The position of the epipole (or focus of expansion), when a camera moves under pure translation, provides useful information in a range of computer vision applications. Here we present a robust method to estimate the epipole, which is based on the relation between the epipole and the fundamental matrix and which uses both a binning technique and random sample consensus (RANSAC). The required input data is only two uncalibrated images. No prior knowledge of either the parameters of the camera, or camera motion is required. Firstly, we use a linear method to get an initial estimate of the epipole. This is then used to initialise a non-linear optimization method, based on the minimization of the epipolar distance, in order to refine this estimate and yield a highly accurate epipole. Simultaneously, the method computes a highly accurate fundamental matrix. Extensive experimental results on real images and simulated data illustrate that the new method, which leads to an enormous improvement on the accuracy of the epipole, performs very well in terms of robustness to outliers and noises.
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