Classification of Complex Wishart Matrices with a Diffusion-Reaction System guided by Stochastic Distances

Abstract

We propose a new method for PolSAR (Polarimetric Synthetic Aperture Radar) imagery classification based on stochastic distances in the space of random matrices obeying complex Wishart distributions. Given a collection of prototypes $\{Z_m\}_{m=1}^M$ and a stochastic distance $d(.,.)$, we classify any random matrix $X$ using two criteria in an iterative setup. Firstly, we associate $X$ to the class which minimizes the weighted stochastic distance $w_md(X,Z_m)$, where the positive weights $w_m$ are computed to maximize the class discrimination power. Secondly, we improve the result by embedding the classification problem into a diffusion-reaction partial differential system where the diffusion term smooths the patches within the image, and the reaction term tends to move the pixel values towards the closest class prototype. In particular, the method inherits the benefits of speckle reduction by diffusion-like methods. Results on synthetic and real PolSAR data show the performance of the method.