Motion trajectory reproduction from generalized signature description

Free form motion trajectories prove to be an informative and compact motion clue in sketching long-term, spatiotemporal motions. Hence, motion trajectories have been used for characterizing human behaviors/activities, robot actions and other objects' movements. However, it is observed that most of the previous studies merely use motion trajectories straightforwardly in the raw data form, which is inflexible as they rely largely on the absolute positions. To solve this problem, we propose to achieve effective motion trajectory descriptions by developing a systematic trajectory description mechanism. To this end, a flexible motion trajectory signature descriptor has been proposed in our previous work, which can offer generalized descriptions to the raw trajectory data thanks to its rich description invariants. Moreover, for an effective descriptor, it is sometimes desired to have mutual description functions, i.e. describing and un-describing capability to support some applications like robot learning. Hence, opposite to describing a motion trajectory using the signature, this paper focuses on the un-describing problem, that is, reproducing a trajectory instance from a given signature description. The moving frame technique is used in formulating the trajectory reproduction method. A nonlinear signature matching-based metric is also developed to measure the quality of the reproductions. Experiments are conducted to verify the effectiveness of the trajectory reproduction. It is shown that the trajectory signature is flexible and easy to implement in both the description and reproduction of trajectory instances.