Skip to main content
SpringerLink
Log in

An Efficient Linearisation Approach for Variational Perspective Shape from Shading

  • Conference paper
  • First Online:
Pattern Recognition (DAGM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9358))

Included in the following conference series:

  • 2193 Accesses

Abstract

Recently, variational methods have become increasingly more popular for perspective shape from shading due to their robustness under noise and missing information. So far, however, due to the strong nonlinearity of the data term, existing numerical schemes for minimising the corresponding energy functionals were restricted to simple explicit schemes that require thousands or even millions of iterations to provide accurate results. In this paper we tackle the problem by proposing an efficient linearisation approach for the recent variational model of Ju et al. [14]. By embedding such a linearisation in a coarse-to-fine Gauß-Newton scheme, we show that we can reduce the runtime by more than three orders of magnitude without degrading the quality of results. Hence, it is not only possible to apply variational methods for perspective SfS to significantly larger image sizes. Our approach also allows a practical choice of the regularisation parameter so that noise can be suppressed efficiently at the same time.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Abdelrahim, A.S., Abdelrahman, M.A., Abdelmunim, H., Farag, A., Miller, M.: Novel image-based 3D reconstruction of the human jaw using shape from shading and feature descriptors. In: Proceedings of the British Machine Vision Conference, pp. 1–11 (2011)

    Google Scholar 

  2. Abdelrahim, A.S., Abdelmunim, H., Graham, J., Farag, A.: Novel variational approach for the perspective shape from shading problem using calibrated images. In: Proceedings of the IEEE International Conference on Image Processing, pp. 2563–2566 (2013)

    Google Scholar 

  3. Barron, J.T., Malik, J.: Shape, illumination, and reflectance from shading. IEEE Trans. Pattern Anal. Mach. Intell. 37(8), 1670–1687 (2015)

    Google Scholar 

  4. Bors, A.G., Hancock, E.R., Wilson, R.C.: Terrain analysis using radar shape-from-shading. IEEE Trans. Pattern Anal. Mach. Intell. 25, 974–992 (2003)

    Article  Google Scholar 

  5. Breuß, M., Cristiani, E., Durou, J.-D., Falcone, M., Vogel, O.: Perspective shape from shading: ambiguity analysis and numerical approximations. SIAM J. Imaging Sci. 5(1), 311–342 (2012)

    Article  MathSciNet  Google Scholar 

  6. Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High accuracy optical flow estimation based on a theory for warping. In: Pajdla, T., Matas, J.G. (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Charbonnier, P., Blanc-Féraud, L., Aubert, G., Barlaud, M.: Deterministic edge-preserving regularization in computed imaging. IEEE Trans. Image Process. 6(2), 298–311 (1997)

    Article  Google Scholar 

  8. Courteille, F., Crouzil, A., Durou, J.-D., Gurdjos, P.: Towards shape from shading under realistic photographic conditions. In: Proceedings of the IEEE International Conference on Pattern Recognition, pp. 277–280 (2004)

    Google Scholar 

  9. Fassold, H., Danzl, R., Schindler, K., Bischof, H.: Reconstruction of archaeological finds using shape from stereo and shape from shading. In: Proceedings of the Computer Vision Winter Workshop, pp. 21–30 (2004)

    Google Scholar 

  10. Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Dover, New York (2000)

    Google Scholar 

  11. Horn, B.K.P.: Shape from shading: a method for obtaining the shape of a smooth opaque object from one view. Ph.D. thesis, Department of Electrical Engineering, MIT, Cambridge, Massachusetts, USA (1970)

    Google Scholar 

  12. Ikeuchi, K., Horn, B.K.P.: Numerical shape from shading and occluding boundaries. Artif. Intell. 17(1–3), 141–184 (1981)

    Article  Google Scholar 

  13. Ju, Y.C., Bruhn, A., Breuß, M.: Variational perspective shape from shading. In: Aujol, J.-F., Nikolova, M., Papadakis, N. (eds.) SSVM 2015. LNCS, vol. 9087, pp. 538–550. Springer, Heidelberg (2015)

    Chapter  Google Scholar 

  14. Ju, Y.C., Maurer, D., Breuß, M., Bruhn, A.: Direct variational perspective shape from shading with Cartesian depth parametrisation. In: Perspectives in Shape Analysis, Mathematics and Visualization. Springer (2015, to appear)

    Google Scholar 

  15. Kimmel, R., Sethian, J.A.: Optimal algorithm for shape from shading and path planning. J. Math. Imaging Vis. 14(3), 237–244 (2001)

    Article  MathSciNet  Google Scholar 

  16. Lee, K.M., Kuo, C.-C.J.: Shape from shading with a generalized reflectance map model. Comput. Vis. Image Underst. 67, 143–160 (1997)

    Article  Google Scholar 

  17. Nayar, S.K.: Shape recovery methods for visual inspection. In: Proceedings of the IEEE Workshop on Applications in Computer Vision, pp. 136–145 (1992)

    Google Scholar 

  18. Okatani, T., Deguchi, K.: Shape reconstruction from an endoscope image by shape from shading technique for a point light source at the projection center. Comput. Vis. Image Underst. 66, 119–131 (1997)

    Article  Google Scholar 

  19. Oren, M., Nayar, S.: Generalization of the Lambertian model and implications for machine vision. Int. J. Comput. Vis. 14(3), 227–251 (1995)

    Article  Google Scholar 

  20. Pentland, A.: Shape information from shading: a theory about human perception. In: Proceedings of the IEEE International Conference on Computer Vision, pp. 404–413 (1988)

    Google Scholar 

  21. Phong, B.T.: Illumination for computer-generated pictures. Commun. ACM 18(6), 311–317 (1975)

    Article  Google Scholar 

  22. Prados, E., Faugeras, O.: “Perspective shape from shading” and viscosity solutions. In: Proceedings of the IEEE International Conference Computer Vision, pp. 826–831 (2003)

    Google Scholar 

  23. Prados, E., Faugeras, O.: Shape from shading: a well-posed problem? In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 870–877 (2005)

    Google Scholar 

  24. Rindfleisch, T.: Photometric method for lunar topography. Photogram. Eng. 32(2), 262–277 (1966)

    Google Scholar 

  25. Rouy, E., Tourin, A.: A viscosity solution approach to shape-from-shading. SIAM J. Numer. Anal. 29(3), 867–884 (1992)

    Article  MathSciNet  Google Scholar 

  26. Sethian, J.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  27. Tankus, A., Sochen, N., Yeshurun, Y.: Shape-from-shading under perspective projection. Int. J. Comput. Vis. 63(1), 21–43 (2005)

    Article  Google Scholar 

  28. Tsai, P.-S., Shah, M.: Shape from shading using linear approximation. Image Vis. Comput. 12(8), 487–498 (1994)

    Article  Google Scholar 

  29. Vogel, O., Bruhn, A., Weickert, J., Didas, S.: Direct shape-from-shading with adaptive higher order regularisation. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 871–882. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  30. Vogel, O., Breuß, M., Leichtweis, T., Weickert, J.: Fast shape from shading for Phong-type surfaces. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 733–744. Springer, Heidelberg (2009)

    Google Scholar 

  31. Wu, C., Narasimhan, S., Jaramaz, B.: A multi-image shape-from-shading framework for near-lighting perspective endoscopes. Int. J. Comput. Vis. 86, 211–228 (2010)

    Article  MathSciNet  Google Scholar 

  32. Zhang, L., Yip, A.M., Tan, C.T.: Shape from shading based on Lax-Friedrichs fast sweeping and regularization techniques with applications to document image restoration. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2007)

    Google Scholar 

Download references

Acknowledgements

This work has been partly funded by the Deutsche Forschungsgemeinschaft (BR 2245/3-1, BR 4372/1-1).

Author information

Authors and Affiliations

  1. Institute for Visualization and Interactive Systems, University of Stuttgart, Stuttgart, Germany

    Daniel Maurer, Yong Chul Ju & Andrés Bruhn

  2. Applied Mathematics and Computer Vision Group, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany

    Michael Breuß

Authors
  1. Daniel Maurer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Chul Ju
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Breuß
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrés Bruhn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Maurer .

Editor information

Editors and Affiliations

  1. Institute of Computer Science III, University of Bonn, Bonn, Germany

    Juergen Gall

  2. MPI for Intelligent Systems, University of Tübingen, Tübingen, Germany

    Peter Gehler

  3. Computer Vision Group, Visual Computing Institute, RWTH Aachen, Aachen, Germany

    Bastian Leibe

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Maurer, D., Ju, Y.C., Breuß, M., Bruhn, A. (2015). An Efficient Linearisation Approach for Variational Perspective Shape from Shading. In: Gall, J., Gehler, P., Leibe, B. (eds) Pattern Recognition. DAGM 2015. Lecture Notes in Computer Science(), vol 9358. Springer, Cham. https://doi.org/10.1007/978-3-319-24947-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-24947-6_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24946-9

  • Online ISBN: 978-3-319-24947-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation