In defense of the eight-point algorithm

TLDR

The eight‑point algorithm is a simple, widely cited method for estimating the fundamental matrix from two uncalibrated camera views, but it is generally considered highly noise‑sensitive and therefore largely ineffective. The authors aim to demonstrate that normalizing point coordinates before applying the eight‑point algorithm yields performance comparable to state‑of‑the‑art iterative methods. They achieve this by normalizing the matched point coordinates through translation and scaling before running the eight‑point algorithm, and support the approach with theoretical justification and extensive real‑image experiments. The normalized eight‑point algorithm performs comparably to the best iterative algorithms, as confirmed by theory and extensive real‑image experiments.

Abstract

The fundamental matrix is a basic tool in the analysis of scenes taken with two uncalibrated cameras, and the eight-point algorithm is a frequently cited method for computing the fundamental matrix from a set of eight or more point matches. It has the advantage of simplicity of implementation. The prevailing view is, however, that it is extremely susceptible to noise and hence virtually useless for most purposes. This paper challenges that view, by showing that by preceding the algorithm with a very simple normalization (translation and scaling) of the coordinates of the matched points, results are obtained comparable with the best iterative algorithms. This improved performance is justified by theory and verified by extensive experiments on real images.