We refine the 2D transformation estimate using RANSAC. RANSAC has the ad- vantage that it is largely insensitive to outliers, but it will fail if the fraction of outliers is too great. This is why we use Hough transform clustering as a first step. See figure 4.
If the scene is 3-dimensional, we first select inliers which are loosely consistent with a 2D transformation using the above methods, using a large error tolerance. This will hopefully find a dominant plane in the image, with the error tolerance allowing for parallax due to displacement from the plane. Then, given a set of points with relatively few outliers, we compute the fundamental matrix. This is used to find a final set of feature matches which is consistent with the epipolar geometry (figure 5).