Copula-Based Joint Statistical Model for Polarimetric Features and Its Application in PolSAR Image Classification

Polarimetric features are essential to polarimetric synthetic aperture radar (PolSAR) image classification for their better physical understanding of terrain targets. The designed classifiers often achieve better performance via feature combination. However, the simply combination of polarimetric features cannot fully represent the information in PolSAR data, and the statistics of polarimetric features are not extensively studied. In this paper, we propose a joint statistical model for polarimetric features derived from the covariance matrix. The model is based on copula for multivariate distribution modeling and alphastable distribution for marginal probability density function estimations. We denote such model by CoAS. The proposed model has several advantages. First, the model is designed for real-valued polarimetric features, which avoids the complex matrix operations associated with the covariance and coherency matrices. Second, these features consist of amplitudes, correlation magnitudes, and phase differences between polarization channels. They efficiently encode information in PolSAR data, which lends itself to interpretability of results in the PolSAR context. Third, the CoAS model takes advantage of both copula and the alpha-stable distribution, which makes it general and flexible to construct the joint statistical model accounting for dependence between features. Finally, a supervised Markovian classification scheme based on the proposed CoAS model is presented. The classification results on several PolSAR data sets validate the efficacy of CoAS in PolSAR image modeling and classification. The proposed CoAS-based classifiers yield superior performance, especially in building areas. The overall accuracies are higher by 5%-10%, compared with other benchmark statistical modelbased classification techniques.