Efficient algorithms for robust estimation of relative translation *

• Two new algorithms for relative pose with known rotation
• The algorithms find the optimal solutions in the presence of outliers.
• Outperforms RANSAC on datasets with a high number of outliers
• Competitive runtimes for both real and synthetic data

One of the key challenges for structure from motion systems in order to make them robust to failure is the ability to handle outliers among the correspondences. In this paper we present two new algorithms that find the optimal solution in the presence of outliers when the camera undergoes a pure translation. The first algorithm has polynomial-time computational complexity, independently of the amount of outliers. The second algorithm does not offer such a theoretical complexity guarantee, but we demonstrate that it is magnitudes faster in practice. No random sampling approaches such as RANSAC are guaranteed to find an optimal solution, while our two methods do. We evaluate and compare the algorithms both on synthetic and real experiments. We also embed the algorithms in a larger system, where we optimize for the rotation angle as well (the rotation axis is measured by other means). The experiments show that for problems with a large amount of outliers, the RANSAC estimates may deteriorate compared to our optimal methods.