  Although various clustering methods have been successfully applied to
polarimetric synthetic aperture radar (PolSAR) image clustering tasks, most of
the available approaches fail to realize automatic determination of cluster
number, nor have they derived an exact distribution for the number of looks. To
overcome these limitations and achieve robust unsupervised classification of
PolSAR images, this paper proposes the variational Bayesian Wishart mixture
model (VBWMM), where variational Bayesian expectation maximization (VBEM)
technique is applied to estimate the variational posterior distribution of
model parameters iteratively. Besides, covariance matrix similarity and
geometric similarity are combined to incorporate spatial information of PolSAR
images. Furthermore, we derive a new distribution named inverse gamma-gamma
(IGG) prior that originates from the log-likelihood function of proposed model
to enable efficient handling of number of looks. As a result, we obtain a
closed-form variational lower bound, which can be used to evaluate the
convergence of proposed model. We validate the superiority of proposed method
in clustering performance on four real-measured datasets and demonstrate
significant improvements towards conventional methods. As a by-product, the
experiments show that our proposed IGG prior is effective in estimating the
number of looks.
