New Development in Robot Vision pp 111-136

Part of the Cognitive Systems Monographs book series (COSMOS, volume 23)

Incremental Light Bundle Adjustment: Probabilistic Analysis and Application to Robotic Navigation

Chapter

Abstract

This paper focuses on incremental light bundle adjustment (iLBA), a recently introduced [13] structureless bundle adjustment method, that reduces computational complexity by algebraic elimination of camera-observed 3D points and using incremental smoothing to efficiently optimize only the camera poses.We consider the probability distribution that corresponds to the iLBA cost function, and analyze how well it represents the true density of the camera poses given the image measurements. The latter can be exactly calculated in bundle adjustment (BA) by marginalizing out the 3D points from the joint distribution of camera poses and 3D points. We present a theoretical analysis of the differences in the way that light bundle adjustment and bundle adjustment use measurement information. Using indoor and outdoor datasets we show that the first two moments of the iLBA and the true probability distributions are very similar in practice. Moreover, we present an extension of iLBA to robotic navigation, considering information fusion between high-rate IMU and a monocular camera sensor while avoiding explicit estimation of 3D points.We evaluate the performance of this method in a realistic synthetic aerial scenario and show that iLBA and incremental BA result in comparable navigation state estimation accuracy, while computational time is significantly reduced in the former case.

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References

  1. 1.
    Avidan, S., Shashua, A.: Threading fundamental matrices. IEEE Trans. Pattern Anal. Machine Intell. 23(1), 73–77 (2001)CrossRefGoogle Scholar
  2. 2.
    Crandall, D., Owens, A., Snavely, N., Huttenlocher, D.: Discrete-continuous optimization for large-scale structure from motion. In: IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 3001–3008 (2011)Google Scholar
  3. 3.
    Dellaert, F., Kaess, M.: Square Root SAM: Simultaneous localization and mapping via square root information smoothing. Intl. J. of Robotics Research 25(12), 1181–1203 (2006)CrossRefMATHGoogle Scholar
  4. 4.
    Eustice, R., Singh, H., Leonard, J.: Exactly sparse delayed-state filters for view-based SLAM. IEEE Trans. Robotics 22(6), 1100–1114 (2006)CrossRefGoogle Scholar
  5. 5.
    Farrell, J.: Aided Navigation: GPS with High Rate Sensors. McGraw-Hill (2008)Google Scholar
  6. 6.
    Strasdat, H., Montiel, J.M.M., Davison, A.J.: Scale drift-aware large scale monocular SLAM. In: Robotics: Science and Systems (RSS), Zaragoza, Spain (2010)Google Scholar
  7. 7.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press (2000)Google Scholar
  8. 8.
    Ila, V., Porta, J.M., Andrade-Cetto, J.: Information-based compact Pose SLAM. IEEE Trans. Robotics 26(1) (2010), http://dx.doi.org/10.1109/TRO.2009.2034435 (in press)
  9. 9.
    Indelman, V.: Navigation performance enhancement using online mosaicking. Ph.D. thesis, Technion - Israel Institute of Technology (2011)Google Scholar
  10. 10.
    Indelman, V.: Bundle adjustment without iterative structure estimation and its application to navigation. In: IEEE/ION Position Location and Navigation System (PLANS) Conference (2012)Google Scholar
  11. 11.
    Indelman, V., Gurfil, P., Rivlin, E., Rotstein, H.: Real-time vision-aided localization and navigation based on three-view geometry. IEEE Trans. Aerosp. Electron. Syst. 48(3), 2239–2259 (2012)CrossRefGoogle Scholar
  12. 12.
    Indelman, V., Melim, A., Dellaert, F.: Incremental light bundle adjustment for robotics navigation. In: IEEE/RSJ Intl. Conf. on Intelligent Robots and Systems, IROS (2013)Google Scholar
  13. 13.
    Indelman, V., Roberts, R., Beall, C., Dellaert, F.: Incremental light bundle adjustment. In: British Machine Vision Conf., BMVC (2012)Google Scholar
  14. 14.
    Indelman, V., Roberts, R., Dellaert, F.: Probabilistic analysis of incremental light bundle adjustment. In: IEEE Workshop on Robot Vision, WoRV (2013)Google Scholar
  15. 15.
    Indelman, V., Wiliams, S., Kaess, M., Dellaert, F.: Factor graph based incremental smoothing in inertial navigation systems. In: Intl. Conf. on Information Fusion, FUSION (2012)Google Scholar
  16. 16.
    Indelman, V., Wiliams, S., Kaess, M., Dellaert, F.: Information fusion in navigation systems via factor graph based incremental smoothing. Robotics and Autonomous Systems 61(8), 721–738 (2013)CrossRefGoogle Scholar
  17. 17.
    Kaess, M., Ila, V., Roberts, R., Dellaert, F.: The Bayes tree: An algorithmic foundation for probabilistic robot mapping. In: Hsu, D., Isler, V., Latombe, J.-C., Lin, M.C. (eds.) Algorithmic Foundations of Robotics IX. STAR, vol. 68, pp. 157–173. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Kaess, M., Johannsson, H., Roberts, R., Ila, V., Leonard, J., Dellaert, F.: iSAM2: Incremental smoothing and mapping using the Bayes tree. Intl. J. of Robotics Research 31, 217–236 (2012)CrossRefGoogle Scholar
  19. 19.
    Kaess, M., Ranganathan, A., Dellaert, F.: iSAM: Incremental smoothing and mapping. IEEE Trans. Robotics 24(6), 1365–1378 (2008)CrossRefGoogle Scholar
  20. 20.
    Kaess, M., Wiliams, S., Indelman, V., Roberts, R., Leonard, J., Dellaert, F.: Concurrent filtering and smoothing. In: Intl. Conf. on Information Fusion, FUSION (2012)Google Scholar
  21. 21.
    Konolige, K.: Sparse sparse bundle adjustment. In: British Machine Vision Conf., BMVC (2010)Google Scholar
  22. 22.
    Konolige, K., Agrawal, M.: FrameSLAM: from bundle adjustment to realtime visual mapping. IEEE Trans. Robotics 24(5), 1066–1077 (2008)CrossRefGoogle Scholar
  23. 23.
    Kschischang, F., Frey, B., Loeliger, H.A.: Factor graphs and the sum-product algorithm. IEEE Trans. Inform. Theory 47(2) (2001)Google Scholar
  24. 24.
    Lourakis, M.A., Argyros, A.: SBA: A Software Package for Generic Sparse Bundle Adjustment. ACM Trans. Math. Software 36(1), 1–30 (2009), doi:http://doi.acm.org/10.1145/1486525.1486527
  25. 25.
    Lu, F., Milios, E.: Globally consistent range scan alignment for environment mapping. Autonomous Robots, 333–349 (1997)Google Scholar
  26. 26.
    Lupton, T., Sukkarieh, S.: Visual-inertial-aided navigation for high-dynamic motion in built environments without initial conditions. IEEE Trans. Robotics 28(1), 61–76 (2012)CrossRefGoogle Scholar
  27. 27.
    Ma, Y., Soatto, S., Kosecka, J., Sastry, S.: An Invitation to 3-D Vision. Springer (2004)Google Scholar
  28. 28.
    Mourikis, A., Roumeliotis, S.: A multi-state constraint Kalman filter for vision-aided inertial navigation. In: IEEE Intl. Conf. on Robotics and Automation (ICRA), pp. 3565–3572 (2007)Google Scholar
  29. 29.
    Mourikis, A., Roumeliotis, S.: A dual-layer estimator architecture for long-term localization. In: Proc. of the Workshop on Visual Localization for Mobile Platforms at CVPR, Anchorage, Alaska (2008)Google Scholar
  30. 30.
    Ni, K., Steedly, D., Dellaert, F.: Out-of-core bundle adjustment for large-scale 3D reconstruction. In: Intl. Conf. on Computer Vision (ICCV), Rio de Janeiro (2007)Google Scholar
  31. 31.
    Rodríguez, A.L., de Teruel, P.E.L., Ruiz, A.: Reduced epipolar cost for accelerated incremental sfm. In: IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), pp. 3097–3104 (2011)Google Scholar
  32. 32.
    Snavely, N., Seitz, S., Szeliski, R.: Photo tourism: Exploring photo collections in 3D. In: SIGGRAPH, pp. 835–846 (2006)Google Scholar
  33. 33.
    Snavely, N., Seitz, S.M., Szeliski, R.: Skeletal graphs for efficient structure from motion. In: IEEE Conf. on Computer Vision and Pattern Recognition, CVPR (2008)Google Scholar
  34. 34.
    Steffen, R., Frahm, J.-M., Förstner, W.: Relative bundle adjustment based on trifocal constraints. In: Kutulakos, K.N. (ed.) ECCV 2010 Workshops, Part II. LNCS, vol. 6554, pp. 282–295. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  35. 35.
    Vidal, R., Ma, Y., Soatto, S., Sastry, S.: Two-View Multibody Structure from Motion. Intl. J. of Computer Vision 68(1), 7–25 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.College of ComputingGeorgia Institute of TechnologyAtlantaUSA

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