On the efficient evaluation of probabilistic similarity functions for image retrieval

Probabilistic approaches are a promising solution to the image retrieval problem that, when compared to standard retrieval methods, can lead to a significant gain in retrieval accuracy. However, this occurs at the cost of a significant increase in computational complexity. In fact, closed-form solutions for probabilistic retrieval are currently available only for simple probabilistic models such as the Gaussian or the histogram. We analyze the case of mixture densities and exploit the asymptotic equivalence between likelihood and Kullback-Leibler (KL) divergence to derive solutions for these models. In particular, 1) we show that the divergence can be computed exactly for vector quantizers (VQs) and 2) has an approximate solution for Gauss mixtures (GMs) that, in high-dimensional feature spaces, introduces no significant degradation of the resulting similarity judgments. In both cases, the new solutions have closed-form and computational complexity equivalent to that of standard retrieval approaches.