In the present paper, we review and complete the equations and the formalism which allow to achieve a minimal parameterization of the retinal displacement for a monocular visual system without calibration. Considering the emergence of active visual systems for which we {\bf can not} consider that the calibration parameters are either known or fixed, we develop an alternative strategy using the fact that certain class of special displacements induces enough equations to evaluate the calibration parameters, so that we can recover the affine or Euclidean structure of the scene when needed. A synthesis of what can be recovered for singular displacements in terms of camera calibration, scene geometry and kinematics is proposed. We give, for the different levels of calibration, an exhaustive list of the geometric and kinematic information which can be recovered. Following a strategy based on special kind of displacements, such as fixed axis rotations or pure translations for instance, we describe how to detect this particular classes of displacement. The implementation of these equations is analyzed here and the realization is reported as a single module, to be embedded in a high-level Image Understanding Environment.