  The detection and tracking of human landmarks in video streams has gained in
reliability partly due to the availability of affordable RGB-D sensors. The
analysis of such time-varying geometric data is playing an important role in
the automatic human behavior understanding. However, suitable shape
representations as well as their temporal evolution, termed trajectories, often
lie to nonlinear manifolds. This puts an additional constraint (i.e.,
nonlinearity) in using conventional Machine Learning techniques. As a solution,
this paper accommodates the well-known Sparse Coding and Dictionary Learning
approach to study time-varying shapes on the Kendall shape spaces of 2D and 3D
landmarks. We illustrate effective coding of 3D skeletal sequences for action
recognition and 2D facial landmark sequences for macro- and micro-expression
recognition. To overcome the inherent nonlinearity of the shape spaces,
intrinsic and extrinsic solutions were explored. As main results, shape
trajectories give rise to more discriminative time-series with suitable
computational properties, including sparsity and vector space structure.
Extensive experiments conducted on commonly-used datasets demonstrate the
competitiveness of the proposed approaches with respect to state-of-the-art.
