Advertisement

View-Based Robot Localization Using Spherical Harmonics: Concept and First Experimental Results

  • Holger Friedrich
  • David Dederscheck
  • Kai Krajsek
  • Rudolf Mester
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4713)

Abstract

Robot self-localization using a hemispherical camera system can be done without correspondences. We present a view-based approach using view descriptors, which enables us to efficiently compare the image signal taken at different locations. A compact representation of the image signal can be computed using Spherical Harmonics as orthonormal basis functions defined on the sphere. This is particularly useful because rotations between two representations can be found easily. Compact view descriptors stored in a database enable us to compute a likelihood for the current view corresponding to a particular position and orientation in the map.

Keywords

Mobile Robot Spherical Harmonic Image Signal Robot Localization Spherical Image 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Blaer, P., Allen, P.: Topological mobile robot localization using fast vision techniques. In: International Conference on Robotics and Automation, vol. 1, May 2002, pp. 1031–1036 (2002)Google Scholar
  2. 2.
    Burel, G., Henoco, H.: Determination of the orientation of 3D objects using Spherical Harmonics. Graph. Models Image Process 57(5), 400–408 (1995)CrossRefGoogle Scholar
  3. 3.
    Driscoll, J.R., Healy Jr., D.M.: Computing Fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15(2), 202–250 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    The Blender Foundation. Blender (2007), http://www.blender.org
  5. 5.
    Gonzalez-Barbosa, J.-J., Lacroix, S.: Rover localization in natural environments by indexing panoramic images. In: Proceedings of the ICRA 2002 IEEE International Conference on Robotics and Automation, pp. 1365–1370. IEEE, Los Alamitos (2002)Google Scholar
  6. 6.
    Groemer, H.: Geometric Applications of Fourier Series and Spherical Harmonics. In: Encyclopedia of Mathematics and Its Applications, Cambridge Univ. Press (1996)Google Scholar
  7. 7.
    Healy Jr., D.M., Rockmore, D.N., Kostelec, P.J., Moore, S.: FFTs for the 2-sphere – improvements and variations. Journal of Fourier Analysis and Applications 9(4), 341–385 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Jogan, M., Leonardis, A.: Robust localization using an omnidirectional appearance-based subspace model of environment. Robotics and Autonomous Systems 45, 57–72 (2003)CrossRefGoogle Scholar
  9. 9.
    Kazhdan, M., Funkhouser, T., Rusinkiewicz, S.: Rotation invariant Spherical Harmonic representation of 3D shape descriptors. In: Kobbelt, L., Schröder, P., Hoppe, H. (eds.) Eurographics Symposium on Geometry Processing (June 2003)Google Scholar
  10. 10.
    Kovacs, J.A., Wriggers, W.: Fast rotational matching. Acta Crystallographica Section D 58(8), 1282–1286 (2002)Google Scholar
  11. 11.
    Kröse, B., Vlassis, N., Bunschoten, R., Motomura, Y.: A probabilistic model for appearance-based robot localization. Image and Vision Computing 19(6), 381–391 (2001)CrossRefGoogle Scholar
  12. 12.
    Kudlicki, A., Rowicka, M., Gilski, M., Otwinowski, Z.: An efficient routine for computing symmetric real Spherical Harmonics for high orders of expansion. Journal of Applied Crystallography 39, 501–504 (2005)CrossRefGoogle Scholar
  13. 13.
    Labbani-Igbida, O., Charron, C., Mouaddib, E.M.: Extraction of Haar integral features on omnidirectional images: Application to local and global localization. In: DAGM-Symposium, pp. 334–343 (2006)Google Scholar
  14. 14.
    Levin, A., Szeliski, R.: Visual odometry and map correlation. In: IEEE Conf. on Comp. Vision and Pattern Recognition, June 2004, vol. I, pp. 611–618. IEEE Computer Society Press, Los Alamitos (2004)Google Scholar
  15. 15.
    Makadia, A., Daniilidis, K.: Direct 3D-rotation estimation from spherical images via a generalized shift theorem. In: IEEE Comp. Society Conference on Computer Vision and Pattern Recognition (CVPR 2003), vol. 2, pp. 217–224 (2003)Google Scholar
  16. 16.
    Makadia, A., Daniilidis, K.: Rotation recovery from spherical images without correspondences. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(7), 1170–1175 (2006)CrossRefGoogle Scholar
  17. 17.
    Makadia, A., Sorgi, L., Daniilidis, K.: Rotation estimation from spherical images. In: Proceedings ICPR 2004, vol. 3 (2004)Google Scholar
  18. 18.
    Menegatti, E., Maeda, T., Ishiguro, H.: Image-based memory for robot navigation using properties of the omnidirectional images (2004)Google Scholar
  19. 19.
    Menegatti, E., Zoccarato, M., Pagello, E., Ishiguro, H.: Hierarchical image-based localisation for mobile robots with monte-carlo localisation. In: Proceedings ECMR 2003, Warsaw, Poland, September 2003, pp. 13–20 (2003)Google Scholar
  20. 20.
    Oliver, N., Rosario, B., Pentland, A.: A bayesian computer vision system for modeling human interaction. In: Proceedings ICVS 1999, pp. 255–272 (1999)Google Scholar
  21. 21.
    Pajdla, T., Hlavac, V.: Zero phase representation of panoramic images for image based localization. In: Comp. Analysis of Images and Patterns, pp. 550–557 (1999)Google Scholar
  22. 22.
    Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. The MIT Press, Cambridge (2005)zbMATHGoogle Scholar
  23. 23.
    Weisstein, E.W.: Legendre Polynomial. A Wolfram Web Resource (2007), http://mathworld.wolfram.com/LegendrePolynomial.html

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Holger Friedrich
    • 1
  • David Dederscheck
    • 1
  • Kai Krajsek
    • 1
  • Rudolf Mester
    • 1
  1. 1.Visual Sensorics and Information Processing Lab, J.W. Goethe University, FrankfurtGermany

Personalised recommendations