Information properties in fine-to-coarse image transformations

The notion of entropy production 𝒫, as defined by the thermodynamics of irreversible transformations, is used to quantify information loss during a transformation from fine-to-coarse image representations. To this aim we first show the existence of a precise relation between 𝒫 and the Kullback-Leibler distance. This relation allows one to gauge local and global information losses which are associated with the global and local information content information of the images. Connections between the proposed approach, segmentation issues, and classical information theory are discussed