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Group-Valued Regularization for Analysis of Articulated Motion

  • Guy Rosman
  • Alex M. Bronstein
  • Michael M. Bronstein
  • Xue-Cheng Tai
  • Ron Kimmel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7583)

Abstract

We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vector- and matrix- valued functions on parametric surfaces.

We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a powerful tool in articulated scene understanding, providing a basis for rigid parts segmentation, with little prior assumptions on the scene, despite the noisy depth measurements that often appear in commodity depth scanners.

Keywords

Parameteric Surfaces Motion Segmentation Articulated Motion 

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References

  1. 1.
    Adiv, G.: Determining three-dimensional motion structure from optic flow generated by several moving object. IEEE Trans. PAMI 7(4), 384–401 (1985)CrossRefGoogle Scholar
  2. 2.
    Anguelov, D., Koller, D., Pang, H.-C., Srinivasan, P., Thrun, S.: Recovering articulated object models from 3D range data. In: Proc. Conf. on Uncertainty in Artificial Intelligence, pp. 18–26. AUAI Press (2004)Google Scholar
  3. 3.
    Benhabiles, H., Lavoué, G., Vandeborre, J.-P., Daoudi, M.: Learning boundary edges for 3D-mesh segmentation. Comp. Graphics Forum (2011)Google Scholar
  4. 4.
    Besl, P.J., McKay, N.D.: A method for registration of 3D shapes. IEEE Trans. PAMI 14(2), 239–256 (1992)CrossRefGoogle Scholar
  5. 5.
    Bronstein, A.M., Bronstein, M.M., Kimmel, R.: Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching. Proc. Natl. Acad. Sci. USA 103(5), 1168–1172 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Brox, T., Rousson, M., Deriche Dr., R., Weickert, J.: Colour, texture, and motion in level set based segmentation and tracking. Image and Vision Computing 28(3), 376–390 (2010)CrossRefGoogle Scholar
  7. 7.
    Celledoni, E., Owren, B.: Lie group methods for rigid body dynamics and time integration on manifolds. Computer Methods in Applied Mechanics and Engineering 19, 421–438 (1999)MathSciNetGoogle Scholar
  8. 8.
    Chen, H., Bhanu, B.: 3D free form object recognition in range images using local surface patches. Pattern Recognition Letters 28, 1252–1262 (2007)CrossRefGoogle Scholar
  9. 9.
    Chen, Y., Medioni, G.: Object modelling by registration of multiple range images. Image Vision Comput. 10, 145–155 (1992)CrossRefGoogle Scholar
  10. 10.
    Comaniciu, D., Meer, P.: Mean shift: A robust approach toward feature space analysis. IEEE Trans. PAMI 24, 603–619 (2002)CrossRefGoogle Scholar
  11. 11.
    Combettes, P.L., Pesquet, J.-C.: Proximal splitting methods in signal processing (May 2010)Google Scholar
  12. 12.
    Cremers, D., Soatto, S.: Motion competition: A variational framework for piecewise parametric motion segmentation. IJCV 62(3), 249–265 (2005)CrossRefGoogle Scholar
  13. 13.
    do Carmo, M.P.: Differential Geometry of Curves and Surfaces. Prentice-Hall (1976)Google Scholar
  14. 14.
    Fayad, J., Russell, C., de Agapito, L.: Automated articulated structure and 3D shape recovery from point correspondences. In: ICCV, pp. 431–438 (2011)Google Scholar
  15. 15.
    Hall, B.C.: Lie Groups, Lie Algebras,and Representations, An Elementary Introduction. Springer (2004)Google Scholar
  16. 16.
    Hesteness, M.R.: Multipliers and gradient methods. J. of Optimization Theory and Applications 4, 303–320 (1969)CrossRefGoogle Scholar
  17. 17.
    Kim, E., Medioni, G.G.: 3D object recognition in range images using visibility context. In: IROS, pp. 3800–3807 (2011)Google Scholar
  18. 18.
    Kobilarov, M., Crane, K., Desbrun, M.: Lie group integrators for animation and control of vehicles. ACM Trans. Graph. 28(2), 1–14 (2009)CrossRefGoogle Scholar
  19. 19.
    Lai, R., Chan, T.F.: A framework for intrinsic image processing on surfaces. Comput. Vis. Image Underst. 115, 1647–1661 (2011)CrossRefGoogle Scholar
  20. 20.
    Larochelle, P.M., Murray, A.P., Angeles, J.: A Distance Metric for Finite Sets of Rigid-Body Displacements via the Polar Decomposition. Journal of Mechanical Design 129 (2007)Google Scholar
  21. 21.
    Li, H., Sumner, R.W., Pauly, M.: Global correspondence optimization for non-rigid registration of depth scans. Computer Graphics Forum 27(5) (July 2008)Google Scholar
  22. 22.
    Lin, D., Grimson, W., Fisher, J.: Learning visual flows: A Lie algebraic approach. In: CVPR, pp. 747–754 (2009)Google Scholar
  23. 23.
    Lo, T.-W.R., Siebert, J.P.: Local feature extraction and matching on range images: 2.5D SIFT. Comput. Vis. Image Underst. 113, 1235–1250 (2009)CrossRefGoogle Scholar
  24. 24.
    Myronenko, A., Song, X.B.: Point-set registration: Coherent point drift. CoRR, abs/0905.2635 (2009)Google Scholar
  25. 25.
    Nir, T., Bruckstein, A.M., Kimmel, R.: Over-parameterized variational optical flow. IJCV 76(2), 205–216 (2008)CrossRefGoogle Scholar
  26. 26.
    Paladini, M., Del Bue, A., Xavier, J.a., Agapito, L., Stošić, M., Dodig, M.: Optimal metric projections for deformable and articulated Structure-from-Motion. IJCV, 1–25 (July 2011)Google Scholar
  27. 27.
    Park, F.C., Bobrow, J.E., Ploen, S.R.: A Lie group formulation of robot dynamics. Int. J. Rob. Res. 14, 609–618 (1995)CrossRefGoogle Scholar
  28. 28.
    Powell, M.J.: A method for nonlinear constraints in minimization problems. In: Optimization. Academic Press (1969)Google Scholar
  29. 29.
    Rosman, G., Bronstein, M.M., Bronstein, A.M., Kimmel, R.: Articulated motion segmentation of point clouds by group-valued regularization. In: Eurographics Workshop on 3D Object Retrieval (2012)Google Scholar
  30. 30.
    Rosman, G., Shem-Tov, S., Bitton, D., Nir, T., Adiv, G., Kimmel, R., Feuer, A., Bruckstein, A.M.: Over-Parameterized Optical Flow Using a Stereoscopic Constraint. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds.) SSVM 2011. LNCS, vol. 6667, pp. 761–772. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  31. 31.
    Rosman, G., Wang, Y., Tai, X.-C., Kimmel, R., Bruckstein, A.M.: Fast Regularization of Matrix-Valued Images. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 173–186. Springer, Heidelberg (2012)Google Scholar
  32. 32.
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D Letters 60, 259–268 (1992)zbMATHGoogle Scholar
  33. 33.
    Shotton, J., Fitzgibbon, A., Cook, M., Sharp, T., Finocchio, M., Moore, R., Kipman, A., Blake, A.: Real-Time human pose recognition in parts from single depth images (June 2011)Google Scholar
  34. 34.
    Spira, A., Kimmel, R.: Geometric curve flows on parametric manifolds. J. Comput. Phys. 223, 235–249 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Subbarao, R., Meer, P.: Nonlinear mean shift over Riemannian manifolds. IJCV 84(1), 1–20 (2009)CrossRefGoogle Scholar
  36. 36.
    Tai, X.-C., Wu, C.: Augmented Lagrangian method, dual methods and split Bregman iteration for ROF model. In: SSVM, pp. 502–513 (2009)Google Scholar
  37. 37.
    Tuzel, O., Porikli, F., Meer, P.: Learning on Lie groups for invariant detection and tracking. In: CVPR (2008)Google Scholar
  38. 38.
    Žefran, M., Kumar, V., Croke, C.: On the generation of smooth three-dimensional rigid body motions. IEEE Transactions on Robotics and Automation 14(4), 576–589 (1998)CrossRefGoogle Scholar
  39. 39.
    Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imag. Sci. 1(3), 248–272 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    Wu, C., Zhang, J., Duan, Y., Tai, X.-C.: Augmented lagrangian method for total variation based image restoration and segmentation over triangulated surfaces. J. Sci. Comput. 50(1), 145–166 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  41. 41.
    Yacoob, Y., Davis, L.S.: Learned models for estimation of rigid and articulated human motion from stationary or moving camera. IJCV 36, 5–30 (2000)CrossRefGoogle Scholar
  42. 42.
    Zhang, Y., Kambhamettu, C.: Integrated 3D scene flow and structure recovery from multiview image sequences. In: CVPR, vol. 2, p. 2674 (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Guy Rosman
    • 1
  • Alex M. Bronstein
    • 2
  • Michael M. Bronstein
    • 3
  • Xue-Cheng Tai
    • 4
  • Ron Kimmel
    • 1
  1. 1.Dept. of Computer ScienceTechnion - IITHaifaIsrael
  2. 2.School of Electrical Engineering Faculty of EngineeringTel Aviv UniversityRamat AvivIsrael
  3. 3.Institute of Computational Science, Faculty of InformaticsUniversitá della Svizzera ItalianaLuganoSwitzerland
  4. 4.Dept. of MathematicsUniversity of BergenBergenNorway

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