Image distortion analysis based on normalized perceptual information distance

Image distortion analysis is a fundamental issue in many image processing problems, including compression, restoration, recognition, classification, and retrieval. Traditional image distortion evaluation approaches tend to be heuristic and are often limited to specific application environment. In this work, we investigate the problem of image distortion measurement based on the theory of Kolmogorov complexity, which has rarely been studied in the context of image processing. This work is motivated by the normalized information distance (NID) measure that has been shown to be a valid and universal distance metric applicable to similarity measurement of any two objects (Li et al. in IEEE Trans Inf Theory 50:3250–3264, 2004). Similar to Kolmogorov complexity, NID is non-computable. A useful practical solution is to approximate it using normalized compression distance (NCD) (Li et al. in IEEE Trans Inf Theory 50:3250–3264, 2004), which has led to impressive results in many applications such as construction of phylogeny trees using DNA sequences (Li et al. in IEEE Trans Inf Theory 50:3250–3264, 2004). In our earlier work, we showed that direct use of NCD on image processing problems is difficult and proposed a normalized conditional compression distance (NCCD) measure (Nikvand and Wang, 2010), which has significantly wider applicability than existing image similarity/distortion measures. To assess the distortions between two images, we first transform them into the wavelet transform domain. Assuming stationarity and good decorrelation of wavelet coefficients beyond local regions and across wavelet subbands, the Kolmogorov complexity may be approximated using Shannon entropy (Cover et al. in Elements of information theory. Wiley-Interscience, New York, 1991). Inspired by Sheikh and Bovik (IEEE Trans Image Process 15(2):430–444, 2006), we adopt a Gaussian scale mixture model for clusters of neighboring wavelet coefficients and a Gaussian channel model for the noise distortions in the human visual system. Combining these assumptions with the NID framework, we derive a novel normalized perceptual information distance measure, where maximal likelihood estimation and least square regression are employed for parameter fitting. We validate the proposed distortion measure using three large-scale, publicly available, and subject-rated image databases, which include a wide range of practical image distortion types and levels. Our results demonstrate the good prediction power of the proposed method for perceptual image distortions.