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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
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)
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)
Björck, A.: Numerical Methods for Least Squares Problems. SIAM Publications (1996)
Boman, E., Chen, D., Parekh, O., Toledo, S.: On factor width and symmetric h-matrices. Linear Algebra and its Applications 405, 239–248 (2005)
Boman, E., Hendrickson, B.: Support theory for preconditioning. SIAM Journal on Matrix Analysis and Applications 25(3), 694–717 (2003)
Byröd, M., Åström, K.: Bundle adjustment using conjugate gradients with multiscale preconditioning. In: British Machine Vision Conference (2009)
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)
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)
Davis, T.: Algorithm 915, SuiteSparseQR: multifrontal multithreaded rank-revealing sparse QR factorization. ACM Transactions on Mathematical Software 38(1) (2011)
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)
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)
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)
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)
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)
Konolige, K., Garage, W.: Sparse sparse bundle adjustment. In: Proc. of the British Machine Vision Conference (2010)
Lourakis, M., Argyros, A.: SBA: A software package for generic sparse bundle adjustment. ACM Transactions on Mathematical Software 36(1), 1–30 (2009)
MacKay, D.: Information theory, inference, and learning algorithms. Cambridge Univ. Press (2003)
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)
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)
Saad, Y.: Iterative methods for sparse linear systems. Society for Industrial Mathematics (2003)
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)
Snavely, N., Seitz, S., Szeliski, R.: Modeling the world from internet photo collections. International Journal of Computer Vision 80(2), 189–210 (2008)
Spielman, D.A.: Algorithms, graph theory, and linear equations. In: International Congress of Mathematicians (2010)
Trefethen, L., Bau, D.: Numerical linear algebra, vol. 50. Society for Industrial Mathematics (1997)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Computer ScienceComputer Science (R0)