## 1 Introduction
(**a**) Fall detection using a complete depth-map video sequence in which the frames cover the entire fall incident [30]; (**b**) Fall prediction using incomplete depth-map video sequence in which a subset of frames that cover the beginning of the fall incident is observed, while the frames that cover the rest of the fall incident are not observed [27]; (**c**) Fall detection using a partially-observed depth-map video sequence in which the observed frames cover discontinuous parts of the fall incident. was proposed for analyzing human-human interactions and elderly fall detection using complete depth-map video sequences. The MPGD consists of two profiles, namely motion and pose profiles. These profiles enable effective capturing of the semantic context of human activities being performed at each video frame. In this work, we expand the motion and pose profiles in the MPGD by introducing a new set of geometrical relational-based features, to better describe fall-related activities. In order to detect falls in partially-observed depth-map video sequences, we segment fully-observed training video sequences into overlapping segments. Then, we construct a histogram-based representation (HBR) of the MPGDs for the video frames of each segment. The HBR describes the distribution of the MPGDs within each video segment and captures the spatiotemporal configurations encapsulated within the activities of an elderly person during each video segment. Using the computed HBRs of MPGDs, we train a support vector machine (SVM) classifier with a probabilistic output [33] to predict the class of the performed activity in a given video segment. For any new video with unobserved frames subsequences, we compute the HBR of the MPGDs that are associated with video frames in each observed video subsequence. Then, for each observed video subsequence, we utilize the learned SVM model to compute the class posteriori probability of the observed subsequence given its HBR. Finally, to predict the class of the performed activity in the given partially-observed video, we combine the obtained posteriori probabilities from all observed subsequences to obtain an overall posteriori probability estimation for the partially-observed video. In order to evaluate the proposed fall detection approach, we have utilized the Microsoft Kinect sensor to record a dataset of depth-map video sequences that simulates fall-related activities of elderly people. The recorded activities include: walking, sitting, falling form standing and falling from sitting. Three evaluation procedures are developed to quantify the performance of the proposed approach at various configurations, including: fully-observed video sequence, partially-observed video sequence that includes one unobserved video subsequence of random length and partially-observed video sequence that includes two unobserved video subsequences of random lengths. The experimental results reported in this study demonstrate the feasibility of employing the proposed approach for detecting falls based on partially-observed videos. The remainder of this paper is organized as follows. In Section 2, we describe the collected dataset of fall-related activities, the modified MPGD and HBR for human activities and the proposed fall detection approach based on partially-observed depth-map videos. Section 3 presents the experimental results and discussion. Finally, conclusions are presented in Section 4.