Optimal RANSAC - Towards a repeatable algorithm for finding the optimal set

A novel idea on how to make RANSAC repeatable is presented, which will find the optimal set in nearly every run for certain types of applications. The proposed algorithm can be used for such transformations that can be constructed by more than the minimal points required. We give examples on matching of aerial images using the Direct Linear Transformation, which requires at least four points. Moreover, we give examples on how the algorithm can be used for finding a plane in 3D using three points or more. Due to its random nature, standard RANSAC is not always able to find the optimal set even for moderately contaminated sets and it usually performs badly when the number of inliers is less than 50%. However, our algorithm is capable of finding the optimal set for heavily contaminated sets, even for an inlier ratio under 5%. The proposed algorithm is based on several known methods, which we modify in a unique way and together they produce a result that is quite different from what each method can produce on its own.