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We present a method for characterizing human activities using 3D deformable shape models. The motion trajectories of points extracted from objects involved in the activity are used to build models for each activity, and these models are used for classification and detection of unusual activities. The deformable models are learnt using the factorization theorem for nonrigid 3D models. We present a theory for characterizing the degree of deformation in the 3D models from a sequence of tracked observations. This degree, termed as deformation index (DI), is used as an input to the 3D model estimation process. We study the special case of ground plane activities in detail because of its importance in video surveillance applications. We present results of our activity modeling approach using videos of both high-resolution single individual activities and ground plane surveillance activities.