Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

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.

Accepted for publication in the IEEE Transactions on Geoscience and Remote Sensing journal

References in corpus (6)

• Goodness-of-fit tests via phi-divergences
• Hypothesis Testing in Speckled Data with Stochastic Distances
• Polarimetric SAR Image Segmentation with B-Splines and a New Statistical Model
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• Classification of Complex Wishart Matrices with a Diffusion-Reaction System guided by Stochastic Distances
• Texture and Color-based Image Retrieval Using the Local Extrema Features and Riemannian Distance
• Contrast Measures based on the Complex Correlation Coefficient for PolSAR Imagery
• Revisiting the effect of spatial resolution on information content based on classification results
• A clustering approach to heterogeneous change detection