Covariance Matrices Encoding Based on the Log-Euclidean and Affine Invariant Riemannian Metrics

This paper presents coding methods used to encode a set of covariance matrices. Starting from a Gaussian mixture model adapted to the log-Euclidean or affine invariant Riemannian metric, we propose a Fisher Vector (FV) descriptor adapted to each of these metrics: the log Euclidean FV (LE FV) and the Riemannian Fisher Vector (RFV). An experiment is conducted on four conventional texture databases to compare these two metrics and to illustrate the potential of these FV based descriptors compared to state-of-the-art BoW and VLAD based descriptors. A focus is also done to illustrate the advantage of using the Fisher information matrix during the derivation of the FV.