 fall videos in the dataset.

Figure 10 .
Figure 10.The duration of each fall in the self-collected dataset.There are in total 100 fall videos in the dataset.

Figure 10 .
Figure 10.The duration of each fall in the self-collected dataset.There are in total 100 fall videos in the dataset.

Figure 11 .
Figure 11.The torso angle changing curves of falsely judged samples.

Figure 12 .
Figure 12.The centroid height changing curves of falsely judged samples.

Figure 13 .
Figure 13.The time consumptions of each frame in walk and fall.The two test videos of this graph

Figure 11 .
Figure 11.The torso angle changing curves of falsely judged samples.

Figure 11 .
Figure 11.The torso angle changing curves of falsely judged samples.

Figure 12 .
Figure 12.The centroid height changing curves of falsely judged samples.

Figure 13 .
Figure 13.The time consumptions of each frame in walk and fall.The two test videos of this graph

Figure 12 .
Figure 12.The centroid height changing curves of falsely judged samples.

Figure 12 .
Figure 12.The centroid height changing curves of falsely judged samples.

Figure 13 .Figure 13 .
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.

Table 1 .
The test results on the self-collected dataset with different Tvα.TP: true positive; FN: false negative; FP: false positive; TN: true negative

Table 1 .
The test results on the self-collected dataset with different T vα .TP: true positive; FN: false negative; FP: false positive; TN: true negative.

Table 1 .
The test results on the self-collected dataset with different Tvα.TP: true positive; FN: false negative; FP: false positive; TN: true negative

Table 2 .
Experimental results and evaluation of our approach.

Table 2 .
Experimental results and evaluation of our approach.

Table 3 .
Comparison of the fall detection capability on our self-collected dataset with other Kinect-based fall detection approaches.

Table 2 .
Experimental results and evaluation of our approach.

Table 3 .
Comparison of the fall detection capability on our self-collected dataset with other Kinect-based fall detection approaches.

Table 3 .
Comparison of the fall detection capability on our self-collected dataset with other Kinect-based fall detection approaches.