On estimating the local entropy of an image in a sliding window

The paper considers a number of issues related to the calculation of the local entropy in a sliding window for image processing tasks. A new algorithm for entropy estimation is proposed, which has several times lower computational complexity than the known ones. The algorithm is based on the approximate representation of the histogram in the form of a truncated series expansion over some system of orthogonal basis functions, recursive calculation of the coefficients of this expansion in a sliding window and subsequent recalculation of the coefficients into the entropy estimate. Questions of an orthogonal basis selection for representing the local histogram as a truncated series are considered and the appropriateness of using the Haar basis is shown. A technique of constructing hierarchical approximator, which realizes fast recalculation of histogram decomposition coefficients into entropy value, is described. The theoretical statements of the paper are verified by experiments on the Earth remote sensing images.