Invariant representations to reduce the variability in recognition of rigid body motion trajectories

In this paper, the use of a coordinate-free representation for recognizing six DOF rigid body motion trajectories is experimentally validated. In the recognition part of 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. During the experiments, a person manipulated an object. The camera viewpoints, time scales, motions profiles, and linear or angular scales were changed between different motion recordings. The experimental results validate that not only in similar but also in different recording conditions, through using the invariant representation, the dependency on the parameters mentioned above are eliminated, and therefore better recognition results are obtained.