Average Entropy: A New Uncertainty Measure with Application to Image Segmentation

Various modifications have been suggested in the past to extend Shannon entropy to continuous random variables. This article investigates these modifications, and suggests a new entropy measure with the name of average entropy (AE). AE is more general than Shannon entropy in the sense that its definition encompasses both continuous as well as discrete domains. It is additive, positive and attains zero only when the distribution is uniform. The main characteristic of the suggested measure lies in its consistency behavior. Many properties of AE, including its relationship with Kullback-Leibler information measure, are studied. Precise theorems about the vanishing of the conditional AE for both continuous and discrete distributions are provided. Toward the end, the measure is tested for its effectiveness in image segmentation.