Fisher Vector Coding for Covariance Matrix Descriptors Based on the Log-Euclidean and Affine Invariant Riemannian Metrics

This paper presents an overview of coding methods used to encode a set of covariance matrices. Starting from a Gaussian mixture model (GMM) adapted to the Log-Euclidean (LE) or affine invariant Riemannian metric, we propose a Fisher Vector (FV) descriptor adapted to each of these metrics: the Log-Euclidean Fisher Vectors (LE FV) and the Riemannian Fisher Vectors (RFV). Some experiments on texture and head pose image classification are conducted 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 applied to illustrate the advantage of using the Fisher information matrix during the derivation of the FV. In addition, finally, some experiments are conducted in order to provide fairer comparison between the different coding strategies. This includes some comparisons between anisotropic and isotropic models, and a estimation performance analysis of the GMM dispersion parameter for covariance matrices of large dimension.