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Generalized Subgraph Preconditioners for Large-Scale Bundle Adjustment

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Outdoor and Large-Scale Real-World Scene Analysis

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7474))

Abstract

We propose the Generalized Subgraph Preconditioners (GSP) to solve large-scale bundle adjustment problems efficiently. In contrast with previous work using either direct or iterative methods alone, GSP combines their advantages and is significantly faster on large datasets. Similar to [12], the main idea is to identify a sub-problem (subgraph) that can be solved efficiently by direct methods and use its solution to build a preconditioner for the conjugate gradient method. The difference is that GSP is more general and leads to more effective preconditioners. When applied to the “bal” datasets [2], our method shows promising results.

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References

  1. Agarwal, S., Snavely, N., Simon, I., Seitz, S., Szeliski, R.: Building rome in a day. In: IEEE 12th International Conference on Computer Vision, pp. 72–79 (2009)

    Google Scholar 

  2. Agarwal, S., Snavely, N., Seitz, S.M., Szeliski, R.: Bundle Adjustment in the Large. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6312, pp. 29–42. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Alon, N., Karp, R., Peleg, D., West, D.: A graph-theoretic game and its application to the k-server problem. SIAM Journal on Computing 24(1), 78–100 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Björck, A.: Numerical Methods for Least Squares Problems. SIAM Publications (1996)

    Google Scholar 

  5. Boman, E., Chen, D., Parekh, O., Toledo, S.: On factor width and symmetric h-matrices. Linear Algebra and its Applications 405, 239–248 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Boman, E., Hendrickson, B.: Support theory for preconditioning. SIAM Journal on Matrix Analysis and Applications 25(3), 694–717 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Byröd, M., Åström, K.: Bundle adjustment using conjugate gradients with multiscale preconditioning. In: British Machine Vision Conference (2009)

    Google Scholar 

  8. Byröd, M., Åström, K.: Conjugate Gradient Bundle Adjustment. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6312, pp. 114–127. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  9. Chen, Y., Davis, T., Hager, W., Rajamanickam, S.: Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Transactions on Mathematical Software 35(3), 1–14 (2009)

    Article  MathSciNet  Google Scholar 

  10. Davis, T.: Algorithm 915, SuiteSparseQR: multifrontal multithreaded rank-revealing sparse QR factorization. ACM Transactions on Mathematical Software 38(1) (2011)

    Google Scholar 

  11. Dellaert, F., Kaess, M.: Square root sam: Simultaneous localization and mapping via square root information smoothing. International Journal of Robotics Research 25(12), 1181–1203 (2006)

    Article  MATH  Google Scholar 

  12. Dellaert, F., Carlson, J., Ila, V., Ni, K., Thorpe, C.E.: Subgraph-preconditioned conjugate gradient for large scale slam. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (2010)

    Google Scholar 

  13. Frahm, J.-M., Fite-Georgel, P., Gallup, D., Johnson, T., Raguram, R., Wu, C., Jen, Y.-H., Dunn, E., Clipp, B., Lazebnik, S., Pollefeys, M.: Building Rome on a Cloudless Day. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6314, pp. 368–381. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Jeong, Y., Nister, D., Steedly, D., Szeliski, R., Kweon, I.: Pushing the envelope of modern methods for bundle adjustment. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1474–1481 (2010)

    Google Scholar 

  15. Jian, Y.D., Balcan, D.C., Dellaert, F.: Generalized subgraph preconditioners for large-scale bundle adjustment. In: IEEE 13th International Conference on Computer Vision (2011)

    Google Scholar 

  16. Konolige, K., Garage, W.: Sparse sparse bundle adjustment. In: Proc. of the British Machine Vision Conference (2010)

    Google Scholar 

  17. Lourakis, M., Argyros, A.: SBA: A software package for generic sparse bundle adjustment. ACM Transactions on Mathematical Software 36(1), 1–30 (2009)

    Article  MathSciNet  Google Scholar 

  18. MacKay, D.: Information theory, inference, and learning algorithms. Cambridge Univ. Press (2003)

    Google Scholar 

  19. Ni, K., Steedly, D., Dellaert, F.: Out-of-core bundle adjustment for large-scale 3D reconstruction. In: IEEE 11th International Conference on Computer Vision (2007)

    Google Scholar 

  20. Olson, E., Leonard, J., Teller, S.: Fast iterative alignment of pose graphs with poor initial estimates. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 2262–2269 (2006)

    Google Scholar 

  21. Saad, Y.: Iterative methods for sparse linear systems. Society for Industrial Mathematics (2003)

    Google Scholar 

  22. Snavely, N., Seitz, S.M., Szeliski, R.S.: Skeletal graphs for efficient structure from motion. In: IEEE Conference on Computer Vision and Pattern Recognition (2008)

    Google Scholar 

  23. Snavely, N., Seitz, S., Szeliski, R.: Modeling the world from internet photo collections. International Journal of Computer Vision 80(2), 189–210 (2008)

    Article  Google Scholar 

  24. Spielman, D.A.: Algorithms, graph theory, and linear equations. In: International Congress of Mathematicians (2010)

    Google Scholar 

  25. Trefethen, L., Bau, D.: Numerical linear algebra, vol. 50. Society for Industrial Mathematics (1997)

    Google Scholar 

  26. Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle Adjustment – A Modern Synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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Jian, YD., Balcan, D.C., Dellaert, F. (2012). Generalized Subgraph Preconditioners for Large-Scale Bundle Adjustment. In: Dellaert, F., Frahm, JM., Pollefeys, M., Leal-Taixé, L., Rosenhahn, B. (eds) Outdoor and Large-Scale Real-World Scene Analysis. Lecture Notes in Computer Science, vol 7474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34091-8_6

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  • DOI: https://doi.org/10.1007/978-3-642-34091-8_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34090-1

  • Online ISBN: 978-3-642-34091-8

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