Sensitivity in Translation Averaging
Dec 10, 2023
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Lalit Manam
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Venu Madhav Govindu
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In 3D computer vision, translation averaging solves for absolute translations given a set of pairwise relative translation directions. While there has been much work on robustness to outliers and studies on the uniqueness of the solution, in this paper, we deal with a distinctly different problem of sensitivity in translation averaging under uncertainty. We first analyze the sensitivity in estimating scales corresponding to relative directions under small perturbations of the relative directions. Then, we formally define the conditioning of the translation averaging problem, which assesses the reliability of the absolute translations based solely on the input directions. We give a sufficient condition to ensure that the problem is well-conditioned. Then, we provide an efficient algorithm to identify and remove combinations of directions which make the problem ill-conditioned while ensuring the uniqueness of the solution. We demonstrate the usefulness of such analysis in global structure-from-motion pipelines, which reveals the benefits of filtering the ill-conditioned set of directions for obtaining 3D reconstructions in terms of reduced translation errors, more 3D points triangulated and faster convergence of bundle adjustment by improving the conditioning of translation averaging.In 3D computer vision, translation averaging solves for absolute translations given a set of pairwise relative translation directions. While there has been much work on robustness to outliers and studies on the uniqueness of the solution, in this paper, we deal with a distinctly different problem of sensitivity in translation averaging under uncertainty. We first analyze the sensitivity in estimating scales corresponding to relative directions under small perturbations of the relative directions…
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NeurIPS 2023
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