Soft Inextensibility Constraints for Template-Free Non-rigid Reconstruction

  • Sara Vicente
  • Lourdes Agapito
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7574)


In this paper, we exploit an inextensibility prior as a way to better constrain the highly ambiguous problem of non-rigid reconstruction from monocular views. While this widely applicable prior has been used before combined with the strong assumption of a known 3D-template, our work achieves template-free reconstruction using only inextensibility constraints. We show how to formulate an energy function that includes soft inextensibility constraints and rely on existing discrete optimisation methods to minimise it. Our method has all of the following advantages: (i) it can be applied to two tasks that have been so far considered independently – template based reconstruction and non-rigid structure from motion – producing comparable or better results than the state-of-the art methods; (ii) it can perform template-free reconstruction from as few as two images; and (iii) it does not require post-processing stitching or surface smoothing.


Non-rigid reconstruction inextensiblility priors MRF optimization 


  1. 1.
    Salzmann, M., Moreno-Noguer, F., Lepetit, V., Fua, P.: Closed-Form Solution to Non-rigid 3D Surface Registration. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part IV. LNCS, vol. 5305, pp. 581–594. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Perriollat, M., Hartley, R., Bartoli, A.: Monocular template-based reconstruction of inextensible surfaces. In: BMVC (2008)Google Scholar
  3. 3.
    Brunet, F., Hartley, R., Bartoli, A., Navab, N., Malgouyres, R.: Monocular Template-Based Reconstruction of Smooth and Inextensible Surfaces. In: Kimmel, R., Klette, R., Sugimoto, A. (eds.) ACCV 2010, Part III. LNCS, vol. 6494, pp. 52–66. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3D shape from image streams. In: CVPR (June 2000)Google Scholar
  5. 5.
    Torresani, L., Hertzmann, A., Bregler., C.: Non-rigid structure-from-motion: Estimating shape and motion with hierarchical priors. PAMI (2008)Google Scholar
  6. 6.
    Russell, C., Fayad, J., Agapito, L.: Energy based multiple model fitting for non-rigid structure from motion. In: CVPR (2011)Google Scholar
  7. 7.
    Varol, A., Salzmann, M., Tola, E., Fua, P.: Template-free monocular reconstruction of deformable surfaces. In: ICCV (2009)Google Scholar
  8. 8.
    Taylor, J., Jepson, A.D., Kutulakos, K.N.: Non-rigid structure from locally-rigid motion. In: CVPR (2010)Google Scholar
  9. 9.
    Salzmann, M., Fua, P.: Reconstructing sharply folding surfaces: A convex formulation. In: CVPR (2009)Google Scholar
  10. 10.
    Ferreira, R., Xavier, J., Costeira, J.P.: Shape from motion of nonrigid objects: the case of isometrically deformable flat surfaces. In: BMVC (2009)Google Scholar
  11. 11.
    Fayad, J., Agapito, L., Del Bue, A.: Piecewise Quadratic Reconstruction of Non-Rigid Surfaces from Monocular Sequences. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 297–310. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Ullman, S.: Maximizing rigidity: the incremental recovery of 3-d structure from rigid and rubbery motion. Perception (1984)Google Scholar
  13. 13.
    Jasinschi, R., Yuille, A.: Nonrigid motion and regge calculus. Journal of the Optical Society of America 6(7), 1088–1095 (1989)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Woodford, O.J., Torr, P.H.S., Reid, I.D., Fitzgibbon, A.W.: Global stereo reconstruction under second order smoothness priors. In: CVPR (2008)Google Scholar
  15. 15.
    Lempitsky, V., Rother, C., Roth, S., Blake, A.: Fusion moves for markov random field optimization. PAMI 8, 1392–1405 (2010)CrossRefGoogle Scholar
  16. 16.
    Ishikawa, H.: Higher-order clique reduction in binary graph cut. In: CVPR (2009)Google Scholar
  17. 17.
    Rother, C., Kolmogorov, V., Lempitsky, V., Szummer, M.: Optimizing binary MRFs via extended roof duality. In: CVPR (2007)Google Scholar
  18. 18.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. PAMI (September 2004)Google Scholar
  19. 19.
    Ishikawa, H.: Higher-order gradient descent by fusion-move graph cut. In: ICCV (2009)Google Scholar
  20. 20.
    Salzmann, M., Hartley, R., Fua, P.: Convex optimization for deformable surface 3-d tracking. In: ICCV (2007)Google Scholar
  21. 21.
    Perriollat, M., Bartoli, A.: A quasi-minimal model for paper-like surfaces. In: CVPR (2007)Google Scholar
  22. 22.
    Yan, J., Pollefeys, M.: A General Framework for Motion Segmentation: Independent, Articulated, Rigid, Non-rigid, Degenerate and Non-degenerate. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006, Part IV. LNCS, vol. 3954, pp. 94–106. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sara Vicente
    • 1
  • Lourdes Agapito
    • 1
  1. 1.School of Electronic Engineering and Computer ScienceQueen Mary University of LondonLondonUK

Personalised recommendations