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Change-Point Detection on the Lie Group SE(3)

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Computer Vision, Imaging and Computer Graphics. Theory and Applications (VISIGRAPP 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 229))

Abstract

This paper presents a novel method for discovering change-points in a time series of elements in the set of rigid-body motion in space SE(3). Although numerous change-points detection techniques are available for dealing with scalar, or vector, time series, the generalization of these techniques to more complex structures may require overcoming difficult challenges. The group SE(3) does not satisfy closure under linear combination. Consequently, most of the statistical properties, such as the mean, cannot be properly estimated in a straightforward manner. We present a method that takes advantage of the Lie group structure of SE(3) to adapt a difference of means method. Especially, we show that the change-point in SE(3) can be discovered in its Lie algebra se(3) that forms a vector space. The performance of our method is evaluated through both synthetic and real-data.

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References

  1. Merckel, L., Nishida, T.: Towards expressing situated knowledge for complex instruments by 3D items creation and animation. In: The 8th International Workshop on Social Intelligence Design, Kyoto, Japan, pp. 301–315 (2009)

    Google Scholar 

  2. van Dam, A.: Post-wimp user interfaces. Communications of the ACM 40, 63–67 (1997)

    Google Scholar 

  3. Sezgin, T.M., Davis, R.: Scale-space based feature point detection for digital ink. In: AAAI Fall Symposium on Making Pen-based Interaction Intelligent and Natural (2004)

    Google Scholar 

  4. Fiorentino, M., Monno, G., Renzulli, P.A., Uva, A.E.: 3D sketch stroke segmentation and fitting in virtual reality. In: International Conference on the Computer Graphics and Vision, Moscow, Russia, pp. 188–191 (2003)

    Google Scholar 

  5. Qin, S.F., Wright, D.K., Jordanov, I.N.: On-line segmentation of freehand sketches by knowledge-based nonlinear thresholding operations. Pattern Recognition 34, 1885–1893 (2001)

    Article  MATH  Google Scholar 

  6. Agarwal, M., Gupta, M., Mann, V., Sachindran, N., Anerousis, N., Mummert, L.: Problem determination in enterprise middleware systems using change point correlation of time series data. In: 2006 IEEE/IFIP Network Operations and Management Symposium NOMS 2006, pp. 471–482. IEEE, Los Alamitos (2006)

    Chapter  Google Scholar 

  7. Basseville, M., Nikiforov, I.V.: Detection of Abrupt Changes - Theory and Application. Prentice-Hall, Inc., Englewood Cliffs (1993)

    Google Scholar 

  8. Ide, T., Inoue, K.: Knowledge discovery from heterogeneous dynamic systems using change-point correlations. In: SIAM International Conference on Data Mining, pp. 571–576 (2005)

    Google Scholar 

  9. Moskvina, V., Zhigljavsky, A.: An algorithm based on singular spectrum analysis for change-point detection. Communications in Statistics: Simulation and Computation 32, 319–352 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ide, T., Tsuda, K.: Change-point detection using krylov subspace learning. In: SIAM International Conference on Data Mining, pp. 515–520 (2007)

    Google Scholar 

  11. Gombay, E.: Change detection in autoregressive time series. Journal of Multivariate Analysis 99, 451–464 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kawahara, Y., Sugiyama, M.: Change-point detection in time-series data by direct density-ratio estimation. In: SIAM International Conference on Data Mining (2009)

    Google Scholar 

  13. Lee, J., Shin, Y.S.: General construction of time-domain filters for orientation data. IEEE Transactions on Visualization and Computer Graphics 8, 119–128 (2002)

    Article  Google Scholar 

  14. Courty, N.: Bilateral human motion filtering. In: The 16th European Signal Processing Conference, Lausanne, Switzerland (2008)

    Google Scholar 

  15. Tuzel, O., Subbarao, R., Meer, P.: Simultaneous multiple 3d motion estimation via mode finding on lie groups. In: Tenth IEEE International Conference on Computer Vision, pp. 18–25. IEEE, Los Alamitos (2005)

    Google Scholar 

  16. Subbarao, R., Meer, P.: Nonlinear mean shift for clustering over analytic manifolds. In: Computer Vision and Pattern Recognition, pp. 1168–1175. IEEE, Los Alamitos (2006)

    Google Scholar 

  17. Fletcher, P.T., Lu, C., Joshi, S.: Statistics of shape via principal geodesic analysis on lie groups. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 95–101. IEEE Comput. Soc., Los Alamitos (2003)

    Google Scholar 

  18. Buss, S.R., Fillmore, J.P.: Spherical averages and applications to spherical splines and interpolation. ACM Trans. Graph. 20, 95–126 (2001)

    Article  Google Scholar 

  19. Srivastava, A., Klassen, E.: Monte Carlo extrinsic estimators of manifold-valued parameters. IEEE Transactions on Signal Processing 50, 299–308 (2002)

    Article  Google Scholar 

  20. Govindu, V.M.: Lie-algebraic averaging for globally consistent motion estimation. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 684–691. IEEE Comput. Soc., Los Alamitos (2004)

    Google Scholar 

  21. Drummond, T., Cipolla, R.: Real-time visual tracking of complex structures. IEEE Transactions on PAMI 24, 932–946 (2002)

    Article  Google Scholar 

  22. Grassia, F.S.: Practical parameterization of rotations using the exponential map. Journal of Graphics, Gpu, and Game Tools 3, 29–48 (1998)

    Article  Google Scholar 

  23. Stuelpnagel, J.: On the parametrization of the three-dimensional rotation group. SIAM Review 6, 422–430 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  24. Huang, J.S.: 7. In: Introduction to Lie Groups, pp. 71–89. World Scientific Publishing Company, Singapore (2000)

    Google Scholar 

  25. Zefran, M., Kumar, V., Croke, C.: On the generation of smooth three-dimensional rigid body motions. IEEE Transactions on Robotics and Automation 14, 576–589 (1998)

    Article  Google Scholar 

  26. Selig, J.M.: 4. In: Lie Algebra. Monographs in Computer Science, pp. 51–83. Springer, New York (2005)

    Google Scholar 

  27. Foxlin, E., Naimark, L.: Vis-tracker: A wearable vision-inertial self-tracker. In: IEEE Virtual Reality Conference, p. 199 (2003)

    Google Scholar 

  28. Hofer, M., Pottmann, H.: Energy-minimizing splines in manifolds. ACM Transactions on Graphics 23, 284–293 (2004)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, Japan

    Loic Merckel & Toyoaki Nishida

Authors
  1. Loic Merckel
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  2. Toyoaki Nishida
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Editor information

Editors and Affiliations

  1. LISA-ISTIA, Université d’Angers, 62, avenue Notre-Dame du Lac, 49000, Angers, France

    Paul Richard

  2. Departamento de Sistemas e Informática, Escola Superior de Tecnologia do IPS, Rua do Vale de Chaves Estefanilha, 2910, Setúbal, Portugal

    José Braz

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Merckel, L., Nishida, T. (2011). Change-Point Detection on the Lie Group SE(3). In: Richard, P., Braz, J. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Applications. VISIGRAPP 2010. Communications in Computer and Information Science, vol 229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25382-9_16

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  • DOI: https://doi.org/10.1007/978-3-642-25382-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25381-2

  • Online ISBN: 978-3-642-25382-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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