Advertisement

Representing objects using topology

  • Charlie Rothwell
  • Joe Mundy
  • Bill Hoffman
Geometric and Topological Representations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1144)

Abstract

In this paper we call for the revival of the study of topological representations in computer vision. Topology allows us to express the connectivity relationships which exist between different primitives in images and in scenes. Although topology was once of significant interest in vision, it has recently become over-shadowed by geometric considerations. We believe that it has a very important role to play in visual processing.

First we introduce an object-oriented class hierarchy which records the topological descriptions which exist in images and scenes. Once we have shown how the image topology relates to that of the scene, we demonstrate how it can be extracted from raw images. Subsequent to this, we describe how the newly found topological descriptions can be employed to facilitate feature grouping, the recognition of polyhedra, and the evaluation of recognition hypothesis which result from a mature object recognition system.

Keywords

Topological Representation Topological Description Occlusion Event Image Support Connectivity Relationship 
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. 1.
    N. Ayache and O. Faugeras. HYPER: A New Approach for the Recognition and Positioning of Two-Dimensional Objects. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(1):44–54, January 1986.Google Scholar
  2. 2.
    T. Binford and T. Levitt. Quasi-invariants: Theory and explanation. In Proceedings of the ARPA Image Understanding Workshop, pages 819–829, Washington, DC, April 1993.Google Scholar
  3. 3.
    T. Binford. Inferring surfaces from images. Artificial Intelligence Journal, (Special Edition on Computer Vision) 17:205–244, 1981.Google Scholar
  4. 4.
    J. Canny. Finding edges and lines in images. Technical Report AI-TR-720, Massachusets Institute of Technology, Artificial Intelligence Laboratory, June 1983.Google Scholar
  5. 5.
    M. Clowes. On seeing things. Artificial Intelligence Journal, 2:79–116, 1971.Google Scholar
  6. 6.
    I. Cox, J. Rehg, and S. Hingorani. A bayesian multiple hypothesis approach to contour grouping. In G. Sandini, editor, Proceedings of the 2nd European Conference on Computer Vision, volume 588 of Lecture Notes in Computer Science, pages 72–77, Santa Margherita Ligure, Italy, May 1992. Springer-Verlag.Google Scholar
  7. 7.
    R. Deriche and T. Blaszka. Recovering and characterizing image features using an efficient model based approach. In Proceedings of the International Conference on Computer Vision and Pattern Recognition, pages 530–535, New-York, June 1993.Google Scholar
  8. 8.
    J. Dickson. Image Structure and Model-Based Vision. PhD thesis, Department of Engineering Science, Oxford University, Oxford, UK, 1991.Google Scholar
  9. 9.
    W. E. L. Grimson. Object Recognition by Computer: The Role of Geometric Constraints. The MIT Press, Cambridge, Massachusetts, London, England, 1990.Google Scholar
  10. 10.
    A. Guzman. Decomposition of a visual scene into three-dimensional bodies. In FJCC, volume 33, pages 291–304, 1968.Google Scholar
  11. 11.
    R. Haralick and L. Shapiro. Computer and Robot Vision, volume 1. Addison-Wesley, 1992.Google Scholar
  12. 12.
    F. Heitger and R. von der Heydt. A computational model of neural contour processing: Figure-ground segregation and illusory contours. In Proceedings of the 4th Proc. International Conference on Computer Vision, pages 32–40, Berlin, Germany, May 1993.Google Scholar
  13. 13.
    M. Hueckel. A local visual operator which recognizes edges and lines. Journal of the ACM, 20(4):634–647, 1973.Google Scholar
  14. 14.
    D. Huffman. Impossible objects as nonsense sentences. In B. Meltzer and D. Michie, editors, Machine Intelligence, volume 6, Edinburgh University Press, 1971.Google Scholar
  15. 15.
    D. Huttenlocher, J. Noh, and W. Rucklidge. Tracking non-rigid objects in complex scenes. In Proceedings of the 4th Proc. International Conference on Computer Vision, pages 93–101, Berlin, Germany, May 1993.Google Scholar
  16. 16.
    T. Kanade. Recovery of the three-dimensional shape of an object from a single view. Artificial Intelligence Journal, 17:409–460, 1981.Google Scholar
  17. 17.
    D. Lowe. Perceptual Organization and Visual Recognition. Kluwer Academic Publishers, 1985.Google Scholar
  18. 18.
    J. Malik. Interpreting Line Drawings of Curved Objects. The International Journal of Computer Vision, 1(1):73–103, 1987.Google Scholar
  19. 19.
    L. Morin. Quelque Contributions des Invariants Projectifs à la Vision par Ordinateur. PhD thesis, Institute National Polytechnique de Grenoble, LIFIA-IMAG-INRIA Rhone-Alpes, January 1993.Google Scholar
  20. 20.
    J. Mundy and A. Heller. The evolution and testing of a model-based object recognition system. In Proceedings of the 3rd Proc. International Conference on Computer Vision, pages 268–282, Osaka, Japan, December 1990.Google Scholar
  21. 21.
    L. Robert and O. Faugeras. Relative 3-D positioning and 3-D convex hull computation from a weakly calibrated stereo pair. Image and Vision Computing, 13(3): 189–197, 1995.Google Scholar
  22. 22.
    K. Rohr. Recognizing corners by fitting parametric models. The International Journal of Computer Vision, 9(3):213–230, 1992.Google Scholar
  23. 23.
    C. Rothwell, J. Mundy, W. Hoffman, and V.-D. Nguyen. Driving vision by topology. In IEEE International Symposium on Computer Vision, pages 395–400, November 1995.Google Scholar
  24. 24.
    C. Rothwell. Reasoning about occlusions during hypothesis verification. In Bernard Buxton, editor, Proceedings of the 4th European Conference on Computer Vision, Vol. 1, pages 599–609, Cambridge, UK, April 1996.Google Scholar
  25. 25.
    C. Rothwell and J. Stern. Understanding the shape properties of trihedral polyhedra. In Bernard Buxton, editor, Proceedings of the 4th European Conference on Computer Vision, Vol. 1, pages 175–185, Cambridge, UK, April 1996.Google Scholar
  26. 26.
    C. Rothwell. Object recognition through invariant indexing. Oxford University Science Publications. Oxford University Press, February 1995.Google Scholar
  27. 27.
    S. Sarkar and K. Boyer. Perceptual organization in computer vision: A review and a proposal for a classificatory structure. IEEE Transactions on Systems, Man, and Cybernetics, 23:382–399, 1993.Google Scholar
  28. 28.
    R. Shapira and H. Freeman. Computer description of bodies bounded by quadric surfaces from sets of imperfect projections. IEEE Transactions on Computers, pages 841–854, 1978.Google Scholar
  29. 29.
    K. Sugihara. Machine Interpretation of Line Drawings. MIT Press, 1986.Google Scholar
  30. 30.
    D. Thompson and J. Mundy. Three-dimensional model matching from an unconstrained viewpoint. In Proceedings of the International Conference on Robotics and Automation, Raleigh, pages 208–220, 1987.Google Scholar
  31. 31.
    Y. Tsao and K. Fu. Parallel thinning operations for digital binary images. In Proceedings of the International Conference on Computer Vision and Pattern Recognition, pages 150–155. 1981.Google Scholar
  32. 32.
    D. Waltz. Understanding line drawings of scenes with shadows. In Patrick H. Winston, editor, The Psychology of Computer Vision, pages 19–91. McGraw-Hill, 1975.Google Scholar
  33. 33.
    H. Whitney. Singularities of mappings of Euclidean spaces. I: Mappings of the plane into the plane. Ann. Math, 62:374–41, 1955.Google Scholar
  34. 34.
    M. Zerroug and R. Nevatia. Three dimensional part-based descriptions from a real intensity image. In Proceedings of the ARPA Image Understanding Workshop, pages 1367–1374. 1994.Google Scholar
  35. 35.
    A. Zisserman, D. Forsyth, J. Mundy, C. Rothwell, J. Liu, and N. Pillow. 3D object recognition using invariance. Artificial Intelligence Journal, 78:239–288, 1995.Google Scholar
  36. 36.
    A. Zisserman, J. Mundy, D. Forsyth, J. Liu, N. Pillow, C. Rothwell, and S. Utcke. Class-based grouping in perspective images. In Proceedings of the 5th Proc. International Conference on Computer Vision, pages 183–188, Boston, June 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Charlie Rothwell
    • 1
  • Joe Mundy
    • 2
  • Bill Hoffman
    • 2
  1. 1.INRIASophia Antipolis, 06902 CedexFrance
  2. 2.General Electric CRDSchenectadyUSA

Personalised recommendations