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In this paper an algorithmic framework for posture analysis using a single view 3D TOF camera is presented. The 3D human posture parameters are recovered automatically from range data without the usage of body markers. A topological approach is investigated in order to define descriptors suitable to estimate location of body parts and orientation of body articulations. Two Morse function are exploited, the first one provides an Euclidean distance mapping helpful to deal with body self-occlusions. The second Morse function is based on geodesic distance and provides an extended Discrete Reeb Graph description of the main body parts that are head, torso, arms and legs. Geodesic distance function exhibits the property of invariance under isometric transformations that typically occur when the human body changes its posture. The geodesic map of the body is obtained with a two steps procedure. Firstly, a Delaunay meshing is carried out starting from the depth map provided by the 3D TOF camera; secondly, geodesic distances are computed applying Dijkstra algorithm to previously computed mesh. Moreover, a re-meshing method is proposed in order to deal with self-occlusion problem which occurs in the depth data when a human body is partially occluded by other body segments. Experimental results on both synthetic and real data validate the effectiveness of the proposed approach to classifying four main postures: standing, lying, sitting and bending.