Decomposition and dictionary learning for 3D trajectories

• Published in: Signal processing 2014-05, Vol.98, p.423-437
• Main Authors: Barthélemy, Q., Larue, A., Mars, J.I.
• Format: Article
• Language: English
• Subjects: 3D motion trajectory; Algorithms; Applications; Applied sciences; Artificial Intelligence; Computational Geometry; Computer Science; Decomposition; Detection, estimation, filtering, equalization, prediction; Dictionaries; Dictionary learning; Engineering Sciences; Exact sciences and technology; Information, signal and communications theory; Learning; Machine Learning; Matching; Mathematical models; Orthogonal matching pursuit; Procrustes registration; Rotation invariant; Shift-invariant; Signal and communications theory; Signal and Image processing; Signal, noise; Statistics; Telecommunications and information theory; Three dimensional; Trajectories
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2013.12.004

A new model for describing a three-dimensional (3D) trajectory is proposed in this paper. The studied trajectory is viewed as a linear combination of rotatable 3D patterns. The resulting model is thus 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. This paper is divided into two parts based on this model. On the one hand, the 3DRI decomposition 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. •A new 3D rotation invariant model is proposed to analyze 3D trajectories.•Sparse approximations based on Matching Pursuit estimate coefficients and rotation matrices.•A dictionary learning algorithm estimates a dictionary of rotatable patterns.•This approach provides a better data representation than the state-of-the-art, even when data are not revolved.