  The bag-of-words (BoW) model treats images as sets of local descriptors and
represents them by visual word histograms. The Fisher vector (FV)
representation extends BoW, by considering the first and second order
statistics of local descriptors. In both representations local descriptors are
assumed to be identically and independently distributed (iid), which is a poor
assumption from a modeling perspective. It has been experimentally observed
that the performance of BoW and FV representations can be improved by employing
discounting transformations such as power normalization. In this paper, we
introduce non-iid models by treating the model parameters as latent variables
which are integrated out, rendering all local regions dependent. Using the
Fisher kernel principle we encode an image by the gradient of the data
log-likelihood w.r.t. the model hyper-parameters. Our models naturally generate
discounting effects in the representations; suggesting that such
transformations have proven successful because they closely correspond to the
representations obtained for non-iid models. To enable tractable computation,
we rely on variational free-energy bounds to learn the hyper-parameters and to
compute approximate Fisher kernels. Our experimental evaluation results
validate that our models lead to performance improvements comparable to using
power normalization, as employed in state-of-the-art feature aggregation
methods.
