Action Recognition Using Sparse Representation on Covariance Manifolds of Optical Flow

A novel approach to action recognition in video based on the analysis of optical flow is presented. Properties of optical flow useful for action recognition are captured using only the empirical covariance matrix of a bag of features such as flow velocity, gradient, and divergence. The feature covariance matrix is a low-dimensional representation of video dynamics that belongs to a Riemannian manifold. The Riemannian manifold of covariance matrices is transformed into the vector space of symmetric matrices under the matrix logarithm mapping. The log-covariance matrix of a test action segment is approximated by a sparse linear combination of the log-covariance matrices of training action segments using a linear program and the coefficients of the sparse linear representation are used to recognize actions. This approach based on the unique blend of a logcovariance-descriptor and a sparse linear representation is tested on the Weizmann and KTH datasets. The proposed approach attains leave-one-out cross validation scores of 94.4% correct classification rate for the Weizmann dataset and 98.5% for the KTH dataset. Furthermore, the method is computationally efficient and easy to implement.