Outlier removal using duality

In this paper we consider the problem of outlier removal for large scale multiview reconstruction problems. An efficient and very popular method for this task is RANSAC. However, as RANSAC only works on a subset of the images, mismatches in longer point tracks may go undetected. To deal with this problem we would like to have, as a post processing step to RANSAC, a method that works on the entire (or a larger) part of the sequence. In this paper we consider two algorithms for doing this. The first one is related to a method by Sim & Hartley where a quasiconvex problem is solved repeatedly and the error residuals with the largest error is removed. Instead of solving a quasiconvex problem in each step we show that it is enough to solve a single LP or SOCP which yields a significant speedup. Using duality we show that the same theoretical result holds for our method. The second algorithm is a faster version of the first, and it is related to the popular method of L₁-optimization. While it is faster and works very well in practice, there is no theoretical guarantee of success. We show that these two methods are related through duality, and evaluate the methods on a number of data sets with promising results.