An Invariant Representation to Facilitate Recognition of Rigid Body Motion Trajectories

This paper presents the experimental validation of an approach based on a coordinate-free representation to recognize six DOF rigid body motion trajectories. In this approach, the three dimensional measured position trajectories of arbitrary and uncalibrated points attached to the rigid body are transformed to an invariant, coordinate-free representation of the rigid body motion trajectory. This representation is theoretically independent of the reference frame in which the motion is observed, the chosen marker positions, the linear scale (magnitude) of the motion, the time scale, and the motion profile. To experimentally validate this approach, a large set of motions was recorded with different camera viewpoints, different time scales, motion profiles, and linear or angular scales. The obtained results clearly show that the invariant representation eliminates the dependency on the effects mentioned above, and yields high recognition rates even when motions were recorded under very different conditions.status: publishe