Sensitivity Analysis in Translation Averaging

Translation averaging solves for absolute translations given a set of pairwise relative translation directions. Most of the existing literature focuses on robustness to outliers and studies the uniqueness of the solution. In this paper, we deal with a distinctly different problem of sensitivity in translation averaging under input uncertainty. We first analyze sensitivity in estimating the translation of a camera and extend it to all the cameras involved in the problem. Then, we define the conditioning of the translation averaging problem, which assesses the reliability of estimated translations based solely on the input directions. We provide a sufficient criterion to ensure that the problem is well-conditioned. Based on the criterion, we present an efficient algorithm to identify and remove combinations of directions which make the problem ill-conditioned. Applying our algorithm leads to improved conditioning of translation averaging, resulting in the reduction of absolute translation errors.