## 1 Introduction  
The growing population of elderly people is becoming a pressing issue worldwide, especially in developed countries. In Europe, the official projections indicate that the elderly population is expected to grow rapidly by 58 million between 2004 and 2050 [1]. In the United States, 20% of the population is expected to be elderly by 2030, while in 1994, the percentage of elderly people was only one in eight Americans [2, 3]. In fact, falls are among the major threats to the health of elderly people, particularly those who live by themselves. According to [4], the percentage of elderly people who fall each year is more than 33%. Falls can lead to both physiological and psychological problems for elderly people [5]. Moreover, in the case of falls that do not lead to immediate injuries, around one half of the non-injured elderly fallers require assistance to get up, and hence, delayed assistance can result in long immobile periods, which might affect the faller's health [5; 6]. Therefore, accurate and efficient fall detection systems are crucial to improve the safety of elderly people. Recently, several fall detection systems have been proposed to detect fall incidents. Among these systems, wearable and non-wearable sensor-based systems are the most commonly used [7]. Wearable sensor-based systems employ sensors that are attached to the subject to continuously monitor the subject's activities. For example, several fall detection systems utilize wearable devices that are equipped with gyroscope and accelerometer sensors in order to identify fall incidents [8; 9; 10]. One limitation of wearable sensor-based fall detection systems is the requirement of wearing sensing devices all of the time. Such a requirement might be impractical and inconvenient, especially that wearable sensing devices need to be recharged on a regular basis. The second group of commonly-used fall detection systems is based on using non-wearable sensing devices, such as vision and motion tracking systems, to identify human activities [11; 12; 13]. RGB video cameras (2D cameras) and motion-capturing systems are among the most widely-used non-wearable sensing devices for fall detection [14; 15]. Fall detection systems that are based on analyzing RGB videos recorded by 2D cameras are highly affected by several factors, such as occlusions, illumination, complex background and camera view-angle. Such factors can reduce the accuracy of fall detection. Utilizing motion-capturing systems for fall detection can be a remedy for the aforementioned factors. However, the high cost of the motion-capturing systems and the need to mount markers on the subjects to track their motions might limit the practical application of motion-capturing systems for fall detection. Recently, Microsoft (Microsoft Corporation, Redmond, WA, USA) has introduced a low-cost RGB-D sensor, called the Kinect sensor, which comprises both an RGB camera and a depth sensor. The depth sensor of Kinect enables the recording of depth-map video sequences that preserve the privacy of the subjects. This privacy feature makes the Kinect sensor a non-intrusive sensor compared with the 2D cameras that reveal the identity of the subjects. Furthermore, the capability of the Kinect sensor to detect and track the 3D positions of skeletal joints has attracted several researchers to utilize the Kinect sensor to track human activities and detect falls by analyzing depth-map videos. The literature reveals that the majority of fall detection systems that employ depth-map video sequences are focused on detecting falls by analyzing the frames of a complete video sequence that covers the entire fall incident [16; 17; 18; 19; 20; 21; 22; 23; 24; 25], as illustrated in Figure 1a. Nonetheless, in real-life scenarios, the fall incident might be partially observed due to the presence of an occlusion that blocks the view of the camera or occludes the subject of interest. Moreover, power disconnections may result in missing some video segments, which in turns can lead to partially-observed videos.