Advertisement

Shape and Refractive Index from Polarisation

  • Antonio Robles-Kelly
  • Cong Phuoc Huynh
Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)

Abstract

In this chapter, we address the problem of the simultaneous recovery of the shape and refractive index of an object from a spectro-polarimetric image captured from a single view. Here, we focus on the diffuse polarisation process occurring at dielectric surfaces due to subsurface scattering and transmission from the object surface into the air. The diffuse polarisation of the reflection process is modelled by the Fresnel transmission theory. We present a method for estimating the azimuth angle of surface normals from the spectral variation of the phase of polarisation. Moreover, we estimate the zenith angle of surface normals and index of refraction simultaneously in a well-posed optimisation framework. We achieve well-posedness by introducing two additional constraints to the problem, including the surface integrability and the material dispersion equation. This yields an iterative solution which is computationally efficient due to the use of closed-form solutions for both the zenith angle and the refractive index in each iteration.

Keywords

Refractive Index Zenith Angle Dispersion Equation Dispersion Coefficient Azimuth Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Atkinson, G., & Hancock, E. R. (2005). Multi-view surface reconstruction using polarization. In International conference on computer vision (pp. 309–316). Google Scholar
  2. Atkinson, G. A., & Hancock, E. R. (2006). Recovery of surface orientation from diffuse polarization. IEEE Transactions on Image Processing, 15(6), 1653–1664. CrossRefGoogle Scholar
  3. Atkinson, G. A., & Hancock, E. R. (2007). Shape estimation using polarization and shading from two views. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(11), 2001–2017. CrossRefGoogle Scholar
  4. Belhumeur, P. N., Kriegman, D. J., & Yuille, A. L. (1997). The bas-relief ambiguity. Computer Vision and Pattern Recognition, p. 1060. Google Scholar
  5. Born, M., & Wolf, E. (1999). Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (7th ed.). Cambridge: Cambridge University Press. Google Scholar
  6. Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge University Press. MATHGoogle Scholar
  7. Chen, H., & Wolff, L. B. (1998). Polarization phase-based method for material classification in computer vision. International Journal of Computer Vision, 28(1), 73–83. CrossRefGoogle Scholar
  8. Coleman, T. F., & Li, Y. (1996). A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables. SIAM Journal on Optimization, 6(4), 1040–1058. MathSciNetMATHCrossRefGoogle Scholar
  9. Drbohlav, O., & Sára, R. (2001). Unambigous determination of shape from photometric stereo with unknown light sources. In International conference on computer vision (pp. 581–586). Google Scholar
  10. Frankot, R. T., & Chellappa, R. (1988). A method of enforcing integrability in shape from shading algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 4(10), 439–451. CrossRefGoogle Scholar
  11. Gonzalez, R. C., & Woods, R. E. (2001). Digital image processing (2nd ed.). Boston: Addison-Wesley Longman. Google Scholar
  12. Kasarova, S. N., Sultanova, N. G., Ivanov, C. D., & Nikolo, I. D. (2007). Analysis of the dispersion of optical plastic materials. Optical Materials, 29, 1481–1490. CrossRefGoogle Scholar
  13. Miyazaki, D., Kagesawa, M., & Ikeuchi, K. (2004). Transparent surface modeling from a pair of polarization images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(1), 73–82. CrossRefGoogle Scholar
  14. Miyazaki, D., Saito, M., Sato, Y., & Ikeuchi, K. (2002). Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths. Journal of the Optical Society of America A, 19(4), 687–694. CrossRefGoogle Scholar
  15. Miyazaki, D., Tan, R. T., Hara, K., & Ikeuchi, K. (2003). Polarization-based inverse rendering from a single view. In IEEE international conference on computer vision (Vol. 2, p. 982). CrossRefGoogle Scholar
  16. Rahmann, S. (1999). Inferring 3D scene structure from a single polarization image. In SPIE proceedings on polarization and color techniques in industrial inspection (pp. 22–33). CrossRefGoogle Scholar
  17. Rahmann, S. (2000). Polarization images: a geometric interpretation for shape analysis. In International conference on pattern recognition (Vol. 3, pp. 538–542). Google Scholar
  18. Rahmann, S., & Canterakis, N. (2001). Reconstruction of specular surfaces using polarization imaging. In IEEE conference on computer vision and pattern recognition (Vol. 1, pp. 149–155). Google Scholar
  19. Saito, M., Sato, Y., Ikeuchi, K., & Kashiwagi, H. (1999). Measurement of surface orientations of transparent objects using polarization in highlight. Journal of the Optical Society of America A, 16(9), 2286–2293. CrossRefGoogle Scholar
  20. Schlick, C. (1994). An inexpensive BRDF model for physically-based rendering. Computer Graphics Forum, 13(3), 233–246. CrossRefGoogle Scholar
  21. Sellmeier, W. (1871). Zur Erklärung der abnormen Farbenfolge im Spectrum einiger Substanzen. Annalen der Physik und Chemie, 219(6), 272–282. CrossRefGoogle Scholar
  22. Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the Institute of Radio Engineers, 37(1), 10–21. MathSciNetGoogle Scholar
  23. Thilak, V., Voelz, D. G., & Creusere, C. D. (2007). Polarization-based index of refraction and reflection angle estimation for remote sensing applications. Applied Optics, 46(30), 7527–7536. CrossRefGoogle Scholar
  24. Torrance, K., & Sparrow, E. (1967). Theory for off-specular reflection from roughened surfaces. Journal of the Optical Society of America, 57(9), 1105–1112. CrossRefGoogle Scholar
  25. Torrance, K. E., Sparrow, E. M., & Birkebak, R. C. (1966). Polarization, directional distribution, and off-specular peak phenomena in light reflected from roughened surfaces. Journal of the Optical Society of America, 56, 916–924. CrossRefGoogle Scholar
  26. Wolff, L. B. (1989). Using polarization to separate reflection components. In Computer vision and pattern recognition (pp. 363–369). Google Scholar
  27. Wolff, L. B. (1990). Polarization-based material classification from specular reflection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(11), 1059–1071. CrossRefGoogle Scholar
  28. Wolff, L. B. (1994). Diffuse-reflectance model for smooth dielectric surfaces (No. 11, pp. 2956–2968). Google Scholar
  29. Wolff, L. B., & Boult, T. E. (1991). Constraining object features using a polarization reflectance model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7), 635–657. CrossRefGoogle Scholar
  30. Zhu, Q., & Shi, J. (2006). Shape from shading: recognizing the mountains through a global view. In Computer vision and pattern recognition (pp. 1839–1846). Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Antonio Robles-Kelly
    • 1
  • Cong Phuoc Huynh
    • 1
  1. 1.National ICT AustraliaCanberraAustralia

Personalised recommendations