Global Uncertainty in Epipolar Geometry via Fully and Partially Data-driven Sampling

In this paper we explore the relative efficiency of various data-driven sampling techniques for estimating the epipolar geometry and its global uncertainty. We explore standard fully data-driven methods, specifically the five-point, seven-point, and eight-point methods. We also explore what we refer to as partially data-driven methods, where in the sampling we choose some of the parameters deterministically. The goal of these sampling methods is to approximate full search within a computionally feasible time frame. As a compromise between fully representing posterior likelihood over the space of fundamental matrices and producing a single estimate, we represent the uncertainty over the space of translation directions. In contrast to finding a single estimate, representing the posterior likelihood is always a well-posed problem, albeit an often computionally challenging one. Furthermore, this representation yields an estimate of the global uncertainty, which may be used for comparison between differing methods.