The Jeffries–Matusita distance for the case of complex Wishart distribution as a separability criterion for fully polarimetric SAR data

Abstract

In multidimensional observations, many classification algorithms (supervised or unsupervised) require the selection of optimum bands in which the classes are most distinct. The Jeffries–Matusita (JM) distance is widely used as a separability criterion for optimal band selection and evaluation of classification results. Its original form is based on the assumption of normal distribution of the data. However, in the case of the covariance/coherency matrix of synthetic aperture radar (SAR) polarimetry, the data follow the complex Wishart distribution. In this article, we calculate the JM separability criterion for the case of the complex Wishart distribution. The updated formulation is used for: (1) the estimation of the separability between classes in fully polarimetric SAR data and to evaluate two standard polarimetric SAR classification algorithms, the Wishart and the expectation maximization algorithms, and (2) the classification of fully polarimetric SAR images based on the derived JM separability for the case of complex Wishart distribution. Fully polarimetric RADARSAT-2 images over sea ice in the Canadian Arctic are used to classify different ice surfaces and open water.