Statistical characterisation of block variance and AC DCT coefficients for power law enhanced images

Abstract

The study of statistical distributions of alternating current (AC) discrete cosine transform (DCT) coefficients is one of the key techniques for digital images. In this study, we have analysed original and power law enhanced images in the logarithmic domain. The logarithmic domain linearises the otherwise nonlinear relation between original and power law enhanced images. We have experimentally proved that Gamma distribution is the best distribution for characterisation of block variance in terms of Jensen-Shannon divergence. Therefore, a composite distribution, Gaussian-Gamma, is employed for characterisation of AC DCT coefficients. We have analytically derived and experimentally verified that the scale parameters of power law enhanced image are proportional to scale parameters of the original image whereas shape parameters remain unchanged. On further experimentation, it is established that scale and shape parameters of the composite statistical distribution of AC DCT coefficients do not change if images are compressed in JPEG format after power law enhancement. Furthermore, a novel feature set of scale parameters is constructed and is applied to train decision tree to classify original, brightened, and darkened images. The comparison of achieved classification results with the state-of-the-art show the efficacy of proposed analysis.