Motion trajectory can be an informative and descriptive clue that is suitable for the characterization of motion. Studying motion trajectory for effective motion description and recognition is important in many applications. For instance, motion trajectory can play an important role in the representation, recognition and learning of most long-term human or robot actions, behaviors and activities. However, effective trajectory descriptors are lacking and most reported work just uses motion trajectory in its raw data form. In this paper, we propose a novel motion trajectory signature descriptor and study its rich descriptive invariants which benefit effective motion trajectory recognition. These invariants are key measures of the flexibility and effectiveness of a descriptor. Substantial descriptive invariants can be deduced from the proposed trajectory signature, which is attributed to the computational locality of the signature components. We first present the signature definition and its robust implementation. Then the signature's invariants are elaborated. A non-linear inter-signature matching algorithm is developed to measure the signature's similarity for trajectory recognition. Experiments are conducted to recognize human sign language, in which both synthetic and real data are used to verify the signature's invariants, and to illustrate the effectiveness in the signature recognition.
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