Decomposition and Dictionary Learning for 3D Trajectories

A new model for describing a three-dimensional (3D) trajectory is proposed in this article. The studied trajectory is viewed as a lin-ear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This article is divided into two parts based on this model. On the one hand, the 3DRI decom-position estimates the active patterns, their coefficients, their rotations and their shift parameters. Based on sparse approximation, this is carried out by two non-convex optimizations: 3DRI matching pursuit (3DRI-MP) and 3DRI orthogonal matching pursuit (3DRI-OMP). On the other hand, a 3DRI learning method learns the characteristic patterns of a database through a 3DRI dictionary learning algorithm (3DRI-DLA). The proposed algorithms are first applied to simulation data to evaluate their performances and to compare them to other algorithms. Then, they are applied to real motion data of cued speech, to learn the 3D trajectory patterns characteristic of this gestural language