Polarimetric SAR images have a large number of applications. To extract a physical interpretation of such images, a classification on their polarimetric properties can be a real advantage. However, most classification techniques are developed under a Gaussian assumption of the signal and compute cluster centers using the standard arithmetical mean. This paper will present classification results on simulated and real images using a non-Gaussian signal model, more adapted to the high resolution images and a geometrical definition of the mean for the computation of the class centers. We will show notable improvements on the classification results with the geometrical mean over the arithmeti-cal mean and present a physical interpretation for these improvements, using the Cloude-Pottier decomposition.