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Robust Single Rotation Averaging Revisited (2309.05388v5)

Published 11 Sep 2023 in cs.CV and cs.RO

Abstract: In this work, we propose a novel method for robust single rotation averaging that can efficiently handle an extremely large fraction of outliers. Our approach is to minimize the total truncated least unsquared deviations (TLUD) cost of geodesic distances. The proposed algorithm consists of three steps: First, we consider each input rotation as a potential initial solution and choose the one that yields the least sum of truncated chordal deviations. Next, we obtain the inlier set using the initial solution and compute its chordal $L_2$-mean. Finally, starting from this estimate, we iteratively compute the geodesic $L_1$-mean of the inliers using the Weiszfeld algorithm on $SO(3)$. An extensive evaluation shows that our method is robust against up to 99% outliers given a sufficient number of accurate inliers, outperforming the current state of the art.

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References (31)
  1. D. Maggio, M. Abate, J. Shi, C. Mario, and L. Carlone, “Loc-NeRF: Monte Carlo localization using neural radiance fields,” in IEEE Intl. Conf. on Robotics and Automation (ICRA), 2023, pp. 4018–4025.
  2. K. Joo, T.-H. Oh, F. Rameau, J.-C. Bazin, and I. S. Kweon, “Linear RGB-D SLAM for Atlanta world,” in IEEE Intl. Conf. on Robotics and Automation (ICRA), 2020, pp. 1077–1083.
  3. H. Yang and M. Pavone, “Object pose estimation with statistical guarantees: Conformal keypoint detection and geometric uncertainty propagation,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023, pp. 8947–8958.
  4. R. I. Hartley, K. Aftab, and J. Trumpf, “L1 rotation averaging using the Weiszfeld algorithm,” in IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 2011, pp. 3041–3048.
  5. S. H. Lee and J. Civera, “HARA: A hierarchical approach for robust rotation averaging,” in IEEE Conf. Comput. Vis. Pattern Recog., 2022, pp. 15 777–15 786.
  6. S. Kumar and L. Van Gool, “Organic priors in non-rigid structure from motion,” in Eur. Conf. Comput. Vis., 2022, pp. 71–88.
  7. L. Sun, “Practical, fast and robust point cloud registration for scene stitching and object localization,” IEEE Access, vol. 10, pp. 3962–3978, 2022.
  8. Y. Dai, J. Trumpf, H. Li, N. Barnes, and R. Hartley, “Rotation averaging with application to camera-rig calibration,” in Asian Conf. on Computer Vision, 2009, pp. 335–346.
  9. I. Sharf, A. Wolf, and M. Rubin, “Arithmetic and geometric solutions for average rigid-body rotation,” Mechanism and Machine Theory, vol. 45, no. 9, pp. 1239 – 1251, 2010.
  10. Q. M. Lam and J. L. Crassidis, “Precision attitude determination using a multiple model adaptive estimation scheme,” in IEEE Aerospace Conference, 2007, pp. 1–20.
  11. L. Markley, Y. Cheng, J. Crassidis, and Y. Oshman, “Averaging quaternions,” Journal of Guidance, Control, and Dynamics, vol. 30, pp. 1193–1196, 07 2007.
  12. M. Humbert, N. Gey, J. Muller, and C. Esling, “Determination of a Mean Orientation from a Cloud of Orientations. Application to Electron Back-Scattering Pattern Measurements,” Journal of Applied Crystallography, vol. 29, no. 6, pp. 662–666, 1996.
  13. A. Morawiec, “A note on mean orientation,” Journal of Applied Crystallography, vol. 31, no. 5, pp. 818–819, 1998.
  14. R. Hartley, J. Trumpf, Y. Dai, and H. Li, “Rotation averaging,” International Journal of Computer Vision, 2013.
  15. K. Aftab and R. Hartley, “Convergence of iteratively re-weighted least squares to robust m-estimators,” in IEEE Winter Conf. on Applications of Computer Vision, 2015, pp. 480–487.
  16. P.-Y. Lajoie, S. Hu, G. Beltrame, and L. Carlone, “Modeling perceptual aliasing in SLAM via discrete–continuous graphical models,” IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 1232–1239, 2019.
  17. A. E. Beaton and J. W. Tukey, “The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data,” Technometrics, vol. 16, no. 2, pp. 147–185, 1974.
  18. H. Yang, P. Antonante, V. Tzoumas, and L. Carlone, “Graduated non-convexity for robust spatial perception: From non-minimal solvers to global outlier rejection,” IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 1127–1134, 2020.
  19. J. Manton, “A globally convergent numerical algorithm for computing the centre of mass on compact lie groups,” in Int. control, automation, robotics and vision conf., vol. 3, 2004, pp. 2211–2216.
  20. F. L. Markley, Y. Cheng, J. L. Crassidis, and Y. Oshman, “Averaging quaternions,” Journal of Guidance, Control, and Dynamics, vol. 30, no. 4, pp. 1193–1197, 2007.
  21. A. Sarlette and R. Sepulchre, “Consensus optimization on manifolds,” SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 56–76, 2009.
  22. S. H. Lee and J. Civera, “Robust single rotation averaging,” CoRR, abs/2004.00732, 2020.
  23. E. Weiszfeld, “Sur le point pour lequel la somme des distances de n points donnés est minimum,” Tohoku Mathematical Journal, vol. 43, pp. 355–386, 1937.
  24. E. Weiszfeld and F. Plastria, “On the point for which the sum of the distances to n given points is minimum,” Annals of Operations Research, vol. 167, no. 1, pp. 7–41, 2009.
  25. H. Yang and L. Carlone, “One ring to rule them all: Certifiably robust geometric perception with outliers,” in Advances in Neural Information Processing Systems, vol. 33, 2020, pp. 18 846–18 859.
  26. J. Shi, H. Yang, and L. Carlone, “ROBIN: a graph-theoretic approach to reject outliers in robust estimation using invariants,” in IEEE Intl. Conf. on Robotics and Automation (ICRA), 2021, pp. 13 820–13 827.
  27. N. Mankovich and T. Birdal, “Chordal averaging on flag manifolds and its applications,” CoRR, vol. abs/2303.13501, 2023.
  28. C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-manifold preintegration for real-time visual–inertial odometry,” IEEE Trans. Robot., vol. 33, no. 1, pp. 1–21, 2017.
  29. K. S. Arun, T. S. Huang, and S. D. Blostein, “Least-squares fitting of two 3-D point sets,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 9, no. 5, pp. 698–700, 1987.
  30. D. Eppstein, M. Löffler, and D. Strash, “Listing all maximal cliques in sparse graphs in near-optimal time,” in Algorithms and Computation, 2010, pp. 403–414.
  31. B. Curless and M. Levoy, “A volumetric method for building complex models from range images,” in SIGGRAPH.   ACM, 1996, pp. 303–312.
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