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Efficient Algorithms for Rotation Averaging Problems

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Published:28 April 2021Publication History
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Abstract

The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature, there is a lack of a fast convergent algorithm to achieve stationary points. In this paper, by exploring the problem structure, we first propose a block coordinate descent (BCD)-based rotation averaging algorithm with guaranteed convergence to stationary points. Afterwards, we further propose an alternative rotation averaging algorithm by applying successive upper-bound minimization (SUM) method. The SUM-based rotation averaging algorithm can be implemented in parallel and thus is more suitable for addressing large-scale rotation averaging problems. Numerical examples verify that the proposed rotation averaging algorithms have superior convergence performance as compared to the state-of-the-art algorithm. Moreover, by checking the sufficient optimality condition, we find from extensive numerical experiments that the proposed two algorithms can achieve globally optimal solutions.

References

  1. Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, and Ludwig Schmidt. 2015. Practical and optimal LSH for angular distance. In Advances in Neural Information Processing Systems. 1225--1233.Google ScholarGoogle Scholar
  2. Dimitri P Bertsekas. 1997. Nonlinear programming. Journal of the Operational Research Society 48, 3 (1997), 334--334.Google ScholarGoogle ScholarCross RefCross Ref
  3. Yuchao Dai, Jochen Trumpf, Hongdong Li, Nick Barnes, and Richard Hartley. 2009. Rotation averaging with application to camera-rig calibration. In Asian Conference on Computer Vision. Springer, 335--346.Google ScholarGoogle Scholar
  4. Olof Enqvist, Fredrik Kahl, and Carl Olsson. 2011. Non-sequential structure from motion. In 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops). IEEE, 264--271.Google ScholarGoogle ScholarCross RefCross Ref
  5. Anders Eriksson, Carl Olsson, Fredrik Kahl, and Tat-Jun Chin. 2018. Rotation averaging and strong duality. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition. 127--135.Google ScholarGoogle ScholarCross RefCross Ref
  6. Johan Fredriksson and Carl Olsson. 2012. Simultaneous multiple rotation averaging using lagrangian duality. In Asian Conference on Computer Vision. Springer, 245--258.Google ScholarGoogle Scholar
  7. Venu Madhav Govindu. 2001. Combining two-view constraints for motion estimation. In Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, Vol. 2. IEEE, II--II.Google ScholarGoogle ScholarCross RefCross Ref
  8. Andrew J Hanson. 2005. Visualizing quaternions. In ACM SIGGRAPH 2005 Courses. ACM, 1.Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Richard Hartley, Jochen Trumpf, Yuchao Dai, et al. 2010. Rotation averaging and weak convexity. In Proc. of the 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS'10). 2435--2442.Google ScholarGoogle Scholar
  10. Richard Hartley, Jochen Trumpf, Yuchao Dai, and Hongdong Li. 2013. Rotation averaging. International journal of computer vision 103, 3 (2013), 267--305.Google ScholarGoogle ScholarCross RefCross Ref
  11. Jan J Koenderink and Andrea J Van Doorn. 1991. Affine structure from motion. JOSA A 8, 2 (1991), 377--385.Google ScholarGoogle ScholarCross RefCross Ref
  12. Daniel Martinec and Tomas Pajdla. 2007. Robust rotation and translation estimation in multiview reconstruction. In 2007 IEEE Conference on Computer Vision and Pattern Recognition. IEEE, 1--8.Google ScholarGoogle ScholarCross RefCross Ref
  13. Pauline C Ng and Steven Henikoff. 2003. SIFT: Predicting amino acid changes that affect protein function. Nucleic acids research 31, 13 (2003), 3812--3814.Google ScholarGoogle Scholar
  14. Sverker Rasmuson, Erik Sintorn, and Ulf Assarsson. 2020. User-guided 3D reconstruction using multi-view stereo. In Symposium on Interactive 3D Graphics and Games. 1--9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Meisam Razaviyayn, Mingyi Hong, and Zhi-Quan Luo. 2013. A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM Journal on Optimization 23, 2 (2013), 1126--1153.Google ScholarGoogle ScholarCross RefCross Ref
  16. Denise Sakai. 1994. Labeling chordal graphs: distance two condition. SIAM Journal on Discrete Mathematics 7, 1 (1994), 133--140.Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Noah Snavely, Steven M Seitz, and Richard Szeliski. 2006. Photo tourism: exploring photo collections in 3D. In ACM transactions on graphics (TOG), Vol. 25. ACM, 835--846.Google ScholarGoogle Scholar
  18. Camillo J Taylor and David J Kriegman. 1994. Minimization on the Lie group SO (3) and related manifolds. Yale University 16, 155 (1994), 6.Google ScholarGoogle Scholar
  19. Kyle Wilson, David Bindel, and Noah Snavely. 2016. When is rotations averaging hard?. In European Conference on Computer Vision. Springer, 255--270.Google ScholarGoogle ScholarCross RefCross Ref
  20. Stephen J Wright. 2015. Coordinate descent algorithms. Mathematical Programming 151, 1 (2015), 3--34.Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Yihong WU Zhanyi Hu, Fuchao Wu and Qiulei Dong. [n.d.]. 3D reconstruction dataset. http://vision.ia.ac.cn/data.Google ScholarGoogle Scholar

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      cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
      Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 4, Issue 1
      April 2021
      274 pages
      EISSN:2577-6193
      DOI:10.1145/3463840
      Issue’s Table of Contents

      Copyright © 2021 ACM

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      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 28 April 2021
      Published in pacmcgit Volume 4, Issue 1

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