We refine the 2D transformation estimate using RANSAC. RANSAC has the advantage 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).