The Shannon entropy which is widely used in many fields of science, some advantage and disadvantage of it are noticeable. In view of disadvantage formulated, other entropies like exponential entropy. In this paper, we study some characterisation and properties of exponential entropy such as asymptotic equipartition property, chain rule, the subadditivity, invariancy under monotone transformation in parallel to those for the Shannon entropy in continuous and discrete cases. Also, the relationship between exponential entropy with Tsallis entropy and Renyi entropy obtained. Finally, we show that in the image segmentation, algorithms based on exponential entropy has a better performance than the algorithms which are based on the Shannon entropy.

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