Recognition of 6 DOF rigid body motion trajectories using a coordinate-free representation

Abstract

This paper presents an approach to recognize 6 DOF rigid body motion trajectories (3D translation + rotation), such as the 6 DOF motion trajectory of an object manipulated by a human. As a first step in the recognition process, 3D 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 invariant representation is 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 velocity profile along the trajectory. Two classification algorithms which use the invariant representation as input are developed and tested experimentally: one approach based on a Dynamic Time Warping algorithm, and one based on Hidden Markov Models. Both approaches yield high recognition rates (up to 95 % and 91 %, respectively). The advantage of the invariant approach is that motion trajectories observed in different contexts (with different reference frames, marker positions, time scales, linear scales, velocity profiles) can be compared and averaged, which allows us to build models from multiple demonstrations observed in different contexts, and use these models to recognize similar motion trajectories in still different contexts.

Invariant representation for user independent motion recognition

“…The proposed approach is tested on two different datasets: the MSR-Action3D dataset 7 [12] and a Continuous Motion (CM) dataset. Both datasets are challenging: the first contains many similar actions, the second is a continuous stream of data in which the starting and the ending points of each gesture are unknown.…”

“…All the users perform come, handover, stop with the right hand, and handover with the left hand. Like in an on-line recognition 7 http://research.microsoft.com/en-us/um/ people/zliu/actionrecorsrc/default.htm scenario, the gesture segmentation is unknown. This dataset was created during the AUTOMATICA fair in 2012 8 .…”

“…A complete set (6 elements) of invariants, computed by the meaning of Instantaneous Screw Axes is adopted in [7] to recognise the motions of a rigid body. To make this representations invariant to linear and angular scale, one needs to divide the invariants by two scaling factors depending on the duration of the gesture.…”

Bidirectional invariant representation of rigid body motions and its application to gesture recognition and reproduction

“…When a moving average filter (window size w = 5) is applied, the performance of DS/EFS is improved a lot. A more sophisticated, off-line filtering technique as the linear Kalman smoother [29] used in [37,7] could further improve the performance. Nevertheless, the usage of off-line filtering techniques limits the applicability of invariant representations in on-line gesture recognition problems and it increases the computational cost of the recognition procedure.…”

Incremental action recognition and generalizing motion generation based on goal-directed features

“…Using torques from four selected joints, their approach allows to classify seven distinct full-body movements. De Schutter et al [4] developed a coordinatefree representation of 6 DOF rigid body movements which exhibits several invariance properties.…”