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This appendix presents the basic axiomatic characterization of a measure of information gain between the reference image R and the input image I. The objective is twofold: first, to characterize the information gain between two distributions with a minimal number of properties that are natural and thus desirable; and second, to determine the form of all error functions satisfying these properties which we have stated to be desirable in our investigation. The first postulate states a property of how unexpected was a single event of a digital image.
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