Information measures based on fractional calculus

In this letter, fractional calculus is used to propose the fractional entropy (FE) and the fractional mutual information (FMI) as the new forms of the information measure in a generalized Euclidean metric space. Being position-related and causal, FE and FMI are natural extensions and more generalized forms of Shannon entropy and mutual information, respectively.

► FE and FMI are the natural extensions and generalized forms of Shannon and MI respectively.
► Some of the mathematical properties about FE and FMI are rigorously studied.
► Counterexamples demonstrate the value of this work.
► FMI and NFMI can be adopted as the similarity measures in image registration.