In this paper, we explore the different minimal solutions for egomotion estimation of a camera based on homography knowing the gravity vector between calibrated images. These solutions depend on the prior knowledge about the reference plane used by the homography. We then demonstrate that the number of matched points can vary from two to three and that a direct closed-form solution or a Gröbner basis based solution can be derived according to this plane. Many experimental results on synthetic and real sequences in indoor and outdoor environments show the efficiency and the robustness of our approach compared to standard methods.