  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.
