  In this paper, we introduce an end-to-end framework for video analysis
focused towards practical scenarios built on theoretical foundations from
sparse representation, including a novel descriptor for general purpose video
analysis. In our approach, we compute kinematic features from optical flow and
first and second-order derivatives of intensities to represent motion and
appearance respectively. These features are then used to construct covariance
matrices which capture joint statistics of both low-level motion and appearance
features extracted from a video. Using an over-complete dictionary of the
covariance based descriptors built from labeled training samples, we formulate
low-level event recognition as a sparse linear approximation problem. Within
this, we pose the sparse decomposition of a covariance matrix, which also
conforms to the space of semi-positive definite matrices, as a determinant
maximization problem. Also since covariance matrices lie on non-linear
Riemannian manifolds, we compare our former approach with a sparse linear
approximation alternative that is suitable for equivalent vector spaces of
covariance matrices. This is done by searching for the best projection of the
query data on a dictionary using an Orthogonal Matching pursuit algorithm. We
show the applicability of our video descriptor in two different application
domains - namely low-level event recognition in unconstrained scenarios and
gesture recognition using one shot learning. Our experiments provide promising
insights in large scale video analysis.
