Edgeworth approximations of the Kullback-Leibler distance toward problems in image analysis, (with J.-J. Lin and R. A. Levine), submitted for publication, 2001.


Evaluation of syntheses or simulated data is often done subjectively through visual comparisons with the original samples. This subjective evaluation is particularly dominant in the area of texture modeling and simulation. In order to objectively evaluate the similarity (or difference) between original samples and syntheses, we propose an approximation for the Kullback-Leibler distance based on Edgeworth expansions (EKLD). We use this approximation to study the sampling distribution of the original and synthesized images. As part of our development, we present numerical examples to study the behavior of EKLD for sample mean distributions and illustrate the advantages of our approach for evaluating the differential entropy and choosing the least statistically dependent basis from wavelet packet dictionaries. Finally, we introduce how to use EKLD in statistical image processing to validate synthetic representations of images.

Keywords: Differential entropy, cumulants, least statistically dependent basis, wavelet packet dictionary, image processing.

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