Statistical characterization of the Sinclair matrix: Application to polarimetric image segmentation

This paper focuses on the flexibility of a multidimensional model of probability density function (pdf) to describe distribution of complex data in polarimetric SAR images. This model is based on Copulas Theory for characterizing the dependence between the polarimetric channels (HH, VV, HV, VH). This corresponds to finding a model based on multidimensional copulas to describe the behavior of the target vector. The advantage in using copulas theory is to extend correlation concept to a wider dependence one, which may be non-linear, especially when processing high-resolution data. So, from this point of view, the model is more flexible than the classical Wishart distribution since no speckle filtering is required as preprocessing step to model accurately the pdfs. The other advantage of copulas is to split dependence concept and marginal distributions. Then, this multidimensional characterization may be linked to pdf which are not necessary of circular Gaussian law. So, specific parametric distribution may be choosen to fit each component (modulus and phase) of the Sinclair matrix. It yields a flexible model, for characterizing statistical behavior of the polarimetric SAR data, that may be derived to produce a segmentation algorithm.