In this article we address the problem of minimal pose under the framework of the generalized camera models. Previous approaches were based on geometric properties, such as the preservation of distance between points. In this paper we propose a novel formulation of the problem using an algebraic-based approach. We represent the pose by a 3×3 matrix. Using both the algebraic relationship between three incident 3D points and straight lines and the underlying constraints of the pose matrix, pose can be computed. In terms of experimental results, the main contribution of the proposed method is the robustness to critical configurations. In addition, a full comparison and analysis between state-of-the-art methods is made (so far, there is no published comparison between state-of-the-art methods published).