Many problems in computer vision can be formulated as geometric estimation problems, i.e. given a collection of measurements (e.g. point correspondences) we wish to fit a model (e.g. an essential matrix) that agrees with our observations. This necessitates some measure of how much an observation ``agrees" with a given model. A natural choice is to consider the smallest perturbation that makes the observation exactly satisfy the constraints. However, for many problems, this metric is expensive or otherwise intractable to compute. The so-called Sampson error approximates this geometric error through a linearization scheme. For epipolar geometry, the Sampson error is a popular choice and in practice known to yield very tight approximations of the corresponding geometric residual (the reprojection error). In this paper we revisit the Sampson approximation and provide new theoretical insights as to why and when this approximation works, as well as provide explicit bounds on the tightness under some mild assumptions. Our theoretical results are validated in several experiments on real data and in the context of different geometric estimation tasks.

研究纸试图重新审视Sampson近似，并提供新的理论洞察力，解释了这一近似在何时何地有效，并在一些温和的假设下提供了明确的收敛边界。通过对真实数据和不同的几何估计任务进行验证，我们得出了一些实验证明了我们的理论结果。

重访几何估计问题的Sampson近似