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Vision-based 3-D head detection and tracking systems have been studied in several applications like video surveillance, face-detection systems, and occupant posture analysis. In this paper, we present the development of a topology-based framework using a 3-D skeletal model for the robust detection and tracking of a vehicle occupant's head position from low-resolution range image data for a passive safety system. Unlike previous approaches to head detection, the proposed approach explores the topology information of a scene to detect the position of the head. Among the different available topology representations, the Reeb graph technique is chosen and is adapted to low-resolution 3-D range images. Invariance of the graph under rotations is achieved by using a Morse radial distance function. To cope with the particular challenges such as the noise and the large variations in the density of the data, a voxel neighborhood connectivity notion is proposed. A multiple-hypothesis tracker (MHT) with nearest-neighbor data association and Kalman filter prediction is applied on the endpoints of the Reeb graph to select and filter the correct head candidate out of Reeb graph endpoints. A systematic evaluation of the head detection framework is carried out on full-scale experimental 3-D range images and compared with the ground truth. It is shown that the Reeb graph topology algorithm developed herein allows the correct detection of the head of the occupant with only two head candidates as input to the MHT. Results of the experiments demonstrate that the proposed framework is robust under the large variations of the scene. The processing requirements of the proposed approach are discussed. It is shown that the number of operations is rather low and that real-time processing requirements can be met with the proposed method.