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.