Rigid body motion trajectories can provide sufficient clues in understanding motion behaviors of objects of interest. An invariant descriptor for a motion trajectory can offer substantial advantages over raw data. This paper firstly proposes a Dual Square-Root Function (DSRF) descriptor by only calculating gradient-based shape features of normalized rigid body motion trajectories, while high-order time derivatives are involved in previous works. Our DSRF descriptor has shown richness in description, moreover, it is invariant to scaling, rigid transformation, robust to noise and beneficial for matching rate-variance trajectories. To illustrate these, we then evaluate DSRF descriptor for different trajectory-based rigid body motion recognition tasks. Experimental results on two benchmark datasets demonstrate that it outperforms previous ones in terms of the recognition accuracy and robustness.
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