This paper addresses the optimal recovery of the displacement and projection parameters from uncalibrated monocular video sequences. We study the particular cases of camera and objects displacements and camera projection in order to extract an optimized parameterization of the problem of parameters recovery for each cases. This work follows previous studies on particular cases of displacement, scene geometry and camera analysis and focuses on the particular forms of fundamental matrices. This paper introduces the idea of using not all particular cases as individual cases but grouping these cases into a tractable number of sets, using properties on fundamental matrices. Some experiments were performed in order to demonstrate that if several models are correct, the model with the least parameters gives the best estimate, corresponding to the true case.