International Journal of Computer Vision

, Volume 101, Issue 1, pp 64–94 | Cite as

Shape and Refractive Index from Single-View Spectro-Polarimetric Images

  • Cong Phuoc Huynh
  • Antonio Robles-Kelly
  • Edwin R. Hancock


In this paper, 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 occuring 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. To demonstrate the effectiveness of our approach, we show results of shape recovery and surface rendering for both real-world and synthetic imagery.


Polarisation Shape recovery Refractive index Spectro-polarimetric imagery Multispectral imagery Hyperspectral imagery Fresnel reflection Dispersion equations 


  1. Atkinson, G., & Hancock, E. R. (2005). Recovery of surface height using polarization from two views. In CAIP (pp. 162–170). Google Scholar
  2. Atkinson, G. A., & Hancock, E. R. (2005). Multi-view surface reconstruction using polarization. In IEEE International Conference on Computer Vision (ICCV’05) (Vol. 1, pp. 309–316). Washington: IEEE Comput. Soc. CrossRefGoogle Scholar
  3. Atkinson, G., & Hancock, E. (2006). Recovery of surface orientation from diffuse polarization. IEEE Transactions on Image Processing, 15(6), 1653–1664. CrossRefGoogle Scholar
  4. Atkinson, G., & Hancock, E. R. (2007a). Surface reconstruction using polarization and photometric stereo. In CAIP (pp. 466–473). Google Scholar
  5. Atkinson, G. A., & Hancock, E. R. (2007b). Shape estimation using polarization and shading from two views. IEEE Transactions on Pattern Analysis and Machine Intelligence, 29(11), 2001–2017. CrossRefGoogle Scholar
  6. Belhumeur, P. N., Kriegman, D. J., & Yuille, A. L. (1999). The bas-relief ambiguity. International Journal of Computer Vision, 35(1), 33–44. CrossRefGoogle Scholar
  7. 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
  8. Chen, H., & Wolff, L. (1998). Polarization phase based method for material classification in computer vision. International Journal of Computer Vision, 28(1), 73–83. CrossRefGoogle Scholar
  9. 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. zbMATHCrossRefMathSciNetGoogle Scholar
  10. Denes, L. J., Gottlieb, M. S., & Kaminsky, B. (1998). Acousto-optic tunable filters in imaging applications. Optical Engineering, 37, 1262. CrossRefGoogle Scholar
  11. Drbohlav, O., & Šára, R. (2001). Unambiguous determination of shape from photometric stereo with unknown light sources. In International conference on computer vision (Vol. 1, pp. 581–586). Los Alamitos: IEEE Comput. Soc. Google Scholar
  12. Frankot, R. T., & Chellappa, R. (1988). A method for enforcing integrability in shape from shading algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), 439–451. zbMATHCrossRefGoogle Scholar
  13. Gonzalez, R. C., & Woods, R. E. (1992). Digital image processing (2nd ed.). Boston: Addison-Wesley/Longman. Google Scholar
  14. Goudail, F., Terrier, P., Takakura, Y., Bigué, L., Galland, F., & DeVlaminck, V. (2004). Target detection with a liquid-crystal-based passive stokes polarimeter. Applied Optics, 43(2), 274–282. CrossRefGoogle Scholar
  15. Gupta, N., Dahmani, R., & Choy, S. (2002). Acousto-optic tunable filter based visible- to near-infrared spectropolarimetric imager. Optical Engineering, 41(5), 1033–1038. CrossRefGoogle Scholar
  16. Hall, J. S. (1951). Some polarization measurements in astronomy. Journal of the Optical Society of America, 41(12), 963–966. CrossRefGoogle Scholar
  17. Harris, S. E., & Wallace, R. W. (1969). Acousto-optic tunable filter. Journal of the Optical Society of America, 59(6), 744–747. CrossRefGoogle Scholar
  18. Hawryshyn, C. W. (2000). Ultraviolet polarization vision in fishes: possible mechanisms for coding e-vector. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 355(1401), 1187–1190. CrossRefGoogle Scholar
  19. Hecht, E. (2002). Optics (4th ed.). Reading: Addison-Wesley. Google Scholar
  20. Kasarova, S. N., Sultanova, N. G., Ivanov, C. D., & Nikolov, I. D. (2007). Analysis of the dispersion of optical plastic materials. Optical Materials, 29(11), 1481–1490. CrossRefGoogle Scholar
  21. Mandel, L., & Wolf, E. (1995). Optical coherence and quantum optics. Cambridge: Cambridge University Press. Google Scholar
  22. Marshall, N. J., Land, M. F., King, C. A., & Cronin, T. W. (1991). The compound eyes of mantis shrimps (Crustacea, Hoplocarida, Stomatopoda). I. Compound eye structure: the detection of polarized light. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 334(1269), 33–56. CrossRefGoogle Scholar
  23. 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, Online, 19(4), 687–694. CrossRefGoogle Scholar
  24. 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
  25. 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
  26. Nayar, S. K., Fang, X.-S., & Boult, T. (1997). Separation of reflection components using color and polarization. International Journal of Computer Vision, 21(3), 163–186. CrossRefGoogle Scholar
  27. Nocedal, J., & Wright, S. J. (2006). Numerical optimization (2nd ed.). New York: Springer. zbMATHGoogle Scholar
  28. Oren, M., & Nayar, S. K. (1995). Generalization of the lambertian model and implications for machine vision. International Journal of Computer Vision, 14(3), 227–251. CrossRefGoogle Scholar
  29. Rahmann, S. (1999). Inferring 3D scene structure from a single polarization image. In SPIE proceedings on polarization and color techniques in industrial inspection (Vol. 3826, pp. 22–33). CrossRefGoogle Scholar
  30. Rahmann, S. (2000). Polarization images: a geometric interpretation for shape analysis. International Conference on Pattern Recognition, 3, 538–542. Google Scholar
  31. 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
  32. Sadjadi, F. A., & Chun, C. S. L. (2004). Remote sensing using passive infrared stokes parameters. Optical Engineering, 43, 2283–2291. CrossRefGoogle Scholar
  33. Saito, M., Kashiwagi, H., Sato, Y., & Ikeuchi, K. (1999). Measurement of surface orientations of transparent objects using polarization in highlight. In IEEE conference on computer vision and pattern recognition (Vol. 1, pp. 1381). Google Scholar
  34. Schlick, C. (1994). An inexpensive brdf model for physically-based rendering. Computer Graphics Forum, 13(3), 233–246. CrossRefGoogle Scholar
  35. Sellmeier, W. (1871). Zur erklrung der abnormen farbenfolge im spectrum einiger substanzen. Annalen der Physik, 219(6), 272–282. CrossRefGoogle Scholar
  36. Shannon, C. E. (1949). Communication in the presence of noise. Proceedings of the Institute of Radio Engineers, 37(1), 10–21. MathSciNetGoogle Scholar
  37. Stiles, W. S., & Burch, J. M. (1959). N.P.L. colour-matching investigation: final report (1958). Optica Acta 6, 1–26. CrossRefGoogle Scholar
  38. 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
  39. 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
  40. 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(7), 916–924. CrossRefGoogle Scholar
  41. 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
  42. Wolff, L. B. (1994). Diffuse-reflectance model for smooth dielectric surfaces. Journal of the Optical Society of America, 11(11), 2956–2968. CrossRefMathSciNetGoogle Scholar
  43. Wolff, L. B. (1997). Polarization vision: a new sensory approach to image understanding. Image and Vision Computing, 15(2), 81–93. CrossRefMathSciNetGoogle Scholar
  44. Wolff, L. B., & Andreou, A. G. (1995). Polarization camera sensors. Image and Vision Computing, 13(6), 497–510. CrossRefGoogle Scholar
  45. Wolff, L. B., & Boult, T. E. (1989). Polarization/radiometric based material classification. In Computer vision and pattern recognition (pp. 387–395). Google Scholar
  46. Wolff, L., & Boult, T. (1991). Constraining object features using a polarization reflectance model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7), 635–657. CrossRefGoogle Scholar
  47. Wolff, L. B., Mancini, T. A., Pouliquen, P., & Andreou, A. G. (1997). Liquid crystal polarization camera. IEEE Transactions on Robotics and Automation, 13(2), 195–203. CrossRefGoogle Scholar
  48. Zhu, Q., & Shi, J. (2006). Shape from shading: recognizing the mountains through a global view. In IEEE computer society conference on computer vision and pattern recognition (Vol. 2, pp. 1839–1846). Los Alamitos: IEEE Comput. Soc. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Cong Phuoc Huynh
    • 1
  • Antonio Robles-Kelly
    • 1
    • 2
    • 3
  • Edwin R. Hancock
    • 4
  1. 1.National ICT Australia (NICTA)CanberraAustralia
  2. 2.Research School of EngineeringAustralian National UniversityCanberraAustralia
  3. 3.School of Inf. Tech. and Electrical Eng.UNSW@ADFACanberraAustralia
  4. 4.Department of Computer ScienceUniversity of YorkHeslington, YorkUK

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