This paper introduces an image classification method based on the encoding of a set of covariance matrices. This encoding relies on Fisher vectors adapted to the log-Euclidean metric: the log-Euclidean Fisher vectors (LE FV). This approach is next extended to full local Gaussian descriptors composed by a set of local mean vectors and local covariance matrices. For that, the local Gaussian model is transformed to a zero-mean Gaussian model with an augmented covariance matrix. All these approaches are used to encode handcrafted or deep learning features. Finally, they are applied in a remote sensing application on the UC Merced dataset which consists in classifying land cover images. A sensitivity analysis is carried out to evaluate the potential of the proposed LE FV.