Simultaneous Surface Segmentation and BRDF Estimation via Bayesian Methods

Malte Lenoch, Thorsten Wilhelm, Christian Wöhler

Abstract

We present a novel procedure that achieves segmentation of an arbitrary surface relying on the maximum a-posteriori estimation of its reflectance parameters. The number of surfaces segments is computed by the algorithm without user intervention. We employ Markov Chain Monte Carlo algorithms to compute the probability distributions associated with the model parameters of a Blinn reflectance model based on the input images. The fact that parameters are treated as probability distributions enables us to directly draw additional information about the certainty of the estimation from the results of both parameters and segmentation borders. Reversible jump MCMC allows us to include an unspecified number of change points in the computation, such that the algorithm explores model and parameter space at the same time and derives a segmentation of the surface from the input data. To accomplish this, we extend the existing concept of change points to two dimensions introducing a number of necessary new regulations and properties. The performance of the segmentation and reflectance estimation is evaluated on a synthetic and a real-world dataset.

References

  1. Aittala, M., Weyrich, T., and Lehtinen, J. (2013). Practical svbrdf capture in the frequency domain. ACM Transactions on Graphics, 32.
  2. Alldrin, N., Zickler, T., and Kriegman, D. (2008). Photometric stereo with non-parametric and spatiallyvarying reflectance. Conference on Computer Vision and Pattern Recognition.
  3. Blinn, J. F. (1977). Models of light reflection for computer synthesized pictures. Association for Computing Machinery's Special Interest Group on Computer Graphics and Interactive Techniques, 11(2):192-198.
  4. Cook, R. L. and Torrance, K. E. (1981). A reflectance model for computer graphics. Association for Computing Machinery's Special Interest Group on Computer Graphics and Interactive Techniques, 15(3):307 - 316.
  5. Giesen, F. (2009). Phong and blinnphong normalization factors. online http://www.farbrausch.de/ fg/stuff/phong.pdf, 1:1-2.
  6. Gilks, W., Richardson, S., and Spiegelhalter, D. (1996). Markov Chain Monte Carlo in Practice. Chapman & Hall.
  7. Goldman, D. B., Curless, B., Hertzmann, A., and Seitz, S. (2005). Shape and spatially-varying brdfs from photometric stereo. International Conference on Computer Vision, pages 341-348.
  8. Green, P. J. (1995). Reversible jump markov chain monte carlo computation and bayesian model determination. Biometrika, 82:711-732.
  9. Hastings, W. K. (1970). Monte carlo sampling methods using markov chains and their applications. Biometrika, 57:97-109.
  10. Herbort, S. and Wöhler, C. (2012). Self-consistent 3D surface reconstruction and reflectance model estimation of metallic surfaces. International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications, pages 1-8.
  11. Horn, B. K. P. (1986). Robot Vision. MIT Electrical Engineering and Computer Science.
  12. King, R., Morgan, B. J., Gimenez, O., and Brooks, S. P. (2010). Bayesian Analysis for Population Ecology. CRC Press.
  13. Lafortune, E. P. F., Foo, S.-C., Torrance, K. E., and Greenberg, D. P. (1997). Non-linear approximation of reflectance functions. Association for Computing Machinery's Special Interest Group on Computer Graphics and Interactive Techniques, pages 117-126.
  14. Lambert, J.-H. (1760). Photometria, sive de mensura et gradibus luminis, colorum et umbrae. Vidae Eberhardi Klett.
  15. Laskey, K. and Myers, J. (2003). Population markov chain monte carlo. Machine Learning, 50:175-196.
  16. Lenoch, M., Herbort, S., Grumpe, A., and Wöhler, C. (2014). Linear unmixing in brdf reproduction and 3d shape recovery. International Conference on Pattern Recognition.
  17. Lenoch, M., Herbort, S., and W öhler, C. (2012). Robust and accurate light source calibration using a diffuse spherical calibration object. Oldenburger 3D Tage, 11:212- 219.
  18. Lensch, H. P. A., Kautz, J., Goesele, M., Heidrich, W., and Seidel, H.-P. (2003). Image-based reconstruction of spatial appearance and geometric detail. ACM Transactions on Graphics, 22(2):234-257.
  19. Louw, M. and Nicolls, F. (2010). Surface classification via brdf parameters, using population monte carlo for mrf parameter estimation. Proc. IASTED Int. Conf. Computer Graphics and Imaging, 11:145-154.
  20. Matusik, W., Pfister, H., Brand, M., and McMillan, L. (2003). A data-driven reflectance model. ACM Transactions on Graphics, 22(3):759-769.
  21. McLachlan, G. and Peel, D. (2000). Finite Mixture Models. John Wiley & Sons, Inc.
  22. Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., and Teller, E. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21:1087-1092.
  23. Ntzoufras, I. (2011). Bayesian modeling using WinBUGS. John Wiley & Sons.
  24. Pichler, O. and Hosticka, A. T. B. J. (1995). A multichannel algorithm for image segmentation with iterative feedback. In Image Processing and Its Application.
  25. Seber, G. A. F. (1984). Multivariate Observations. John Wiley & Sons, Inc.
  26. Shi, J. and Malik, J. (2000). Normalized cuts and image segmentation. Trans. Pattern Analysis and Machine Intelligence, 8:888-905.
  27. Spath, H. (1985). Cluster Dissection and Analysis: Theory, FORTRAN Programs, Examples. Halsted Press.
  28. Weyrich, T., Lawrence, J., Lensch, H., Rusinkiewicz, S., and Zickler, T. (2008). Principles of appearance acquisition and representation. Association for Computing Machinery's Special Interest Group on Computer Graphics and Interactive Techniques, pages 1-70.
  29. Woodham, R. J. (1980). Photometric method for determining surface orientation from multiple images. Optical Engineering, 19(1):139-144.
Download


Paper Citation


in Harvard Style

Lenoch M., Wilhelm T. and Wöhler C. (2016). Simultaneous Surface Segmentation and BRDF Estimation via Bayesian Methods . In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, pages 39-48. DOI: 10.5220/0005722600390048


in Bibtex Style

@conference{visapp16,
author={Malte Lenoch and Thorsten Wilhelm and Christian Wöhler},
title={Simultaneous Surface Segmentation and BRDF Estimation via Bayesian Methods},
booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP, (VISIGRAPP 2016)},
year={2016},
pages={39-48},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005722600390048},
isbn={978-989-758-175-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP, (VISIGRAPP 2016)
TI - Simultaneous Surface Segmentation and BRDF Estimation via Bayesian Methods
SN - 978-989-758-175-5
AU - Lenoch M.
AU - Wilhelm T.
AU - Wöhler C.
PY - 2016
SP - 39
EP - 48
DO - 10.5220/0005722600390048