Abstract: Epipolar geometry is the intrinsic projective geometry between two views of a static scene. It is independent of scene structure, and only depends on the camera's internal parameters and relative pose. The fundamental matrix encapsulates the whole epipolar geometry and accurate and robust estimation of the fundamental matrix is very important for many computer vision applications. In this paper, a robust algorithm is used to estimate the fundamental matrix——the random sample algorithm. Given that a large proportion of the data (the set of corner point pairs) may be useless, a small subset of the data (seven correspondences for a fundamental matrix) is feasible to estimate the parameters, and this process is repeated enough times on different subsets to ensure that there is a 95% chance that one of the subsets will contain only good data points. The best solution is that which maximizes the number of points whose residual is below a threshold. Once the outliers are removed, the set of points identified as non-outliers may be combined to give a final solution. Experiment with real images verifies that the random sample algorithm is both accurate and robust.

Key words: random sampling algorithms, epipolar geometry, fundamental matrix, robust estimation