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Recovering surface curvature and orientation from texture distortion: A least squares algorithm and sensitivity analysis

  • Jitendra Malik
  • Ruth Rosenholtz
Shape Estimation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 800)

Abstract

Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the ‘texture distortion’, and (b) Interpreting the ‘texture distortion’ to infer the orientation and shape of the surface. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We use non-linear minimization of a least squares error criterion to estimate the shape parameters from the affine transformations, using a simple linear algorithm to obtain an initial guess. Under the assumption that the measurement errors in the affine parameters are independent and normally distributed, we can find error bounds on the shape parameter estimates. We present results on images of planar and curved surfaces under perspective projection. We find all five local shape and orientation parameters with no a priori assumptions about the shape of the surface.

Keywords

Shape Parameter Affine Transformation Perspective Projection Ideal Observer Image Sphere 
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.

References

  1. 1.
    J. Aloimonos. “Shape from texture.” Biological Cybernetics, Vol. 58, pp. 345–360, 1988.Google Scholar
  2. 2.
    R. Bajcsy and L. Lieberman. “Texture gradient as a depth cue.” CGIP, 5:52–67, 1976.Google Scholar
  3. 3.
    A. Blake, H. Bulthoff, and D. Sheinberg, “Shape from texture: ideal observers and human psychophysics,” Vision Research, 33(12):1723–37, Aug. 1993.Google Scholar
  4. 4.
    A. Blake and C. Marines, “Shape from texture: estimation, isotropy and moments.” Artificial Intelligence, 45(1990):323–380.Google Scholar
  5. 5.
    L.G. Brown and H. Shvaytser,”Surface orientation from projective foreshortening of isotropic texture autocorrelation.” IEEE Trans. on PAMI, 12(6), June 1990, pp. 584–588.Google Scholar
  6. 6.
    L.S. Davis, L. Janos, and S.M. Dunn, “Efficient recovery of shape from texture.” IEEE Trans. on PAMI, 5(5), 1983.Google Scholar
  7. 7.
    J. Gårding. “Shape from surface markings.” Ph.D. Dissertation, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, 1991.Google Scholar
  8. 8.
    J. Gårding. “Shape from texture for smooth curved surfaces in perspective projection.” Journal of Mathematical Imaging and Vision, 2(4):327–50, Dec. 1992.Google Scholar
  9. 9.
    K. Ikeuchi. “Shape From Regular Patterns.” J. of Artificial Intelligence, 22:49–75, 1984.Google Scholar
  10. 10.
    K. Kanatani and T.C. Chou. “Shape from texture: General Principle.” J. of Artificial Intelligence, Vol. 38, pp. 1–48, 1989.Google Scholar
  11. 11.
    J. Krumm and S. Shafer. “Shape from Periodic Texture Using the Spectrogram.” Proc. CVPR, Champaign-Urbana, Illinois, 1992, 284–301.Google Scholar
  12. 12.
    J.Malik and R. Rosenholtz. “A Differential Method for Computing Local Shape-From-Texture for Planar and Curved Surfaces.” Proc. CVPR, New York, 1993.Google Scholar
  13. 13.
    J. Malik and R. Rosenholtz, “A Differential Method for Computing Local Shape-From-Texture for Planar and Curved Surfaces,” CS Division Technical Report, UCB-CSD-93-775, UC Berkeley, 1993.Google Scholar
  14. 14.
    C. Marinos and A. Blake. “Shape from texture: the homogeneity hypothesis.” Proc. ICCV, Osaka, Japan, 1990, pp.350–353.Google Scholar
  15. 15.
    B. O'Neill. “Elementary Differential Geometry.” New York: Academic Press, 1966.Google Scholar
  16. 16.
    W.H. Press, B.P. Flannery, S.A. Teukolski, W.T. Vetterling. “Numerical Recipes in C.” Cambridge University Press, 1988.Google Scholar
  17. 17.
    B. Super and A. Bovik. “Shape-from-Texture by Wavelet-Based Measurement of Local Spectral Moments.” Proc. CVPR, Champaign-Urbana, Illinois, 1992, 296–301.Google Scholar
  18. 18.
    A.P. Witkin. “Recovering surface shape and orientation from texture.” J. of Artificial Intelligence, Vol. 17, pp. 17–45, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Jitendra Malik
    • 1
  • Ruth Rosenholtz
    • 1
  1. 1.Dept. of Electrical Engineering and Computer ScienceUniversity of California at BerkeleyBerkeleyUSA

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