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We propose a method for recognizing dynamic gestures using a 3D sensor. New aspects of the developed system include problem-adapted data conversion and compression as well as automatic detection of different variants of the same gesture via clustering with a suitable metric inspired by Jaccard metric. The combination of Hidden Markov Models and clustering leads to robust detection of different executions based on a small set of training data. We achieved an increase of 5% recognition rate compared to regular Hidden Markov Models. The system has been used for human-machine interaction and might serve as an assistive system in physiotherapy and neurological or orthopedic diagnosis.