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Machine Vision and Applications

, Volume 27, Issue 4, pp 483–497 | Cite as

A photometric sampling method for facial shape recovery

  • Felipe Hernández-Rodríguez
  • Mario Castelán
Original Paper
  • 188 Downloads

Abstract

The authors propose a photometric method to recover facial shape that is consistent with expected facial proportions. The method borrows ideas from photometric sampling, a technique that estimates shape from continuous variations of a light source around a single circular path. This approach aims at enriching photometric information by including variations of the light source along its zenith angle. To this end, a luminance matrix describing lighting response along both azimuth and zenith angles of the light source is built for each pixel. A method based on fitting sine functions onto the singular vectors of the collected luminance matrices is proposed for estimating a surface normal map. The estimated surface normals are later refined to maximize a facial proportion criterion and finally be integrated. Experiments demonstrate that our approach successfully approximates 3D face shape while preserving facial proportions within the limits of expected depth.

Keywords

Photometric sampling Face analysis 3D shape recovery 

References

  1. 1.
    Blanz, V., Vetter, T.: A morphable model for the synthesis of 3D faces. In: Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’99, pp. 187–194. ACM Press/Addison-Wesley, New York (1999)Google Scholar
  2. 2.
    Georghiades, A., Belhumeur, D., Kriegman, D.: From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23(6), 634–660 (2001)Google Scholar
  3. 3.
    Adini, Y., Moses, Y., Ullman, S.: Face recognition: the problem of compensating for changes in illumination direction. IEEE Trans. Pattern Anal. Mach. Intell. 19, 721–732 (1997)CrossRefGoogle Scholar
  4. 4.
    Horn, B.K.P., Brooks, M.J. (eds.): Shape from Shading. MIT Press, Cambridge (1989)Google Scholar
  5. 5.
    Woodham, R.J.: Photometric method for determining surface orientation from multiple images. Opt. Eng. 19(1), 139–144 (1980)Google Scholar
  6. 6.
    Barsky, S., Petrou, M.: The 4-source photometric stereo technique for three-dimensional surfaces in the presence of highlights and shadows. IEEE Trans. Pattern Anal. Mach. Intell. 25(10), 1239–1252 (2003)CrossRefGoogle Scholar
  7. 7.
    Drbohlav, O., Chantler, M.: On optimal light configurations in photometric stereo. In: ICCV’05, pp. 1707–1712 (2005)Google Scholar
  8. 8.
    Ho, J., Yang, M., Lim, J., Lee, K., Kriegman, D.: Clustering appearances of objects under varying illumination conditions. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 11–18 (2003)Google Scholar
  9. 9.
    Argyriou, V., Petrou, M.: Recursive photometric stereo when multiple shadows and highlights are present. In: Proceedings of the CVPR, pp. 1–6 (2008)Google Scholar
  10. 10.
    Hernández, C., Vogiatzis, G., Cipolla, R.: Shadows in three-source photometric stereo. In: Proceedings of the ECCV, pp. 290–303 (2008)Google Scholar
  11. 11.
    Lee, K.-C., Ho, J., Kriegman, D.: Ninepoints of light: acquiring subspaces for face recognition under variable lighting. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 519–526 (2001)Google Scholar
  12. 12.
    Ramamoorthi, R.: Analytic PCA construction for theoretical analysis of lighting variability, including attached shadows, in a single image of a convex lambertian object, IEEE Trans. Pattern Anal. Mach. Intell. 24, 1322–1333 (2002)CrossRefGoogle Scholar
  13. 13.
    Lee, K., Ho, J., Kriegman, D.: Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 684–698 (2005)CrossRefGoogle Scholar
  14. 14.
    Nayar, S., Ikeuchi, K., Kanade, T.: Determining shape and reflectance of hybrid surfaces by photometric sampling. IEEE Trans. Robot. Autom. 6(4), 418–431 (1990)CrossRefGoogle Scholar
  15. 15.
    Saito, H., Omata, K., Ozawa, S.: Recovery of shape and surface reflectance of specular object from relative rotation of light source. Image Vis. Comput. 21, 777–787 (2003)CrossRefGoogle Scholar
  16. 16.
    Liu, R., Han, J.: Recovering surface normal of specular object by hough transform method. Comput. Vis. IET 4(2), 129–137 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Hayakawa, H.: Photometric stereo under a light source with arbitrary motion. J. Opt. Soc. Am. 11(11), 3079–3089 (1994)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Belhumeur, P.N., Kriegman, D.J., Yuille, A.L.: The bas-relief ambiguity. Int. J. Comput. Vis. 35(1), 33–44 (1999)CrossRefGoogle Scholar
  19. 19.
    Hernandez-Rodríguez, F., Castelán, M.: A method for improving consistency in photometric databases. In: British Machine Vision Conference, pp. 1–10 (2012)Google Scholar
  20. 20.
    Wu, L., Ganesh, A., Shi, B., Matsushita, Y., Wang, Y., Ma, Y.: Robust photometric stereo via low-rank matrix completion and recovery. In: Proceedings of the 10th Asian Conference on Computer vision, vol. Part III, ACCV’10, pp. 703–717. Springer, Berlin (2011)Google Scholar
  21. 21.
    Candès, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(3), 11:1–11:37 (2011)Google Scholar
  22. 22.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Mukaigawa, Y., Ishii, Y., Shakunaga, T.: Classification of photometric factors based on photometric linearization. In: Proceedings of the 7th Asian Conference on Computer Vision, vol. Part II, ACCV’06, pp. 613–622. Springer, Berlin (2006)Google Scholar
  24. 24.
    Alldrin, N.G., Mallick, S.P., Kriegman, D.J.: Resolving the generalized bas-relief ambiguity by entropy minimization. In: Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), CVPR ’07, pp. 1–7. IEEE Computer Society, Washington, DC (2007)Google Scholar
  25. 25.
    Favaro, P.: A closed-form solution to uncalibrated photometric stereo via diffuse maxima. In: Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), CVPR ’12, pp. 821–828. IEEE Computer Society, Washington, DC (2012)Google Scholar
  26. 26.
    Nayar, S., Ikeuchi, K., Kanade, T.: Recovering shape in the presence of interreflections. In: Proceedings of IEEE ICRA, vol. 2, pp. 1814–1819 (1991)Google Scholar
  27. 27.
    Chandraker, M.K., Kahl, F., Kriegman, D.J.: Reflections on the generalized bas-relief ambiguity. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05), vol. 1, pp. 788–795. IEEE Computer Society, Washington, DC (2005)Google Scholar
  28. 28.
    Ghoddousi, P.H.D.W.D.G.H., Edler, R.: Comparison of three methods of facial measurement. Int. J. Oral Maxillofac. Surg. 36, 250–258 (2007)CrossRefGoogle Scholar
  29. 29.
    DeCarlo, D., Metaxas, D., Stone, M.: An anthropometric face model using variational techniques. In: Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’98, pp. 67–74. ACM, New York (1998)Google Scholar
  30. 30.
    Edler, D.W.R., Agarwal, P., Greenhill, D.: The use of anthropometric proportion indices in the measurement of facial attractiveness. Eur. J. Orthod. 28, 274–281 (2006)CrossRefGoogle Scholar
  31. 31.
    Arslan, B.O.J.K.A., Genc, C.: Comparison of the aesthetic facial proportions of southern chinese and white women. Aesthet. Plast. Surg. 32, 234–242 (2008)Google Scholar
  32. 32.
    Angelopoulou, M., Petrou, M.: Uncalibrated flatfielding and illumination vector estimationfor photometric stereo face reconstruction. Mach. Vis. Appl. 25(3), 1317–1332 (2014)CrossRefGoogle Scholar
  33. 33.
    Miyasaki, D., Ikeuchi, K.: Photometric stereo under unknown light sources using robust SVD with missing data. In: 2010 17th IEEE International Conference on Image Processing (ICIP), pp. 4057–4060 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Robótica y Manufactura AvanzadaCentro de Investigación y de Estudios Avanzados del Instituto Politécnico NacionalRamos ArizpeMexico

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