Resilient Subclass Discriminant Analysis with Application to Prelens Tear Film Interferometry

  • Kim L. Boyer
  • Dijia Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6718)


The study of tear film thickness and breakup has important implications for understanding tear physiology and dynamics. We have developed a complete end-to-end automated system for robust and accurate measurements of the tear film thickness from interferometric video as a function of position and time (following a blink). This paper will primarily address the problem of identifying dry regions on the surface of the contact lens, which is one of the four major components of the system. (The others are motion stabilization, image normalization, and phase demodulation to infer absolute thickness and map the surface. To address the challenging wet/dry segmentation problem, we propose a new Gaussian clustering method for feature extraction in high dimensional spaces. Each class is modeled as a mixture of Gaussians, clustered using Expectation-Maximization in the lower-dimensional Fisher’s discriminant space. We show that this approach adapts to a wide range of distributions and is insensitive to training sample size. We present experimental results on the real-world problem of identifying regions of breakup (drying) of the prelens tear film from narrowband interferometry for contact lens wearers in vivo.


Mixture of Gaussians Expectation-Maximization Feature Extraction Clustering Prelens Tear Film Interferometry Dry Eye Syndrome 


  1. 1.
    Wong, H., Fatt, I., Radke, C.J.: Deposition and thinning of the human tear film. J. Colloid and Interface Science 184(1), 44–51 (1996)CrossRefGoogle Scholar
  2. 2.
    Berger, R.E., Corrsin, S.: A surface tension gradient mechanism for driving the pre-corneal tear film after a blink. J. Biomechanics 7, 225–238 (1974)CrossRefGoogle Scholar
  3. 3.
    Sharma, A., Tiwari, S., Khanna, R., Tiffany, J.M.: Hydrodynamics of meniscus-induced thinning of the tear film. Adv. Exp. Med. Biol. 438, 425–431 (1998)CrossRefGoogle Scholar
  4. 4.
    Ehlers, N.: The thickness of the precorneal tear film. Acta Ophthalmol (Copenh) 81, 92–100 (1965)Google Scholar
  5. 5.
    King-Smith, P.E., Fink, B.A., Fogt, N., Nichols, K.K., Hill, R.M., Wilson, G.S.: The thickness of the human precorneal tear film: Evidence from reflection spectra. Invest. Ophthalmol. Vis. Sci. 41(11), 3348–3359 (2000)Google Scholar
  6. 6.
    Fogt, N., King-Smith, P.E., Tuell, G.: Interferometric measurement of tear film thickness by use of spectral oscillations. J. Opt. Soc. Am. A 15(1), 268–275 (1998)CrossRefGoogle Scholar
  7. 7.
    Wang, J., Fonn, D., Simpson, T.L., Jones, L.: Precorneal and pre- and postlens tear film thickness measured directly with optical coherence tomography. Invest. Ophthalmol. Vis. Sci. 44, 2524–2528 (2003)CrossRefGoogle Scholar
  8. 8.
    Doughty, M., Fonn, D., Richter, D., Simpson, T., Coffrey, B., Gordon, K.: A patient questionnaire approach to estimating the prevalence of dry eye symptoms in patients presenting to optometric practices across Canada. Optom. Vis. Sci. 74, 624–631 (1997)CrossRefGoogle Scholar
  9. 9.
    King-Smith, P.E., Fink, B.A., Hill, R.M., Koelling, K.W., Tiffany, J.M.: The thickness of the tear film. Current Eye Research 29(4-5), 357–368 (2004)CrossRefGoogle Scholar
  10. 10.
    Benedetto, D.A., Clinch, T.E., Laibson, P.R.: In vivo observation of tear dynamics using fluorophotometry. Arch. Ophthalmol. 102(3), 410–412 (1984)CrossRefGoogle Scholar
  11. 11.
    Benedetto, D.A., Shah, D.O., Kaufman, H.E.: The instilled fluid dynamics and surface chemistry of polymers in the preocular tear film. Invest. Ophthalmol. Vis. Sci. 14, 887–902 (1975)Google Scholar
  12. 12.
    Green, D.G., Frueh, B.R., Shapiro, J.M.: Corneal thickness measured by interferometry. J. Opt. Soc. Am. 65, 119–123 (1975)CrossRefGoogle Scholar
  13. 13.
    Prydal, J.I., Artal, P., Woon, H., Campbell, F.W.: Study of hiuman precorneal tear film thickness and structure using laser interferometry. Invest. Ophthalmol. Vis. Sci. 33, 2006–2011 (1992)Google Scholar
  14. 14.
    King-Smith, P.E., Fink, B.A., Fogt, N.: Three interferometric methods for measuring the thickness of the layers of the tear film. Optom. Vis. Sci. 76, 19–32 (1999)CrossRefGoogle Scholar
  15. 15.
    Nichols, J.J., King-Smith, P.E.: Thickness of the pre- and post-contact lens tear film measured in vivo by interferometry. Invest. Ophthalmol. Vis. Sci. 44, 68–77 (2003)CrossRefGoogle Scholar
  16. 16.
    Doane, M.G., Gelason, W.J.: Tear layer mechanics. Clinical Contact Lens Practice, 1–17 (1994)Google Scholar
  17. 17.
    McLachlan, G.J., Basford, K.E.: Mixture Models: Inference and Applications to Clustering. M. Dekker, New York (1988)zbMATHGoogle Scholar
  18. 18.
    Jain, A.K., Duin, R.P.W., Mao, J.: Statistical Pattern Recognition: A review. IEEE Trans. Pattern Anal. Mach. Intell. 22(1), 4–37 (2000)CrossRefGoogle Scholar
  19. 19.
    Ju, J., Kolaczyk, E.D., Gopal, S.: Gaussian mixture discriminant analysis and sub-pixel land cover classification in remote sensing. Remote Sensing of Environment 84(4), 550–560 (2003)CrossRefGoogle Scholar
  20. 20.
    Zhu, M., Martinez, A.M.: Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 28(8), 1274–1286 (2006)CrossRefGoogle Scholar
  21. 21.
    Hastie, T., Tibshirani, R.: Discriminant analysis by Gaussian mixtures. Journal of the Royal Statistical Society, Series B (Methodological) 58(1), 155–176 (1996)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Hastie, T., Tibshirani, R., Buja, A.: Flexible discriminant and mixture models. In: Kay, J., Titterington, D. (eds.) Statistics and Neural Networks: Advances at the Interface. Oxford University Press, Oxford (1999)Google Scholar
  23. 23.
    Fisher, R.A.: The statistical utilization of multiple measurements. Annals of Eugenics 8, 376–386 (1938)CrossRefzbMATHGoogle Scholar
  24. 24.
    Rao, C.R.: Linear Statistical Inference and its Applications, 2nd edn. Wiley Interscience, Hoboken (2002)Google Scholar
  25. 25.
    Celeux, G., Govaert, G.: Gaussian parsimonious clustering models. Pattern Recognition 28(5), 781–793 (1995)CrossRefGoogle Scholar
  26. 26.
    Halbe, Z., Aladjem, M.: Model-based mixture discriminant analysis – an experimental study. Pattern Recognition 38(3), 437–440 (2005)CrossRefzbMATHGoogle Scholar
  27. 27.
    Zhang, S., Sim, T.: Discriminant subspace analysis: A Fukunaga-Koontz approach. IEEE Trans. Pattern Anal. Mach. Intell. 29(10), 1732–1746 (2007)CrossRefGoogle Scholar
  28. 28.
    Wu, D., Boyer, K.L.: Resilient subclass discriminant analysis. In: 12th International Conference on Computer Vision, Kyoto, Japan, October 2009, pp. 389–396 (2009)Google Scholar
  29. 29.
    Wu, D., Boyer, K.L.: A new Gaussian clustering method for high dimensional classification problems. In: International Conference on Pattern Recognition and Information Processing, Minsk, Belarus (May 2009) (Invited keynote)Google Scholar
  30. 30.
    Doane, M.G.: An instrument for in vivo tear film interferometry. Optom. Vis. Sci. 66(6), 383–388 (1989)CrossRefGoogle Scholar
  31. 31.
    King-Smith, P.E., Fink, B.A., Nichols, J.J., Nichols, K.K., Hill, R.M.: Interferometric Imaging of the full thickness of the precorneal tear film. J. Opt. Soc. Am. A, Opt. Image Sci. Vis. 23(9), 2097–2104 (2006)CrossRefGoogle Scholar
  32. 32.
    Wu, D., Boyer, K.L.: Sign ambiguity resolution for phase demodulation in interferometry with application to prelens tear film analysis. In: IEEE Conference on Computer Vision and Pattern Recognition, San Francisco, CA (June 2010)Google Scholar
  33. 33.
    Itoh, K.: Analysis of the phase unwrapping problem. Appl. Opt. 21(14), 2470 (1982)CrossRefGoogle Scholar
  34. 34.
    Wu, D., Boyer, K.L.: Markov random field based phase demodulation of interferometric images. Computer Vision and Image Understanding 115(6), 759–770 (2011)CrossRefGoogle Scholar
  35. 35.
    Wu, D., Boyer, K.L., Nichols, J.J., King-Smith, P.E.: Texture based prelens tear film segmentation in interferometry images. Machine Vision and Applications 21, 253–259 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kim L. Boyer
    • 1
  • Dijia Wu
    • 1
    • 2
  1. 1.Signal Analysis and Machine Perception Laboratory, Department of Electrical, Computer, and Systems EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.Siemens Corporate ResearchPrincetonUSA

Personalised recommendations