3D rotation invariant decomposition of motion signals

Abstract

A new model for describing a three-dimensional (3D) trajectory is introduced in this article. The studied object is viewed as a linear combination of rotatable 3D patterns. The resulting model is now 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. A novel 3DRI decomposition problem consists of estimating the active patterns, their coefficients, their rotations and their shift parameters. Sparsity allows to select few patterns among multiple ones. Based on the sparse approximation principle, a non-convex optimization called 3DRI matching pursuit (3DRI-MP) is proposed to solve this problem. This algorithm is applied to real and simulated data, and compared in order to evaluate its performances. © 2012 Springer-Verlag.