This paper considers the problem of vision-based robot stabilization where the equilibrium state is defined via a reference image. Differently from most solutions, this study directly exploits the pixel intensities with no feature extraction or matching and uses only nonmetric information of the observed scene. Intensity-based techniques provide higher accuracy, whereas not requiring metric information increases their versatility. In this context, this paper further exploits the epipolar geometry and its intrinsic degeneracies. Such degeneracies always occur when that stabilization is sufficiently close to the equilibrium, regardless of the object shape. This remarkable fact allows the development of new vision-based control strategies with varying degrees of computational complexity and of prior knowledge. Importantly, they are arranged hierarchically from the simplest to the state-of-the-art ones, all in a unified framework. Three new local methods are then presented, and their closed-loop performances are experimentally assessed using both planar and nonplanar objects, under small and large displacements, simulating and employing a six-degree-of-freedom robotic arm.