A Bayesian Framework for Enhanced Geometric Reconstruction of Complex Objects by Helmholtz Stereopsis

Nadejda Roubtsova, Jean-Yves Guillemaut

2014

Abstract

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. Furthermore, 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 reformulating 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.

References

  1. Baumgard, B. (1974). Geometric Modeling for Computer Vision. PhD thesis, University of Stanford.
  2. Delaunoy, A., Prados, E., and Belhumeur, P. (2010). Towards full 3D Helmholtz stereovision algorithms. In Proc. of ACCV, volume 1, pages 39-52.
  3. Frankot, R. and Chellappa, R. (1988). A method for enforcing integrability in shape from shading algorithms. PAMI, 10(4):439-451.
  4. Guillemaut, J.-Y., Drbohlav, O., Illingworth, J., and S? ára, R. (2008). A maximum likelihood surface normal estimation algorithm for Helmholtz stereopsis. In Proc. of VISAPP, volume 2, pages 352-359.
  5. Guillemaut, J.-Y., Drbohlav, O., S? ára, R., and Illingworth, J. (2004). Helmholtz stereopsis on rough and strongly textured surfaces. In Proc. of 3DPVT, pages 10-17.
  6. Helmholtz, H. (1925). Treatise on Physiological Optics, volume 1. Dover (New York).
  7. Kazhdan, M., Bolitho, M., and Hoppe, H. (2006). Poisson surface reconstruction. In Proc. of SGP, pages 61-70.
  8. Kolmogorov, V. (2006). Convergent tree-reweighted message passing for energy minimization. PAMI, 28(10):1568 - 1583.
  9. Kolmogorov, V. and Zabih, R. (2004). What energy functions can be minimized via graph cuts? PAMI, 26:65- 81.
  10. Laurentini, A. (1994). The visual hull concept for silhouette-based image understanding. PAMI, 16(2):150-162.
  11. Li, S. (1994). Markov random field models in computer vision. In Proc. of ECCV, volume B, pages 361-370.
  12. POV-Ray (2013). POV-Ray - The Persistence of Vision Raytracer. http://www.povray.org/.
  13. Scharstein, D. and Szeliski, R. (2002). A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. IJCV, 47(1-3):7-42.
  14. Seitz, S., Curless, B., Diebel, J., Scharstein, D., and Szeliski, R. (2006). A comparison and evaluation of multi-view stereo reconstruction algorithms. In Proc. of CVPR, volume 1, pages 519- 528.
  15. Szeliski, R., Zabih, R., Scharstein, D., Veksler, O., Kolmogorov, V., Agarwala, A., Tappen, M., and Rother, C. (2008). A comparative study of energy minimization methods for markov random fields with smoothness-based priors. PAMI, 30(6):1068-1080.
  16. Tu, P., Mendonc¸a, P. R., Ross, J., and Miller, J. (2003). Surface registration with a helmholtz reciprocity image pair. In Proc. of IEEE Workshop on Color and Photometric Methods in Computer Vision.
  17. Wainwright, M. J., Jaakkola, T. S., and Willsky, A. S. (2005). Map estimation via agreement on trees: Message-passing and linear-programming approaches. IEEE Transactions on Information Theory, 51(11):3697-3717.
  18. Weinmann, M., Ruiters, R., Osep, A., Schwartz, C., and Klein, R. (2012). Fusing structured light consistency and helmholtz normals for 3D reconstruction. In Proc. of BMVC, pages 108.1-108.12. BMVA Press.
  19. Woodham, R. J. (1989). Shape from shading, chapter Photometric method for determining surface orientation from multiple images, pages 513-531. MIT Press, Cambridge, MA, USA.
  20. Wu, T.-P., Tang, K.-L., Tang, C.-K., and Wong, T.-T. (2006). Dense photometric stereo: A Markov Random Field approach. PAMI, 28(11):1830-1846.
  21. Zickler, T. (2006). Reciprocal image features for uncalibrated Helmholtz stereopsis. In Proc. of CVPR, pages 1801- 1808.
  22. Zickler, T., Belhumeur, P. N., and Kriegman, D. J. (2002). Helmholtz stereopsis: Exploiting reciprocity for surface reconstruction. IJCV, 49(2-3):215-227.
  23. Zickler, T. E., Ho, J., Kriegman, D. J., Ponce, J., and Belhumeur, P. N. (2003). Binocular Helmholtz stereopsis. In Proc. of ICCV, volume 2, pages 1411-1417.
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Paper Citation


in Harvard Style

Roubtsova N. and Guillemaut J. (2014). A Bayesian Framework for Enhanced Geometric Reconstruction of Complex Objects by Helmholtz Stereopsis . In Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2014) ISBN 978-989-758-009-3, pages 335-342. DOI: 10.5220/0004683503350342


in Bibtex Style

@conference{visapp14,
author={Nadejda Roubtsova and Jean-Yves Guillemaut},
title={A Bayesian Framework for Enhanced Geometric Reconstruction of Complex Objects by Helmholtz Stereopsis},
booktitle={Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2014)},
year={2014},
pages={335-342},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004683503350342},
isbn={978-989-758-009-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2014)
TI - A Bayesian Framework for Enhanced Geometric Reconstruction of Complex Objects by Helmholtz Stereopsis
SN - 978-989-758-009-3
AU - Roubtsova N.
AU - Guillemaut J.
PY - 2014
SP - 335
EP - 342
DO - 10.5220/0004683503350342