Image Comparison by Compound Disjoint Information with Applications to Perceptual Visual Quality Assessment, Image Registration and Tracking

In this paper, we study (normalized) disjoint information as a metric for image comparison and its applications to perceptual image quality assessment, image registration, and video tracking. Disjoint information is the joint entropy of random variables excluding the mutual information. This measure of statistical dependence and information redundancy satisfies more rigorous metric conditions than mutual information, including self-similarity, minimality, symmetry and triangle inequality. It is applicable to two or more random variables, and can be computed by vector histogramming, vector Parzen window density approximation, and upper bound approximation involving fewer variables. We show such a theoretic advantage does have implications in practice. In the domain of digital image and video, multiple visual features are extracted and (normalized) compound disjoint information is derived from a set of marginal densities of the image distributions, thus enriching the vocabulary of content representation. The proposed metric matching functions are applied to several domain applications to demonstrate their efficacy.