A similarity measure between unordered vector sets with application to image categorization

A novel approach to compute the similarity between two unordered variable-sized vector sets using the maximum a posteriori (MAP) criterion, which provides a more accurate estimate of the GMM parameters compared to standard maximum likelihood estimation (MLE) in the challenging case where the cardinality of the vector set is small.

Abstract

We present a novel approach to compute the similarity between two unordered variable-sized vector sets. To solve this problem, several authors have proposed to model each vector set with a Gaussian mixture model (GMM) and to compute a probabilistic measure of similarity between the GMMs. The main contribution of this paper is to model each vector set with a GMM adapted from a common ldquouniversalrdquo GMM using the maximum a posteriori (MAP) criterion. The advantages of this approach are twofold. MAP provides a more accurate estimate of the GMM parameters compared to standard maximum likelihood estimation (MLE) in the challenging case where the cardinality of the vector set is small. Moreover, there is a correspondence between the Gaussians of two GMMs adapted from a common distribution and one can take advantage of this fact to compute efficiently the probabilistic similarity. This work is applied to the image categorization problem: images are modeled as bags of low-level features and classification is performed using a kernel classifier based on the proposed similarity measure. Experimental results on the PASCAL VOC 2006 and VOC 2007 databases show the excellent performance of our approach.