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Certifiably Optimal Anisotropic Rotation Averaging

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Title: Certifiably Optimal Anisotropic Rotation Averaging
Authors: Olsson, Carl, 1978, Lochman, Yaroslava, 1996, Malmport, Johan, Zach, Christopher, 1974
Source: 2025 IEEE/CVF International Conference on Computer Vision (ICCV), Honolulu, USA Proceedings of the 2025 IEEE/CVF International Conference on Computer Vision. :14856-14865
Subject Terms: rotation averaging, structure from motion, semidefinite programming, convex optimization
Description: Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect that most of these have in common is a focus on the isotropic setting, where the intrinsic uncertainties in the measurements are not fully incorporated into the resulting optimization task. Recent empirical results suggest that moving to an anisotropic framework, where these uncertainties are explicitly included, can result in an improvement of solution quality. However, global optimization for rotation averaging has remained a challenge in this scenario. In this work we show how anisotropic costs can be incorporated in certifiably optimal rotation averaging. We also demonstrate how existing solvers, designed for isotropic situations, fail in the anisotropic setting. Finally, we propose a stronger relaxation and empirically show that it recovers global optima in all tested datasets and leads to more accurate reconstructions in almost all scenes.
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Access URL: https://research.chalmers.se/publication/549568
https://ylochman.github.io/anisotropic-ra
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  Data: Certifiably Optimal Anisotropic Rotation Averaging
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  Data: <searchLink fieldCode="AR" term="%22Olsson%2C+Carl%22">Olsson, Carl</searchLink>, 1978<br /><searchLink fieldCode="AR" term="%22Lochman%2C+Yaroslava%22">Lochman, Yaroslava</searchLink>, 1996<br /><searchLink fieldCode="AR" term="%22Malmport%2C+Johan%22">Malmport, Johan</searchLink><br /><searchLink fieldCode="AR" term="%22Zach%2C+Christopher%22">Zach, Christopher</searchLink>, 1974
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  Data: <i>2025 IEEE/CVF International Conference on Computer Vision (ICCV), Honolulu, USA Proceedings of the 2025 IEEE/CVF International Conference on Computer Vision</i>. :14856-14865
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  Data: <searchLink fieldCode="DE" term="%22rotation+averaging%22">rotation averaging</searchLink><br /><searchLink fieldCode="DE" term="%22structure+from+motion%22">structure from motion</searchLink><br /><searchLink fieldCode="DE" term="%22semidefinite+programming%22">semidefinite programming</searchLink><br /><searchLink fieldCode="DE" term="%22convex+optimization%22">convex optimization</searchLink>
– Name: Abstract
  Label: Description
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  Data: Rotation averaging is a key subproblem in applications of computer vision and robotics. Many methods for solving this problem exist, and there are also several theoretical results analyzing difficulty and optimality. However, one aspect that most of these have in common is a focus on the isotropic setting, where the intrinsic uncertainties in the measurements are not fully incorporated into the resulting optimization task. Recent empirical results suggest that moving to an anisotropic framework, where these uncertainties are explicitly included, can result in an improvement of solution quality. However, global optimization for rotation averaging has remained a challenge in this scenario. In this work we show how anisotropic costs can be incorporated in certifiably optimal rotation averaging. We also demonstrate how existing solvers, designed for isotropic situations, fail in the anisotropic setting. Finally, we propose a stronger relaxation and empirically show that it recovers global optima in all tested datasets and leads to more accurate reconstructions in almost all scenes.
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      – SubjectFull: rotation averaging
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      – SubjectFull: structure from motion
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      – SubjectFull: semidefinite programming
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              M: 01
              Type: published
              Y: 2025
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