Multiresolution-information analysis for images

Abstract This paper is devoted to the analysis and characterization of images in the framework of multiresolution. We use the gray level histogram entropy as the best representation of the information provided by an image. First, we introduce the concept of ‘entropy per pixel’ provided by a class of images given at a certain resolution level, and then we study the ‘entropy per pixel versus resolution’ diagrams for particular images and classes of images. Maximum entropy principle, theory of majorization and other results from information theory are used to prove several properties of these diagrams. The most important property asserts that the entroypy per pixel is strictly decreasing with respect to the resolution, i.e., a coarser resolution observation results in a loss of information. Some examples illustrate the results obtained. Several open problems and applications are proposed.

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