Visual Form pp 231-248 | Cite as

Qualitative Shape—Some Computational Aspects

  • Jan-Olof Eklundh
  • Tony Lindeberg
  • Harald Winroth

Abstract

Theories and methodologies for representing and abstracting shape from visual information are a major concern in computational vision. Important contributions have been made on e.g. theories of dynamic shape, on the detection of salient structures like symmetries and discontinuities and also on the use of mathematical techniques of optimization and approximation.

Here we will survey some of these approaches and discuss what they make explicit and how that can be computed. In particular, we will consider such techniques in view of the figure-ground problem and the desirability of qualitative vs. quantitative descriptions.

Keywords

Machine Intelligence Error Criterion Shape Property Tangent Discontinuity Noise Sensitivity 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Bab86]
    Babaud J., Witkin A.P., Baudin M., Duda R.O. (1986) “Uniqueness of the Gaussian Kernel for Scale-Space Filtering”, IEEE Trans, on Pattern Analysis and Machine Intelligence, Vol. PAMI-8, No. 1, pp 26–33.CrossRefGoogle Scholar
  2. [Ben86]
    Bengtson A., Eklundh J.O., Howako J. (1986) “Shape Representation by Multi-Scale Contour Representation”, Technical Report TRITA-NA-8607, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm.Google Scholar
  3. [Ben91]
    Bengtson A., Eklundh J.O. (1991) “Shape Representation by Multi-Scale Contour Approximation”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 13, No. 1, pp 85–93.CrossRefGoogle Scholar
  4. [Ber87]
    Bergholm F. (1987) “Edge Focusing”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. PAMI-9, No. 6, pp 726–741.CrossRefGoogle Scholar
  5. [Bid87]
    Biederman L, “Matching Image Edges to Object Memory”, Proc. 1st Int. Conf. on Computer Vision, London, England, June 8–11, pp384-392.Google Scholar
  6. [Dah89]
    Dahlquist G. (1989) Personal communication.Google Scholar
  7. [Dic90]
    Dickinson S.J., Pentland A.P., Rosenfeld A. (1990) “Qualitative 3-D Shape Reconstruction using Distributed Aspect Graph Matching”, Proc. 3rd Int. Conf. on Computer Vision, Osaka, Japan, December 4–7, pp257-262.Google Scholar
  8. [Går90]
    Gårding J. (1990) “Shape from Texture and Contour by Weak Isotropy”, Proc. 10th Int. Conf. on Pattern Recognition, pp324-330.Google Scholar
  9. [Går91]
    Gårding J. (1991) Shape from Surface Markings, Ph.D. Thesis, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm.Google Scholar
  10. [Hof84]
    Hoffman D.D., Richards W.A. (1984), “Parts of Recognition”, Cognition, No. 18, pp65-96.Google Scholar
  11. [Koe84]
    Koenderink J.J., van Doom A.J. (1984) “The Structure of Images”, Biological Cybernetics, Vol. 50, pp 363–370.MathSciNetMATHCrossRefGoogle Scholar
  12. [Koe86]
    Koenderink J.J., van Doom A.J. (1986) “Dynamic Shape”, Biological Cybernetics, Vol. 53, pp 383–396.MathSciNetMATHCrossRefGoogle Scholar
  13. [Lev91]
    Levine M.D., Bergevin R., Quang L. (1991) “Shape Description Using Geons as 3-D Primitives”, These proceedings.Google Scholar
  14. [Lin90a]
    Lindeberg T.P. (1990) “Scale-Space for Discrete Signals”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-12, No. 3, pp 234–254.CrossRefGoogle Scholar
  15. [Lin90b]
    Lindeberg T.P., Eklundh J.O. (1990) “Scale Detection and Region Extraction from a Scale-Space Primal Sketch”, Proc. 3:rd Int. Conf. on Computer Vision, Osaka, Japan, December 4–7, pp416-426.Google Scholar
  16. [Lin90c]
    Lindeberg T.P., Weiss R. (1990) “Some Thoughts about Curves Surfaces and Singularity Theory”, Technical Note CVAP-TN03, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm.Google Scholar
  17. [Lin91a]
    Lindeberg T.P. (1991) Discrete Scale-Space Theory and the Scale-Space Primal Sketch, Ph.D. Thesis, Dept. of Numerical Analysis and Computing Science, Royal Institute of Technology, S-100 44 Stockholm.Google Scholar
  18. [Lin91b]
    Lindeberg T.P., Eklundh J.O. (1991) “On the Computation of a Scale-Space Primal Sketch”, Journal of Visual Communication and Image Representation, Vol. 2, No. 1, pp 55–78.CrossRefGoogle Scholar
  19. [Lin91c]
    Lindeberg T.P., Eklundh J.O. (1991) “The Scale-Space Primal Sketch: Construction and Experiments”, To appear in Image and Vision Computing.Google Scholar
  20. [Low85]
    Lowe D.G. (1985) Perceptual Organization and Visual Recognition, Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
  21. [Low88]
    Lowe D.G. (1988) “Organization of Smooth Image Curves at Multiple Scales”, Proc. 2:nd Int. Conf. on Computer Vision, Florida, USA, December 5–8, pp558-567.Google Scholar
  22. [Mal87]
    Malik J. (1987), “Interpreting Line Drawings of Curved Objects”, Int. Journal of Computer Vision, No. 1, pp73-103.Google Scholar
  23. [Nev77]
    Nevatia R., Binford T.O (1977), “Description and Recognition of Curved Objects”, Artificial Intelligence, No. 8, pp77-98.Google Scholar
  24. [Sum88]
    Sumanaweera T.S., et al (1988) “Image Segmentation Using Geometrical and Physical Constraints”, Proc. Image Understanding Workshop, pp 1091-1099.Google Scholar
  25. [Wit83a]
    Witkin A.P. (1983) “Scale-Space Filtering”, Proc. 8:th Int. Joint Conf. on Artificial Intelligence, Karlsruhe, West Germany, August 8–12, pp 1019-1022.Google Scholar
  26. [Yui86]
    Yuille A., Poggio T. (1986) “Scaling Theorems for Zero-Crossings”, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. PAMI-9, No. 1, pp 15–25.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Jan-Olof Eklundh
    • 1
  • Tony Lindeberg
    • 1
  • Harald Winroth
    • 1
  1. 1.Computational Vision and Active Perception Laboratory (CVAP)Royal Institute of TechnologyStockholmSweden

Personalised recommendations