In this paper, we describe novel techniques for automatic classification of the dominant scattering mechanisms associated with the pixels of polarimetric SAR images. Specifically, we investigate two operating scenarios. In the first scenario, it is assumed that the polarimetric image pixels locally share the same covariance (homogeneous environment), whereas the second scenario considers polarimetric pixels with different power levels and the same covariance structure (heterogeneous environment). In the second case, we invoke the Principle of Invariance to get rid of the dependence on the power levels. For both scenarios, we formulate the classification problem in terms of multiple hypothesis tests which is addressed by applying the model-o...