Modeling Image Similarity by Gaussian Mixture Models and the Signature Quadratic Form Distance

Modeling image similarity for browsing and searching in voluminous image databases is a challenging task of nearly all content-based image retrieval systems. One promising way of defining image similarity consists in applying distance-based similarity measures on compact image representations. Beyond feature histograms and feature signatures, more general feature representations are mixture models of which the Gaussian mixture model is the most prominent one. This feature representation can be compared by employing approximations of the Kullback-Leibler Divergence. Although several of those approximations have been successfully applied to model image similarity, their applicability to mixture models based on high-dimensional feature descriptors is questionable. In this paper, we thus introduce the Signature Quadratic Form Distance to measure the distance between two Gaussian mixture models of high-dimensional feature descriptors. We show the analytical computation of the proposed Gaussian Quadratic Form Distance and evaluate its retrieval performance by making use of different benchmark image databases.