Advertisement

A Symmetry Prior for Convex Variational 3D Reconstruction

  • Pablo SpecialeEmail author
  • Martin R. Oswald
  • Andrea Cohen
  • Marc Pollefeys
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9912)

Abstract

We propose a novel prior for variational 3D reconstruction that favors symmetric solutions when dealing with noisy or incomplete data. We detect symmetries from incomplete data while explicitly handling unexplored areas to allow for plausible scene completions. The set of detected symmetries is then enforced on their respective support domain within a variational reconstruction framework. This formulation also handles multiple symmetries sharing the same support. The proposed approach is able to denoise and complete surface geometry and even hallucinate large scene parts. We demonstrate in several experiments the benefit of harnessing symmetries when regularizing a surface.

Keywords

Symmetry prior 3D reconstruction Variational methods Convex optimization 

Notes

Acknowledgments

This work was supported by the Horizon 2020 research and innovation programme under grant agreement No. 637221, and by the CTI Switzerland grant No. 17136.1 Geometric and Semantic Structuring of 3D point clouds.

References

  1. 1.
    Cohen, A., Sattler, T., Pollefeys, M.: Merging the unmatchable: stitching visually disconnected SFM models. In: ICCV, December 2015Google Scholar
  2. 2.
    Cohen, A., Zach, C., Sinha, S., Pollefeys, M.: Discovering and exploiting 3D symmetries in structure from motion. In: CVPR, June 2012Google Scholar
  3. 3.
    Curless, B., Levoy, M.: A volumetric method for building complex models from range images. In: SIGGRAPH (1996)Google Scholar
  4. 4.
    Golovinskiy, A., Podolak, J., Funkhouser, T.: Symmetry-aware mesh processing. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds.) Mathematics of Surfaces XIII. LNCS, vol. 5654, pp. 170–188. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Häne, C., Zach, C., Cohen, A., Angst, R., Pollefeys, M.: Joint 3D scene reconstruction and class segmentation. In: CVPR, pp. 97–104 (2013)Google Scholar
  6. 6.
    Hauagge, D.C., Snavely, N.: Image matching using local symmetry features. In: CVPR, pp. 206–213 (2012)Google Scholar
  7. 7.
    Kazhdan, M.M., Chazelle, B., Dobkin, D.P., Funkhouser, T.A., Rusinkiewicz, S.: A reflective symmetry descriptor for 3D models. Algorithmica 38(1), 201–225 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Kerber, J., Wand, M., Krüger, J.H., Seidel, H.: Partial symmetry detection in volume data. In: Proceedings of the Vision, Modeling, and Visualization Workshop, Berlin, Germany, 4–6 October 2011, pp. 41–48 (2011)Google Scholar
  9. 9.
    Kolev, K., Klodt, M., Brox, T., Cremers, D.: Continuous global optimization in multiview 3D reconstruction. IJCV 84(1), 80–96 (2009)CrossRefGoogle Scholar
  10. 10.
    Kolev, K., Pock, T., Cremers, D.: Anisotropic minimal surfaces integrating photoconsistency and normal information for multiview stereo. In: ECCV, Heraklion, Greece, September 2010Google Scholar
  11. 11.
    Köser, K., Zach, C., Pollefeys, M.: Dense 3D reconstruction of symmetric scenes from a single image. In: Mester, R., Felsberg, M. (eds.) DAGM 2011. LNCS, vol. 6835, pp. 266–275. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Liu, J., Liu, Y.: Curved reflection symmetry detection with self-validation. In: Kimmel, R., Klette, R., Sugimoto, A. (eds.) ACCV 2010, Part IV. LNCS, vol. 6495, pp. 102–114. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Liu, Y., Hel-Or, H., Kaplan, C.S., Gool, L.V.: Computational symmetry in computer vision and computer graphics. Found. Trends Comput. Graph. Vis. 5(12), 1–195 (2010)zbMATHGoogle Scholar
  14. 14.
    Lorensen, W.E., Cline, H.E.: Marching cubes: a high resolution 3D surface construction algorithm. SIGGRAPH Comput. Graph. 21, 163–169 (1987)CrossRefGoogle Scholar
  15. 15.
    Mitra, N.J., Guibas, L.J., Pauly, M.: Symmetrization. ACM Trans. Graph. 26(3), 63 (2007)CrossRefGoogle Scholar
  16. 16.
    Mitra, N.J., Pauly, M., Wand, M., Ceylan, D.: Symmetry in 3D geometry: extraction and applications. Comput. Graph. Forum 32(6), 1–23 (2013)CrossRefGoogle Scholar
  17. 17.
    Oswald, M.R., Cremers, D.: A convex relaxation approach to space time multi-view 3D reconstruction. In: ICCV - Workshop on Dynamic Shape Capture and Analysis (4DMOD) (2013)Google Scholar
  18. 18.
    Oswald, M.R., Cremers, D.: Surface normal integration for convex space-time multi-view reconstruction. In: Proceedings of the British Machine and Vision Conference (BMVC) (2014)Google Scholar
  19. 19.
    Oswald, M.R., Stühmer, J., Cremers, D.: Generalized connectivity constraints for spatio-temporal 3D reconstruction. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014, Part IV. LNCS, vol. 8692, pp. 32–46. Springer, Heidelberg (2014)Google Scholar
  20. 20.
    Pizlo, Z., Sawada, T., Li, Y., Kropatsch, W.G., Steinman, R.M.: New approach to the perception of 3D shape based on veridicality, complexity, symmetry and volume. Vision. Res. 50, 1–11 (2010)CrossRefGoogle Scholar
  21. 21.
    Pock, T., Chambolle, A.: Diagonal preconditioning for first order primal-dual algorithms in convex optimization. In: ICCV, Washington, DC, USA, pp. 1762–1769 (2011)Google Scholar
  22. 22.
    Podolak, J., Golovinskiy, A., Rusinkiewicz, S.: Symmetry-enhanced remeshing of surfaces. In: Proceedings of the Fifth Eurographics Symposium on Geometry Processing, Barcelona, Spain, 4–6 July 2007, pp. 235–242 (2007)Google Scholar
  23. 23.
    Podolak, J., Shilane, P., Golovinskiy, A., Rusinkiewicz, S., Funkhouser, T.A.: A planar-reflective symmetry transform for 3D shapes. ACM Trans. Graph. 25(3), 549–559 (2006)CrossRefGoogle Scholar
  24. 24.
    Reinbacher, C., Pock, T., Bauer, C., Bischof, H.: Variational segmentation of elongated volumetric structures. In: CVPR (2010)Google Scholar
  25. 25.
    Terzopoulos, D., Witkin, A., Kass, M.: Symmetry-seeking models and 3D object reconstruction. IJCV 1, 211–221 (1987)CrossRefGoogle Scholar
  26. 26.
    Thrun, S., Wegbreit, B.: Shape from symmetry. In: ICCV, Bejing, China. IEEE (2005)Google Scholar
  27. 27.
    Ummenhofer, B., Brox, T.: Dense 3D reconstruction with a hand-held camera. In: Pinz, A., Pock, T., Bischof, H., Leberl, F. (eds.) DAGM and OAGM 2012. LNCS, vol. 7476, pp. 103–112. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  28. 28.
    Unger, M., Pock, T., Cremers, D., Bischof, H.: TVSeg - interactive total variation based image segmentation. In: Proceedings of the British Machine and Vision Conference (BMVC), Leeds, UK, September 2008Google Scholar
  29. 29.
    Zach, C., Pock, T., Bischof, H.: A globally optimal algorithm for robust TV-l1 range image integration. In: ICCV, pp. 1–8 (2007)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Pablo Speciale
    • 1
    Email author
  • Martin R. Oswald
    • 1
  • Andrea Cohen
    • 1
  • Marc Pollefeys
    • 1
    • 2
  1. 1.ETH ZürichZurichSwitzerland
  2. 2.MicrosoftRedmondUSA

Personalised recommendations