Metric corrections of the affine camera

•A specific study of the orthographic, weak-perspective and paraperspective cameras.•An algebraic procedure solving the affine correction problem for each camera model.•A closed-form solution for each camera model.•A full characterization of the affine corrections’ generic ambiguities for each camera model.•An experimental evaluation comparing the algebraic procedures to global polynomial optimization and an interior-point method.

Given a general affine camera, we study the problem of finding the closest metric affine camera, where the latter is one of the orthographic, weak-perspective and paraperspective projection models. This problem typically arises in stratified Structure-from-Motion methods such as factorization-based methods. For each type of metric affine camera, we give a closed-form solution and its implementation through an algebraic procedure. Using our algebraic procedure, we can then provide a complete analysis of the problem’s generic ambiguity space. This also gives the means to generate the other solutions if any.