  In the traditional object recognition pipeline, descriptors are densely
sampled over an image, pooled into a high dimensional non-linear representation
and then passed to a classifier. In recent years, Fisher Vectors have proven
empirically to be the leading representation for a large variety of
applications. The Fisher Vector is typically taken as the gradients of the
log-likelihood of descriptors, with respect to the parameters of a Gaussian
Mixture Model (GMM). Motivated by the assumption that different distributions
should be applied for different datasets, we present two other Mixture Models
and derive their Expectation-Maximization and Fisher Vector expressions. The
first is a Laplacian Mixture Model (LMM), which is based on the Laplacian
distribution. The second Mixture Model presented is a Hybrid Gaussian-Laplacian
Mixture Model (HGLMM) which is based on a weighted geometric mean of the
Gaussian and Laplacian distribution. An interesting property of the
Expectation-Maximization algorithm for the latter is that in the maximization
step, each dimension in each component is chosen to be either a Gaussian or a
Laplacian. Finally, by using the new Fisher Vectors derived from HGLMMs, we
achieve state-of-the-art results for both the image annotation and the image
search by a sentence tasks.
