3D Estimation of Extensible Surfaces Through a Local Monocular Reconstruction Technique

  • S. Jafar HosseiniEmail author
  • Helder Araujo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10117)


This paper deals with the monocular reconstruction of an extensible surface by proposing a novel approach for the determination of the 3D positions of a set of points on images of the deformed surface. Given a 3D template, this approach is applied to each image independently of the others. To proceed with the reconstruction, the surface is divided into small patches that overlap in chain-like form. We model these surface patches as being uniformly extensible. Using a linear mapping from the template onto a patch, the variation of the patch shape is split into a rigid body transformation and a pure deformation. To estimate the pure deformation, we use an optimization procedure that minimizes the reprojection error along with the error over a constraint associated with uniform expansion. Having estimated the pure deformation, the rigid body transformation can be determined by decomposing the essential matrix between the current image and the virtual image that results from projecting the 3D positions that correspond to pure deformation of the template. This enables complete estimation of the linear mapping, thereby obtaining the 3D positions of the surface patch up to scale. To define a common scale, the surface smoothness is enforced by considering that the overlapping points of the patches are the same. The experimental results show the feasibility of the approach and that the accuracy of the reconstruction is good.


  1. 1.
    Aans, H., Kahl, F.: Estimation of deformable structure and motion. In: Workshop on Vision and Modelling of Dynamic Scenes, ECCV, Denmark (2002)Google Scholar
  2. 2.
    Del-Bue, A., Llad, X., Agapito, L.: Non-rigid metric shape and motion recovery from uncalibrated images using priors. In: IEEE Conference on Computer Vision and Pattern Recognition, New York (2006)Google Scholar
  3. 3.
    Bregler, C., Hertzmann, A., Biermann, H.: Recovering non-rigid 3D shape from image streams. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 2690–2696 (2000)Google Scholar
  4. 4.
    Bartoli, A., Gay-Bellile, V., Castellani, U., Peyras, J., Olsen, S., Sayd, P.: Coarse-to-fine low-rank structure-from-motion. In: IEEE Conference on Computer Vision and Pattern Recognition (2008)Google Scholar
  5. 5.
    Brand, M.: Morphable 3D models from video. In: CVPR (2001)Google Scholar
  6. 6.
    Bookstein, F.: Principal warps: thin-plate splines and the decomposition of deformations. IEEE Trans. Pattern Anal. Mach. Intell. 11(6), 567–585 (1989)CrossRefzbMATHGoogle Scholar
  7. 7.
    Salzmann, M., Fua, P.: Reconstructing sharply folding surfaces: a convex formulation. In: IEEE Conference on Computer Vision and Pattern Recognition (2007)Google Scholar
  8. 8.
    Gay-Bellile, V., Perriollat, M., Bartoli, A., Sayd, P.: Image registration by combining thin-plate splines with a 3D morphable model. In: International Conference on Image Processing (2006)Google Scholar
  9. 9.
    Gumerov, N., Zandifar, A., Duraiswami, R., Davis, L.S.: Structure of applicable surfaces from single views. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3023, pp. 482–496. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-24672-5_38 CrossRefGoogle Scholar
  10. 10.
    Prasad, M., Zisserman, A., Fitzgibbon, A.: Single view reconstruction of curved surfaces. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1345–1354 (2006)Google Scholar
  11. 11.
    Shen, S., Shi, W., Liu, Y.: Monocular 3-D tracking of inextensible deformable surfaces under L2-norm. IEEE Trans. Image Process. 19, 512–521 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Perriollat, M., Hartley, R., Bartoli, A.: Monocular template-based reconstruction of inextensible surfaces. Int. J. Comput. Vis. 88(1), 85–110 (2010)CrossRefzbMATHGoogle Scholar
  13. 13.
    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. LNCS, vol. 5305, pp. 581–594. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-88693-8_43 CrossRefGoogle Scholar
  14. 14.
    Brunet, F., Bartoli, A., Hartley, R.: Monocular template-based 3D surface reconstruction: convex inextensible and nonconvex isometric methods, pp. 157–186, April 2014 (accepted)Google Scholar
  15. 15.
    Malti, A., Bartoli, A., Collins, T.: Template-based conformal shape-from-motion-and-shading for laparoscopy. In: Abolmaesumi, P., Joskowicz, L., Navab, N., Jannin, P. (eds.) IPCAI 2012. LNCS, vol. 7330, pp. 1–10. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-30618-1_1 CrossRefGoogle Scholar
  16. 16.
    Pizarro, D., Bartoli, A., Collins, T.: Isowarp and conwarp: warps that exactly comply with weak-perspective projection of deforming objects. In: BMVC (2013)Google Scholar
  17. 17.
    Agudo, A., Calvo, B., Montiel, J.M.M.: FEM models to code non-rigid EKF monocular SLAM. In: ICCVW (2011)Google Scholar
  18. 18.
    Malti, A., Hartley, R., Bartoli, A., Collins, T.: Monocular template-based 3D reconstruction of extensible surfaces with local linear elasticity (2013)Google Scholar
  19. 19.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute of Systems and Robotics, Department of Electrical and Computer EngineeringUniversity of CoimbraCoimbraPortugal

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