Refractive Index Estimation Using Polarisation and Photometric Stereo

  • Gule Saman
  • Edwin R. Hancock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6855)


This paper describes a novel approach to the estimation of refractive indices of surfaces using polarisation information. We use a moments estimation method for computing the polarisation image components from intensity images obtained using multiple polariser angles. This yields estimates of the mean-intensity, polarisation and phase at each pixel location.The surface normals are estimated using the photometric stereo. Using the Fresnel theory at each pixel we estimate the refractive index of the surface from the zenith angle of the surface normal and the measured polarisation. The method has been applied to determine the variations in paintings, human skin refractive indices and also for inspecting fruit surfaces. To test the effectiveness of the method, we coat a variety of objects with a layer of transparent liquid of known refractive index. Experiments on naturally occurring surfaces (e.g. human skin and fruits) and manufactured objects such as a plastic balls and paintings illustrate the effectiveness of this method in estimating refractive indices.


Naturally occurring surfaces Manufactured surfaces Polarisation Information Photometric stereo Fresnel Theory Refractive index estimation 


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  1. 1.
    Hecht, E.: Optics, 4th edn. Addison-Wesley, Reading (2002)zbMATHGoogle Scholar
  2. 2.
    Wolff, L.B., Boult, T.E.: Constraining Object Features using a Polarisation Reflectance Model. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 635–657 (1991)CrossRefGoogle Scholar
  3. 3.
    Saman, G., Hancock, E.R.: Robust Computation of the Polarisation Image. In: International Conference on Pattern Recognition (2010)Google Scholar
  4. 4.
    Atkinson, G., Hancock, E.R.: Robust estimation of reflectance functions from polarization. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Woodham, R.J.: Photometric method for determining surface orientation from multiple images. Optical Engineering 19(1) (1980)Google Scholar
  6. 6.
    Coleman, E.N., Jain, R.: Obtaining 3-Dimensional Shape of textured and Specular surfaces using four-source photometry. Computer Graphics and Image Processing 18(4), 309–328 (1982)CrossRefGoogle Scholar
  7. 7.
    Huynh, C.P., Robles-Kelly, A., Hancock, E.R.: Shape and Refractive Index Recovery from single-view polarisation images. In: IEEE Conference on Computer Vision and Pattern Recognition (2010)Google Scholar
  8. 8.
    Chang, H., Charalampopoulos, T.T.: Determination of the wavelength dependence of refractive indices of flame soot. Royal Society (1990)Google Scholar
  9. 9.
    Ding, H., Lu, J.Q., Wooden, W.A., Kragel, P.J., Hu, X.: Refractive indices of human skin tissues at eight wavelengths and estimated dispersion relations between 300 and 1600nm. Journal Physics in Medicine and Biology 51(6) (2006)Google Scholar
  10. 10.
    Cooper, P., Thomas, M.: Geodesic Light Dome. Department of Computer Science, University of York, UK (March 2010), (Accessed On: September 10, 2010)
  11. 11.
    Born, M., Wolf, E.: Principles of Optics, 7th edn. Cambridge university Press, Cambridge (1999)CrossRefGoogle Scholar
  12. 12.
    Yee, K.: Numerical Solutions of initial boundary value problems involving Maxwell’s equations in instotropic media. IEEE Transactions on Antennas Propagation AP-14, 302–307 (1966)CrossRefzbMATHGoogle Scholar
  13. 13.
    Dunn, A., Richards-Kortum, R.: Three-Dimensional Computation of Light Scattering From Cells. IEEE Journal of Selected topics in Quantum Electronics 2(4) (1996)Google Scholar
  14. 14.
    Nieminen, T.A., Rubinsztein-Dunlop, H., Heckenberg, N.R.: Calculation of the T-matrix: general considerations and application of the point-matching method. Journal of Quantitative Spectroscopy and Radiative Transfer 79-80, 1019–1029 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gule Saman
    • 1
  • Edwin R. Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkUK

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