Shape-from-Texture from Eigenvectors of Spectral Distortion

  • Eraldo Ribeiro
  • Edwin R Hancock
Conference paper


This paper presents a simple approach to the recovery of dense orienta­tion estimates for curved textured surfaces. We make two contributions. Firstly, we show how pairs of spectral peaks can be used to make direct estimates of the slant and tilt angles for local tangent planes to the textured surface. We commence by computing the affine distortion matrices for pairs of corresponding spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The main practical benefit furnished by our analysis is that it allows us to estimate the orientation angles in closed form without re­course to numerical optimisation. Based on these theoretical properties we present an algorithm for the analysis of curved regularly textured surfaces. The second contribution of the paper is to show how initial orientation estimates delivered by the eigen-analysis can be refined using a process of robust smoothing. We apply the method to a variety of real-world and synthetic imagery. We show that the new shape-from-texture method can reliably estimate surface topography.


Tilt Angle Spectral Peak Surface Orientation Frequency Vector Spectral Distortion 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Rosenfeld. A note on automatic detection of texture gradients. TC, 24:988–991, 1975.MATHGoogle Scholar
  2. 2.
    R. Bajcsy and L. Lieberman. Texture gradient as a depth cue. Computer Graphics and Image Processing, 5:52–67, 1976.CrossRefGoogle Scholar
  3. 3.
    K.A. Stevens. The information content of texture gradients. Biological Cyber-netics, 42:95–105, 1981.CrossRefGoogle Scholar
  4. 4.
    K.A. Stevens. Slant-tilt: the visual encoding of surface orientation. Biological Cybernetics, 46:183–195, 1983.CrossRefGoogle Scholar
  5. 5.
    A. P. Witkin. Recovering surface shape and orientation from texture. Artificial Intelligence, 17:17–45, 1981.CrossRefGoogle Scholar
  6. 6.
    K. Ikeuchi. Shape from regular patterns. Artificial Intelligence, 22:49–75, 1984.CrossRefGoogle Scholar
  7. 7.
    J. Aloimonos and M.J. Swain. Shape from texture. Biological Cybernetics, 58(5):345–360, 1988.MATHCrossRefGoogle Scholar
  8. 8.
    K. Ikeuchi and B.K.P. Horn. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 17:141–184, 1981.CrossRefGoogle Scholar
  9. 9.
    A. Blake and C. Marinos. Shape from texture: estimation, isotropy and mo-ments. Artificial Intelligence, 45(3):323–380, 1990.CrossRefGoogle Scholar
  10. 10.
    K. Kanatani and T. Chou. Shape from texture: General principle. Artificial Intelligence, 38:1–48, 1989.MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    J. Garding. Shape from texture for smooth curved surfaces. In European Conference on Computer Vision, pages 630–638, 1992.Google Scholar
  12. 12.
    J. Garding. Shape from texture for smooth curved surfaces in perspective projection. J. of Mathematical Imaging and Vision, 2:329–352, 1992.Google Scholar
  13. 13.
    L.G. Brown and H. Shvaytser. Surface orientation from projective foreshorten-ing of isotopic texture autocorrelation. IEEE Trans. on Pattern Analysis and Machine Intelligence, 12(6):584–588, 1990.CrossRefGoogle Scholar
  14. 14.
    B.J. Super and A.C. Bovik. Planar surface orientation from texture spatial frequencies. Pattern Recognition, 28(5):729–743, 1995.CrossRefGoogle Scholar
  15. 15.
    J. Malik and R. Rosenholtz. A differential method for computing local shape­from-texture for planar and curved surfaces. In IEEE Conference on Vision and Pattern Recognition, pages 267–273, 1993.CrossRefGoogle Scholar
  16. 16.
    Ko Sakai and L.H. Finkel. A shape-from-texture algorithm based on human visual psychophysics. In IEEE Conference on Vision and Pattern Recognition, pages 527–532, 1994.Google Scholar
  17. 17.
    J.Y. Jau and R.T. Chin. Shape from texture using wigner distribution. Com-puter Vision, Graphics and Image Processing, 52:248–263, 1990.CrossRefGoogle Scholar
  18. 18.
    J. Krumm and S. A. Shafer. Local spatial frequency analysis of image texture. In IEEE International Conference on Computer Vision, pages 354–358, 1990.Google Scholar
  19. 19.
    J. Krumm and S. A. Shafer. Shape from periodic texture using spectrogram. In IEEE Conference on Computer Vision and Pattern Recognition, pages 284–289,1992.Google Scholar
  20. 20.
    J. Krumm and S. A. Shafer. Texture segmentation and shape in the same image. In IEEE International Conference on Computer Vision, pages 121–127, 1995.Google Scholar
  21. 21.
    B.J. Super and A.C. Bovik. Filters for directly detecting surface orientation in an image. In SPIE Conference on Visual Communications and Image Process-ing, pages 144–155, 1992.Google Scholar
  22. 22.
    J. Malik and R. Rosenholtz. Recovering surface curvature and orientation from texture distortion: a least squares algorithm and sensitive analysis. Lectures Notes in Computer Science – ECCV’94, 800:353–364, 1994.Google Scholar
  23. 23.
    J.V. Stone and S.D. Isard. Adaptive scale filtering: A general method for obtaining shape from texture. IEEE Trans. on Pattern Analysis and Machine Intelligence 17(7):713–718, 1995.CrossRefGoogle Scholar
  24. 24.
    B.K.P. Horn. Robot Vision. MIT Press, Massachusetts, 1986.Google Scholar
  25. 25.
    P. L. Worthington and E.R. Hancock. Needle map recovery using robust reg­ularizers. Image and Vision Computing, 17(8):545–559, 1998.CrossRefGoogle Scholar
  26. 26.
    P.L. Worthington and E.R. Hancock. New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Trans. on Pattern Anal-ysis and Machine Intelligence, 21(12):1250–1267, December 1999.CrossRefGoogle Scholar
  27. 27.
    R.N. Bracewell, K.-Y. Chang, A.K. Jha, and Y.-H. Wang. Affine theorem for two-dimensional fourier transform. Electronics Letters, 29(3):304, 1993.CrossRefGoogle Scholar
  28. 28.
    J. C. Bezdek. Pattern Recognition with Fuzzy Objective Algorithms. Plenum Press, 1981.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2000

Authors and Affiliations

  • Eraldo Ribeiro
    • 1
  • Edwin R Hancock
    • 1
  1. 1.Department of Computer ScienceUniversity of YorkYorkUK

Personalised recommendations