Abstract
The endpoint trajectories of human movements fulfill characteristic power laws linking velocity and curvature. The parameters of these power laws typically vary between different segments of longer action sequences. These parameters might thus be exploited for the unsupervised segmentation of actions into movement primitives. For the example of sign language we investigate whether such segments can be identified by Bayesian binning (BB), using a Gaussian observation model whose mean has a polynomial time dependence. We show that this method yields good segmentation and correctly models ground truth kinematics composed of consecutive segments derived from wrist trajectories recorded from users of Israeli Sign Language (ISL). Importantly, polynomial orders between 3 and 5 yield an optimal trade-off between complexity and accuracy of the trajectory approximation, in accordance with the minimum acceleration and minimum jerk models. Comparing the orders of the polynomials best approximating natural kinematics against those needed to fit the power law ground truth data suggests that kinematic properties not compatible with power laws are also not adequately represented by low order polynomials and require higher order polynomials for a good approximation.
Highlights
Complex motor behavior might be organized in terms of sequences of temporal movement primitives that follow each other sequentially in time
To illustrate that Bayesian binning (BB) is a suitable tool for the computation of compact and accurate Israeli Sign Language (ISL) trajectory representations, we generated ISL-like trajectories with a 3rd order polynomial segment structure and evaluated if BB was able to recover this polynomial order and the segment boundaries
We presented two novel contributions in this paper: firstly, we demonstrated the applicability of BB with piecewise polynomial observation models to motion capture data with a segment-wise www.frontiersin.org power law structure
Summary
Complex motor behavior might be organized in terms of sequences of temporal movement primitives that follow each other sequentially in time. While the appropriate characterization of the temporal organization of complex motor behavior might require hierarchical multi-level representations (Flash and Hochner, 2005), many previous studies that investigated the nature of such primitives have focused on the analysis of movement kinematics. It has been investigated how the temporal and kinematic properties of the movement are influenced by the path followed by the hand (see e.g., Polyakov et al, 2009b). This rule dictates that for figure drawing movements the speed along the motion path is proportional to the curvature of this path raised to the minus one-third power (Lacquaniti et al, 1983):
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