This paper introduces a new statistical hypothesis test for robust image classification. First, we introduce the proposed statistical hypothesis test based on the geodesic distance and on the fixed point estimation algorithm. Next, we analyze its properties in the case of the zero-mean multivariate Gaus-sian distribution by studying its asymptotic distribution under the null hypothesis H0. Then, the performance of the proposed classifier is addressed by analyzing its noise robust-ness. Finally, the robust classification method is employed for the classification of simulated Polarimetric Synthetic Aperture Radar images of maritime pine forests.