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One of the potential applications of polarimetric Synthetic Aperture Radar (SAR) data is the classification of land cover, such as forest canopies, vegetation, sea ice types, and urban areas. In contrast to single or dual polarized SAR systems, full polarimetric SAR systems provide more information about the physical and geometrical properties of the imaged area. This paper proposes a new Bayes risk function which can be minimized to obtain a Likelihood Ratio (LR) for the supervised classification of polarimetric SAR data. The derived Bayes risk function is based on the complex Wishart distribution. Furthermore, a new spatial criterion is incorporated with the LR classification process to produce more homogeneous classes. The application for Arctic sea ice mapping shows that the LR and the proposed spatial criterion are able to provide promising classification results. Comparison with classification results based on the Wishart classifier, the Wishart Likelihood Ratio Test Statistic (WLRTS) proposed by Conradsen et al. (2003) and the Expectation Maximization with Probabilistic Label Relaxation (EMPLR) algorithm are presented. High overall classification accuracy of selected study areas which reaches 97.8% using the LR is obtained. Combining the derived spatial criterion with the LR can improve the overall classification accuracy to reach 99.9%. In this study, fully polarimetric C-band RADARSAT-2 data collected over Franklin Bay, Canadian Arctic, is used.
