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Shape from Texture

  • Kenichi Kanatani
Chapter
Part of the Springer Series in Information Sciences book series (SSINF, volume 20)

Abstract

In Sect. 2.7, we gave an analysis of the shape-from-texture problem. There, we assumed that the “texture density” was somehow observed on the image plane. Then, we showed that the surface parameters were computed in an analytically closed form in terms of invariants. We also studied the ambiguity in interpretation of the surface shape. In this chapter, we give a rigorous mathematical treatment for characterizing discrete textures. In particular, we give precise definitions of texture density and homogeneity in terms of the theory of distributions and differential geometry. Then, we present numerical schemes for solving the resulting 3D recovery equations. We also give some numerical examples for synthetic data.

Keywords

Line Segment Image Plane Planar Surface Fundamental Form Surface Equation 
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.

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Bibliography

  1. L. Schwartz: Théorie des Distributions, Vols. 1, 2 (Hermann, Paris 1950, 1951)zbMATHGoogle Scholar
  2. L. Schwartz: Méthodes Mathématiques pour les Sciences Physiques (Hermann, Paris 1961)zbMATHGoogle Scholar
  3. J. J. Gibson: The Perception of the Visual World (Houghton Mifflin, Boston, MA 1950)Google Scholar
  4. J. J. Gibson: The Senses Considered as Perceptual Systems (Houghton Mifflin, Boston, MA 1966)Google Scholar
  5. J. J. Gibson: The Ecological Approach to Visual Perception (Houghton Mifflin, Boston, MA 1979)Google Scholar
  6. H. A. Sedgwick: “Environment-Centered Representation of Spatial Layout: Available Visual Information from Texture and Perspective”, in Human and Machine Vision, ed. by J. Beck, B. Hope, A. Rosenfeld (Academic, New York 1983) pp. 425–458CrossRefGoogle Scholar
  7. K. Ikeuchi: Shape from Regular Patterns (An Example of Constraint Propagation in Vision). MITAI Memo 567, March 1980.Google Scholar
  8. H. Nakatani, S. Kimura, O. Saito, T. Kitahashi: “Extraction of Vanishing Point and Its Application to Scene Analysis Based on Image Sequence, in Proc. Intl. Conf. Pattern Recog., August 1980, Miami Beach, FL, pp. 370–372Google Scholar
  9. T. Kanade: Recovery of three-dimensional shape of an object from a single view. Artif. Intell. 17, 409–460 (1981)CrossRefGoogle Scholar
  10. Y. Ohta, K. Maenobu, T. Sakai: “Obtaining Surface Orientation from Texels Under Perspective Projection”, in Proc. 7th Intl. Joint Conf. Artif. Intell., August 1981, Vancouver, BC, pp. 746–751Google Scholar
  11. K. A. Stevens. The information content of texture gradients. Biol. Cybern. 42, 183–195 (1981)CrossRefGoogle Scholar
  12. J. R. Kender: “Surface Constraints from Linear Extents”, in Proc. 3rd Natl. Conf. Artif. Intell., August 1983, Washington, DC, pp. 187–190Google Scholar
  13. K. A. Stevens: Slant-tilt: The visual encoding of surface orientation. Biol. Cybern. 46, 183–195 (1983)CrossRefGoogle Scholar
  14. K. A. Stevens: Surface tilt (the direction of slant): A neglected psychological variable. Percept. Psychophys. 33, 241–250 (1983)CrossRefGoogle Scholar
  15. A. P. Witkin: Recovering surface shape and orientation from texture. Artif. Intell. 17, 17–45 (1981)CrossRefGoogle Scholar
  16. L. S. Davis, L. Janos, S. M. Dunn: Efficient recovery of shape from texture. IEEE Trans. PAMI-5, 485–492 (1983)Google Scholar
  17. K. Kanatani: Detection of surface orientation and motion from texture by a stereological technique. Artif. Intell. 23, 213–237 (1984)CrossRefGoogle Scholar
  18. R. Bajcsy, L. Lieberman: Texture gradient as a depth cue. Comput. Vision, Graphics Image Process. 5, 52–67 (1976)CrossRefGoogle Scholar
  19. A. Rosenfeld: A note on automatic detection of texture gradients. IEEE Trans. C-24, 988–991 (1975)zbMATHGoogle Scholar
  20. S. W. Zucker, A. Rosenfeld, L. S. Davis: Picture segmentation by texture discrimination. IEEE Trans. C-24, 1228–1233 (1975)zbMATHGoogle Scholar
  21. S. M. Dunn: Recovering the Orientation of Textured Surfaces, Ph.D. Thesis, Center for Automation Research, University of Maryland (1986)Google Scholar
  22. J. Aloimonos, M. J. Swain: Shape from texture. Biol. Cybern. 58, 345–360 (1988)CrossRefGoogle Scholar
  23. K. Kanatani T.-C. Chou: Shape from Texture: General Principle. Artif. Intell. 38, 1–48 (1989)MathSciNetCrossRefGoogle Scholar
  24. D. Blostein, N. Ahuja: A multiscale region detector. Comput. Vision, Graphics Image Process. 45, 22–41 (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Kenichi Kanatani
    • 1
  1. 1.Department of Computer ScienceGunma University KiryuJapan

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