Integral invariants for space motion trajectory matching and recognition

Motion trajectories provide a key and informative clue in motion characterization of humans, robots and moving objects. In this paper, we propose some new integral invariants for space motion trajectories, which benefit effective motion trajectory matching and recognition. Integral invariants are defined as the line integrals of a class of kernel functions along a motion trajectory. A robust estimation of the integral invariants is formulated based on the blurred segment of noisy discrete curve. Then a non-linear distance of the integral invariants is defined to measure the similarity for trajectory matching and recognition. Such integral invariants, in addition to being invariant to transformation groups, have some desirable properties such as noise insensitivity, computational locality, and uniqueness of representation. Experimental results on trajectory matching and sign recognition show the effectiveness and robustness of the proposed integral invariants in motion trajectory matching and recognition.