Modeling Images as Mixtures of Reference Images
Résumé
A state-of-the-art approach to measure the similarity of
two images is to model each image by a continuous distribution,
generally a Gaussian mixture model (GMM), and
to compute a probabilistic similarity between the GMMs.
One limitation of traditionalmeasures such as the Kullback-
Leibler (KL) divergence and the Probability Product Kernel
(PPK) is that they measure a global match of distributions.
This paper introduces a novel image representation. We
propose to approximate an image, modeled by a GMM, as
a convex combination of K reference image GMMs, and
then to describe the image as the K-dimensional vector of
mixture weights. The computed weights encode a similarity
that favors local matches (i.e. matches of individual Gaussians)
and is therefore fundamentally different from the KL
or PPK. Although the computation of the mixture weights
is a convex optimization problem, its direct optimization is
difficult. We propose two approximate optimization algorithms:
the first one based on traditional sampling methods,
the second one based on a variational bound approximation
of the true objective function.
We apply this novel representation to the image categorization
problem and compare its performance to traditional
kernel-based methods. We demonstrate on the PASCAL
VOC 2007 dataset a consistent increase in classification
accuracy.