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We analyze the application of Shannon entropy and Bhattacharyya distance for the characterization of polarimetric interferometric synthetic aperture radar (PolInSAR) images. We discuss the relevance of the decomposition of the Shannon entropy of a homogeneous region into the sum of three physically meaningful terms that depend respectively on intensity, polarimetry, and interferometry. We also discuss an analogous decomposition property for the Bhattacharyya distance, which is an efficient measure of the contrast between two regions. We illustrate the application of this approach for analyzing different contributions in the information content of PolInSAR images.