Image Similarity based on a Distributional 'Metric' for Multivariate Data

The problem of image similarity has become a challenging task in the field of computer vision through the last two decades. The assessment of (dis)similarity between color (or multichannel, in general) images or parts of images has been studied on several image processing application domains such as image indexing and retrieval, classification and unsupervised segmentation (Rubner et al., 2001). The basic operations that need to be carried out in order to estimate the similarity between two color images are three-fold (Stricker & Orengo, 1995): first, choose an appropriate color space for image representation; then, extract a signature for each image (using, commonly, low-level features) to construct a theoretically valid distribution; finally, establish pairwise comparisons based on these signatures. Each signature constitutes the content description of a corresponding image. It is summarized based on pixel attributes and provides a representation of the image in a multidimensional feature space. There, a proper (dis)similarity measure is defined in order to act as a general rule for comparing any given pair of images. In these directions, several (dis)similarity measures have been developed and used as empirical estimates of the distribution of image features, confirming that distribution-based measures exhibit excellent performance in all areas (Rubner et al., 2001). In the context of visual image similarity, we make use of a nonparametric test from the field of multivariate statistics that deals with the “Multivariate Two-Sample Problem”, originally presented by Friedman and Rafsky (1979). The specific test is a multivariate extension of the classical Wald-Wolfowitz test (WW-test) and compares two different samples of vectorial observations (i.e. two sets of points in