Gesture recognition is topical in computer science and aims at interpreting human gestures via mathematical algorithms. Among the numerous applications are physical rehabilitation and imitation games. In this work, we suggest performing human gesture recognition within the context of a serious imitation game, which would aim at improving social interactions with teenagers with autism spectrum disorders. We use an artificial intelligence algorithm to detect the skeleton of the participant, then model the human pose space and describe an imitation learning method using a Gaussian Mixture Model in the Riemannian manifold.