On Signature Invariants for Motion Trajectory Recognition

Motion trajectory representation and recognition play important roles in characterizing human-robot interactions like in robot Programming by Demonstration. However, effective descriptors are lacking that can fully describe trajectories and offer substantial invariants. In this paper, we propose a novel Euclidean signature mechanism as the 3-D trajectory descriptor. The signature exhibits an important advantage in computational locality, which offers significant Euclidean and metric group symmetries as well as rich invariants with respect to the varying viewpoint or speed profile. Besides the elaboration of the invariants, the signature approximation and nonlinear signatures matching for trajectory recognition are also presented. The conducted trajectory recognition experiments verified the effectiveness and robustness of the proposed descriptor.