## 1 Introduction
Fall detection based on partially-observed videos is considered challenging due to the fact that the unobserved subsequences of video frames might be of different lengths and can occur at any time during video recording. To address this challenge, researchers have recently attempted to predict falls using incomplete depth-map video sequences [26; 27]. Specifically, fall prediction aims to predict the falling event by analyzing an incomplete depth-map video sequence in which a subset of frames that covers only the beginning of the fall is observed, as depicted in Figure 1b. In fact, fall prediction can be viewed as a special case of the general scenario of fall detection based on partially-observed videos, in which the fall is identified by analyzing a video sequence that includes unobserved subsequences of video frames having different durations and occurring at any time. Figure 1c illustrates the general scenario of fall detection based on partially-observed videos. Recently, several approaches have been proposed to detect falls under occluded conditions based on analyzing the depth images acquired using the Kinect sensor. For example, [PERSON] et al. [23] proposed a Kinect-based approach for detecting falls in indoor environments. The approach analyzes the depth images acquired from the Kinect sensor using anthropometric relationships and features to identify depth blobs that represent humans. Then, a fall is detected if the depth blob associated with a human is near the floor. [PERSON] and [PERSON] [28] proposed a two-stage fall detection approach to identify three fall-related positions, including: standing, sitting and lying down. The first stage of their approach analyzes the depth images acquired from a Kinect sensor to identify the vertical characteristics of each person and identify on-ground events based on the computed vertical state information of the subject over time. Then, the second stage employs an ensemble of decision trees classifier to identify falls in the on-ground events. [PERSON] et al. [24] proposed a Kinect-based system to detect falls under occlusion conditions. Their system employs two features for fall detection, including the subject's centroid to measure the distance from the floor, as well as the body velocity. A fall is detected when the velocity is larger than a certain threshold, while the distance from the ground to the subject's centroid is smaller than a specific threshold value. Unlike the aforementioned approaches, in which fall-related activities were recognized while the subject is partially occluded based on depth images, [PERSON] et al. [29] proposed an approach for recognizing human activities from partially-observed videos based on sparse coding analysis. The reported experimental results in [29] show limited recognition accuracy, which might not be suitable for real-world applications. Moreover, the approach employed in [29] considered only RGB videos that include a single unobserved subsequence of video frames. As discussed previously, the use of depth sensors, such as the Microsoft Kinect sensor, for fall detection provides several advantages over the RGB cameras, including subject privacy preservation and the capability to acquire the 3D positions of skeletal joints at interactive rates. To the best of our knowledge, the general scenario of fall detection from partially-observed depth-map video sequences based on utilizing the 3D skeletal joint positions has not been investigated in the literature. In this paper, we propose an approach for detecting falls from partially-observed depth-map video sequences based on the 3D skeletal joint positions provided by the Kinect sensor. The proposed approach utilizes the anatomical planes concept [31] to construct a human representation that can capture both the poses and motions of the human body parts during fall-related activities. In particular, we adopt and expand our earlier work [30; 32] in which a motion pose ge  
Figure 1: Illustration of the different fall detection schemes.