Mixture WG $\Gamma$ -MRF Model for PolSAR Image Classification

Abstract

The WG $\Gamma$ model has been validated as an effective model for the characteristic of polarimetric synthetic aperture radar (PolSAR) data statistics. However, due to the complexity of natural scene and the influence of coherent wave, the WG $\Gamma$ model still needs to be improved to fully consider the polarimetric information. Then, we propose the WG $\Gamma$ mixture model (WG $\Gamma$ MM) for PolSAR data to maintain the correlations among statistics in PolSAR data. To further consider the spatial-contextual information in PolSAR image classification, we propose a novel mixture model, named mixture WG $\Gamma$ -Markov random field (MWG $\Gamma$ -MRF) model, by introducing the MRF to improve the WG $\Gamma$ MM model for classification. In each law of the MWG $\Gamma$ -MRF model, the interaction term based on the edge penalty function is constructed by the edge-based multilevel-logistic model, while the likelihood term being constructed by the WG $\Gamma$ model, so that each law of the MWG $\Gamma$ -MRF model can achieve an energy function and has its contribution to the inference of attributive class. Then, the mixture energy function of the MWG $\Gamma$ -MRF model has the fusion of the weighted component, given the energy functions of every law. The mixture coefficient and the corresponding mean covariance matrix of the MWG $\Gamma$ -MRF model are estimated by the expectation-maximization algorithm, while the parameters of the WG $\Gamma$ model being estimated by the method of matrix log-cumulants. Experiments on simulated data and real PolSAR images demonstrate the effectiveness of the MWG $\Gamma$ -MRF model and illustrate that it can provide strong noise immunity, get smoother homogeneous areas, and obtain more accurate edge locations.