We apply image moment invariant analysis to total intensity and polarimetric images calculated from general relativistic magnetohydrodynamic simulations of accreting black holes. We characterize different properties of the models in our library by their invariant distributions and their evolution in time. We show that they are highly sensitive to different physical effects present in the system which allow for model discrimination. We propose a new model scoring method based on image moment invariants that is uniformly applicable to total intensity and polarimetric images simultaneously. The method does not depend on the type of images considered and its application to other non-ring like images (e.g. jets) is straight forward.