Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

TL;DR

This paper derives analytic expressions for stochastic distances between relaxed complex Wishart distributions, enabling improved statistical tests for SAR data analysis, with the Bhattacharyya distance showing superior performance in discrimination tasks.

Contribution

It introduces new analytic formulas for four stochastic distances between relaxed complex Wishart distributions and develops associated hypothesis tests with proven asymptotic properties.

Findings

Bhattacharyya distance outperforms others in sensitivity.

New test statistics follow chi-square distribution asymptotically.

Distances effectively discriminate and identify homogeneity in SAR data.

Abstract

The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.