Eliminating conditionally independent sets in factor graphs: A unifying perspective based on smart factors

Factor graphs are a general estimation framework that has been widely used in computer vision and robotics. In several classes of problems a natural partition arises among variables involved in the estimation. A subset of the variables are actually of interest for the user: we call those target variables. The remaining variables are essential for the formulation of the optimization problem underlying maximum a posteriori (MAP) estimation; however these variables, that we call support variables, are not strictly required as output of the estimation problem. In this paper, we propose a systematic way to abstract support variables, defining optimization problems that are only defined over the set of target variables. This abstraction naturally leads to the definition of smart factors, which correspond to constraints among target variables. We show that this perspective unifies the treatment of heterogeneous problems, ranging from structureless bundle adjustment to robust estimation in SLAM. Moreover, it enables to exploit the underlying structure of the optimization problem and the treatment of degenerate instances, enhancing both computational efficiency and robustness.