Minkowski-metrics as a combination rule for digital-image-coding impairments

Abstract

The urge to compress the amount of information needed to represent digitized images while preserving perceptual image quality has led to a plethora of image-coding algorithms. At high data compression ratios, these algorithms usually introduce several coding artifacts, each impairing image quality to a greater or lesser extent. These impairments often occur simultaneously. For the evaluation of image-coding algorithms, it is important to find out how these impairments combine and how this can be described. The objective of the present study is to show that Minkowski-metrics can be used as a combination rule for small impairments like those usually encountered in digitally coded images. To this end, an experiment has been conducted in which subjects assessed the perceptual quality of scale-space-coded color images comprising three kinds of impairment, viz., 'unsharpness', 'phantoms' (dark/bright patches within bright/dark homogeneous regions) and 'color desaturation'. The results show an accumulation of these impairments that is efficiently described by a Minkowski-metric with an exponent of about two. The latter suggests that digital-image-coding impairments may be represented by a set of orthogonal vectors along the axes of a multidimensional Euclidean space. An extension of Minkowski-metrics is presented to generalize the proposed combination rule to large impairments.