3D Rotation Invariant Decomposition of Motion Signals

  • Quentin Barthélemy
  • Anthony Larue
  • Jérôme I. Mars
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7585)


A new model for describing a three-dimensional (3D) trajectory is introduced in this article. The studied object is viewed as a linear combination of rotatable 3D patterns. The resulting model is now 3D rotation invariant (3DRI). Moreover, the temporal patterns are considered as shift-invariant. A novel 3DRI decomposition problem consists of estimating the active patterns, their coefficients, their rotations and their shift parameters. Sparsity allows to select few patterns among multiple ones. Based on the sparse approximation principle, a non-convex optimization called 3DRI matching pursuit (3DRI-MP) is proposed to solve this problem. This algorithm is applied to real and simulated data, and compared in order to evaluate its performances.


3D motion trajectory rotation invariant shift-invariant matching pursuit Procrustes registration 


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  1. 1.
    Akhter, I., Sheikh, Y., Khan, S., Kanade, T.: Trajectory space: A dual representation for nonrigid structure from motion. IEEE Trans. on Pattern Analysis and Machine Intelligence 33, 1442–1456 (2011)CrossRefGoogle Scholar
  2. 2.
    Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3D shape from image streams. In: Proc. Computer Vision and Pattern Recognition, CVPR (2000)Google Scholar
  3. 3.
    Barthélemy, Q., Larue, A., Mayoue, A., Mercier, D., Mars, J.: Shift & 2D rotation invariant sparse coding for multivariate signals. IEEE Trans. on Signal Processing 60, 1597–1611 (2012)CrossRefGoogle Scholar
  4. 4.
    Eggert, D., Lorusso, A., Fisher, R.: Estimating 3-D rigid body transformations: a comparison of four major algorithms. Machine Vision and Applications 9, 272–290 (1997)CrossRefGoogle Scholar
  5. 5.
    Gower, J., Dijksterhuis, G.: Procrustes Problems. Oxford Statistical Science Series (2004)Google Scholar
  6. 6.
    Bergevin, R., Soucy, M., Gagnon, H., Laurendeau, D.: Towards a general multi-view registration technique. IEEE Trans. on Pattern Analysis and Machine Intelligence 18, 540–547 (1996)CrossRefGoogle Scholar
  7. 7.
    Besl, P., McKay, H.: A method for registration of 3-D shapes. IEEE Trans. on Pattern Analysis and Machine Intelligence 14, 239–256 (1992)CrossRefGoogle Scholar
  8. 8.
    Davis, G.: Adaptive Nonlinear Approximations. PhD thesis, New York University (1994)Google Scholar
  9. 9.
    Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. on Signal Processing 41, 3397–3415 (1993)zbMATHCrossRefGoogle Scholar
  10. 10.
    Pati, Y., Rezaiifar, R., Krishnaprasad, P.: Orthogonal Matching Pursuit: recursive function approximation with applications to wavelet decomposition. In: Proc. Asilomar Conf. on Signals, Systems and Comput. (1993)Google Scholar
  11. 11.
    Gibert, G., Bailly, G., Beautemps, D., Elisei, F., Brun, R.: Analysis and synthesis of the three-dimensional movements of the head, face, and hand of a speaker using cued speech. Journal of Acoustical Society of America 118, 1144–1153 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Quentin Barthélemy
    • 1
    • 2
  • Anthony Larue
    • 1
  • Jérôme I. Mars
    • 2
  1. 1.CEA-LIST, LOADGif-sur-YvetteFrance
  2. 2.GIPSA-Lab, DISGrenoble-INPGrenobleFrance

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