Abstract
Suitable shape representations as well as their temporal
evolution, termed trajectories, often lie to non-linear manifolds. This puts an additional constraint (i.e., non-linearity)
in using conventional machine learning techniques for the
purpose of classification, event detection, prediction, etc.
This paper accommodates the well-known Sparse Coding
and Dictionary Learning to the Kendall’s shape space and
illustrates effective coding of 3D skeletal sequences for action recognition. Grounding on the Riemannian geometry of
the shape space, an intrinsic sparse coding and dictionary
learning formulation is proposed for static skeletal shapes
to overcome the inherent non-linearity of the manifold. As
a main result, initial trajectories give rise to sparse code
functions with suitable computational properties, including
sparsity and vector space representation. To achieve action recognition, two different classification schemes were
adopted. A bi-directional LSTM is directly performed on
sparse code functions, while a linear SVM is applied after
representing sparse code functions using Fourier temporal
pyramid. Experiments conducted on three publicly available datasets show the superiority of the proposed approach
compared to existing Riemannian representations and its
competitiveness with respect to other recently-proposed approaches. When the benefits of invariance are maintained
from the Kendall’s shape representation, our approach not
only overcomes the problem of non-linearity but also yields
to discriminative sparse code functions