Advertisement

Linear Depth Estimation from an Uncalibrated, Monocular Polarisation Image

  • William A. P. SmithEmail author
  • Ravi Ramamoorthi
  • Silvia Tozza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9912)

Abstract

We present a method for estimating surface height directly from a single polarisation image simply by solving a large, sparse system of linear equations. To do so, we show how to express polarisation constraints as equations that are linear in the unknown depth. The ambiguity in the surface normal azimuth angle is resolved globally when the optimal surface height is reconstructed. Our method is applicable to objects with uniform albedo exhibiting diffuse and specular reflectance. We extend it to an uncalibrated scenario by demonstrating that the illumination (point source or first/second order spherical harmonics) can be estimated from the polarisation image, up to a binary convex/concave ambiguity. We believe that our method is the first monocular, passive shape-from-x technique that enables well-posed depth estimation with only a single, uncalibrated illumination condition. We present results on glossy objects, including in uncontrolled, outdoor illumination.

Keywords

Polarisation Shape-from-x Bas-relief ambiguity 

Notes

Acknowledgments

This work was undertaken while W. Smith was a visiting scholar at UCSD, supported by EPSRC Overseas Travel Grant EP/N028481/1. S. Tozza was supported by Gruppo Nazionale per il Calcolo Scientifico (GNCS-INdAM). This work was supported in part by ONR grant N00014-15-1-2013 and the UC San Diego Center for Visual Computing. We thank Zak Murez for assistance with data collection.

Supplementary material

419983_1_En_7_MOESM1_ESM.pdf (6.8 mb)
Supplementary material 1 (pdf 6991 KB)

References

  1. 1.
    Wolff, L.B., Boult, T.E.: Constraining object features using a polarization reflectance model. IEEE Trans. Pattern Anal. Mach. Intell. 13(7), 635–657 (1991)CrossRefGoogle Scholar
  2. 2.
    Miyazaki, D., Tan, R.T., Hara, K., Ikeuchi, K.: Polarization-based inverse rendering from a single view. In: Proceedings of ICCV, pp. 982–987 (2003)Google Scholar
  3. 3.
    Kadambi, A., Taamazyan, V., Shi, B., Raskar, R.: Polarized 3D: high-quality depth sensing with polarization cues. In: Proceedings of ICCV (2015)Google Scholar
  4. 4.
    Belhumeur, P.N., Kriegman, D.J., Yuille, A.: The Bas-relief ambiguity. Int. J. Comput. Vis. 35(1), 33–44 (1999)CrossRefGoogle Scholar
  5. 5.
    Schechner, Y.Y.: Self-calibrating imaging polarimetry. In: Proceedings of ICCP (2015)Google Scholar
  6. 6.
    Wolff, L.B.: Polarization vision: a new sensory approach to image understanding. Image Vision Comput. 15(2), 81–93 (1997)CrossRefGoogle Scholar
  7. 7.
    Atkinson, G.A., Hancock, E.R.: Recovery of surface orientation from diffuse polarization. IEEE Trans. Image Process. 15(6), 1653–1664 (2006)CrossRefGoogle Scholar
  8. 8.
    Morel, O., Meriaudeau, F., Stolz, C., Gorria, P.: Polarization imaging applied to 3D reconstruction of specular metallic surfaces. In: Proceedings of EI 2005, pp. 178–186 (2005)Google Scholar
  9. 9.
    Huynh, C.P., Robles-Kelly, A., Hancock, E.: Shape and refractive index recovery from single-view polarisation images. In: Proceedings of CVPR, pp. 1229–1236 (2010)Google Scholar
  10. 10.
    Mahmoud, A.H., El-Melegy, M.T., Farag, A.A.: Direct method for shape recovery from polarization and shading. In: Proceedings of ICIP, pp. 1769–1772 (2012)Google Scholar
  11. 11.
    Rahmann, S., Canterakis, N.: Reconstruction of specular surfaces using polarization imaging. In: Proceedings of CVPR (2001)Google Scholar
  12. 12.
    Atkinson, G.A., Hancock, E.R.: Shape estimation using polarization and shading from two views. IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2001–2017 (2007)CrossRefGoogle Scholar
  13. 13.
    Huynh, C.P., Robles-Kelly, A., Hancock, E.R.: Shape and refractive index from single-view spectro-polarimetric images. Int. J. Comput. Vis. 101(1), 64–94 (2013)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Atkinson, G.A., Hancock, E.R.: Surface reconstruction using polarization and photometric stereo. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 466–473. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-74272-2_58 CrossRefGoogle Scholar
  15. 15.
    Drbohlav, O., Šára, R.: Unambiguous determination of shape from photometric stereo with unknown light sources. In: Proceedings of ICCV, pp. 581–586 (2001)Google Scholar
  16. 16.
    Ngo, T.T., Nagahara, H., Taniguchi, R.: Shape and light directions from shading and polarization. In: Proceedings of CVPR, pp. 2310–2318 (2015)Google Scholar
  17. 17.
    Tozza, S., Mecca, R., Duocastella, M., Bue Del, A.: Direct differential photometric stereo shape recovery of diffuse and specular surfaces. JMIV 56(1), 57–76 (2016)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Robles-Kelly, A., Huynh, C.P.: Imaging Spectroscopy for Scene Analysis, p. 219. Springer, London (2013)CrossRefGoogle Scholar
  19. 19.
    Carpinteri, A.: Structural Mechanics, p. 74. Taylor and Francis, London (1997)zbMATHGoogle Scholar
  20. 20.
    Grant, M., Boyd, S., Ye, Y.: Disciplined convex programming. In: Liberti, L., Maculan, N. (eds.) Global Optimization: From Theory to Implementation, pp. 155–210. Springer, New York (2006)CrossRefGoogle Scholar
  21. 21.
    Ramamoorthi, R., Hanrahan, P.: On the relationship between radiance and irradiance: determining the illumination from images of a convex Lambertian object. JOSA A 18(10), 2448–2459 (2001)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Basri, R., Jacobs, D.W.: Lambertian reflectance and linear subspaces. IEEE Trans. Pattern Anal. Mach. Intell. 25(2), 218–233 (2003)CrossRefGoogle Scholar
  23. 23.
    Nehab, D., Rusinkiewicz, S., Davis, J., Ramamoorthi, R.: Efficiently combining positions and normals for precise 3D geometry. ACM Trans. Graph. 24(3), 536–543 (2005)CrossRefGoogle Scholar
  24. 24.
    Nielsen, J.B., Jensen, H.W., Ramamoorthi, R.: On optimal, minimal BRDF sampling for reflectance acquisition. ACM Trans. Graph. 34(6), 1–11 (2015)CrossRefGoogle Scholar
  25. 25.
  26. 26.

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • William A. P. Smith
    • 1
    Email author
  • Ravi Ramamoorthi
    • 2
  • Silvia Tozza
    • 3
  1. 1.University of YorkYorkUK
  2. 2.UC San DiegoSan DiegoUSA
  3. 3.Sapienza - Università di RomaRomeItaly

Personalised recommendations