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. Estimation of the relative orientation between two images is an extensively researched subject in computer vision. Many methods have been proposed and the state of the art is now quite elaborate and mature. In our view, the main requirements on an estimation method are that it • Is accurate (both locally and globally) • Is robust • Is computationally efficient • Can exploit all constraints, exact and approximate • Gives a truthful uncertainty estimate (local and global) It is widely accepted that accuracy is best achieved with iterative refinement, called bundle adjustment [24], according to a cost function that is derived from a realistic model of the problem. However, bundle adjustment is dependent on an initial starting point and only achieves what we refer to as local accuracy, which is the ability to precisely pinpoint a local minimum of the cost function. Perhaps even more important and challenging in computer vision is to, insofar as possible, achieve global accuracy, which is the ability to reliably locate the global minimum of the cost function. Robustness is achieved by using an appropriate data model that includes data distortions and outliers. Computational efficiency is always desirable, although the requirements are more stringent in some applications than others. It is likewise desirable to use all available constraints , such as camera calibration information. Figure 1: We derive an uncertainty representation for epipolar geometry parameterized by the epipole in the first image. The figure shows an example of the uncertainty representation when the number of point correspondences is too low, leading …