Extended Bayesian Helmholtz Stereopsis for Enhanced Geometric Reconstruction of Complex Objects

  • Nadejda Roubtsova
  • Jean-Yves Guillemaut
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 550)


Helmholtz stereopsis is an advanced 3D reconstruction technique for objects with arbitrary reflectance properties that uniquely characterises surface points by both depth and normal. Traditionally, in Helmholtz stereopsis consistency of depth and normal estimates is assumed rather than explicitly enforced. Further, conventional Helmholtz stereopsis performs maximum likelihood depth estimation without neighbourhood consideration. In this paper, we demonstrate that reconstruction accuracy of Helmholtz stereopsis can be greatly enhanced by formulating depth estimation as a Bayesian maximum a posteriori probability problem. In re-formulating the problem we introduce neighbourhood support by formulating and comparing three priors: a depth-based, a normal-based and a novel depth-normal consistency enforcing one. Relative performance evaluation of the three priors against standard maximum likelihood Helmholtz stereopsis is performed on both real and synthetic data to facilitate both qualitative and quantitative assessment of reconstruction accuracy. Observed superior performance of our depth-normal consistency prior indicates a previously unexplored advantage in joint optimisation of depth and normal estimates. Further, we highlight several known artefacts of Helmholtz stereopsis due to sensor saturations, normal corruption by 2D texture and by intensity sampling at grazing angles and enrich the initially proposed pipeline of Bayesian Helmholtz stereopsis with simple yet effective extensions to tackle the artefacts.


3D reconstruction Helmholtz stereopsis Complex reflectance 


  1. 1.
    Baumgard, B.: Geometric Modeling for Computer Vision. Ph.D. thesis, University of Stanford (1974)Google Scholar
  2. 2.
    Delaunoy, A., Prados, E., Belhumeur, P.N.: Towards Full 3D Helmholtz Stereovision Algorithms. In: Kimmel, R., Klette, R., Sugimoto, A. (eds.) ACCV 2010, Part I. LNCS, vol. 6492, pp. 39–52. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  3. 3.
    Frankot, R., Chellappa, R.: A method for enforcing integrability in shape from shading algorithms. PAMI 10(4), 439–451 (1988)CrossRefzbMATHGoogle Scholar
  4. 4.
    Guillemaut, J.Y., Drbohlav, O., Illingworth, J., Šára, R.: A maximum likelihood surface normal estimation algorithm for Helmholtz stereopsis. VISAPP 2, 352–359 (2008)Google Scholar
  5. 5.
    Guillemaut, J.Y., Drbohlav, O., Šára, R., Illingworth, J.: Helmholtz stereopsis on rough and strongly textured surfaces. In: 3DPVT, pp. 10–17 (2004)Google Scholar
  6. 6.
    Helmholtz, H.: Treatise on Physiological Optics, vol. 1. Dover, New York (1925) zbMATHGoogle Scholar
  7. 7.
    Kazhdan, M., Bolitho, M., Hoppe, H.: Poisson surface reconstruction. In: SGP, pp. 61–70 (2006)Google Scholar
  8. 8.
    Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. PAMI 28(10), 1568–1583 (2006)CrossRefGoogle Scholar
  9. 9.
    Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? PAMI 26, 65–81 (2004)CrossRefzbMATHGoogle Scholar
  10. 10.
    Laurentini, A.: The visual hull concept for silhouette-based image understanding. PAMI 16(2), 150–162 (1994)CrossRefGoogle Scholar
  11. 11.
    Li, S.: Markov random field models in computer vision. In: ECCV, vol. B, pp. 361–370 (1994)Google Scholar
  12. 12.
    POV-Ray: POV-Ray - The Persistence of Vision Raytracer. (2013)
  13. 13.
    Roubtsova, N., Guillemaut, J.Y.: A Bayesian framework for enhanced geometric reconstruction of complex objects by Helmholtz Stereopsis. In: VISAPP (2014)Google Scholar
  14. 14.
    Scharstein, D., Szeliski, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. IJCV 47(1–3), 7–42 (2002)CrossRefzbMATHGoogle Scholar
  15. 15.
    Seitz, S., Curless, B., Diebel, J., Scharstein, D., Szeliski, R.: A comparison and evaluation of multi-view stereo reconstruction algorithms. CVPR 1, 519–528 (2006)Google Scholar
  16. 16.
    Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., Rother, C.: A comparative study of energy minimization methods for markov random fields with smoothness-based priors. PAMI 30(6), 1068–1080 (2008)CrossRefGoogle Scholar
  17. 17.
    Tu, P., Mendonça, P.R., Ross, J., Miller, J.: Surface registration with a Helmholtz reciprocity image pair. In: Proceedings of IEEE Workshop on Color and Photometric Methods in Computer Vision (2003)Google Scholar
  18. 18.
    Wainwright, M.J., Jaakkola, T.S., Willsky, A.S.: Map estimation via agreement on trees: message-passing and linear-programming approaches. IEEE Trans. Inf. Theory 51(11), 3697–3717 (2005)CrossRefzbMATHGoogle Scholar
  19. 19.
    Weinmann, M., Ruiters, R., Osep, A., Schwartz, C., Klein, R.: Fusing structured light consistency and helmholtz normals for 3D reconstruction. In: BMVC, pp. 108.1–108.12. BMVA Press (2012)Google Scholar
  20. 20.
    Woodham, R.J.: Shape from shading, chap. Photometric Method for Determining Surface Orientation from Multiple Images, pp. 513–531. MIT Press, Cambridge, MA, USA (1989)Google Scholar
  21. 21.
    Wu, T.P., Tang, K.L., Tang, C.K., Wong, T.T.: Dense photometric stereo: a markov random field approach. PAMI 28(11), 1830–1846 (2006)CrossRefGoogle Scholar
  22. 22.
    Zickler, T.: Reciprocal image features for uncalibrated Helmholtz stereopsis. In: CVPR, pp. 1801–1808 (2006)Google Scholar
  23. 23.
    Zickler, T., Belhumeur, P.N., Kriegman, D.J.: Helmholtz stereopsis: exploiting reciprocity for surface reconstruction. IJCV 49(2–3), 215–227 (2002)CrossRefzbMATHGoogle Scholar
  24. 24.
    Zickler, T.E., Ho, J., Kriegman, D.J., Ponce, J., Belhumeur, P.N.: Binocular helmholtz stereopsis. ICCV 2, 1411–1417 (2003)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Centre for Vision, Speech and Signal ProcessingUniversity of SurreyGuildfordUK

Personalised recommendations