Advertisement

Open Systems & Information Dynamics

, Volume 5, Issue 1, pp 25–39 | Cite as

Curvature Measures in Visual Information Processing

  • Erhardt Barth
  • Christoph Zetzsche
  • Gerhard Krieger
Article

Abstract

The geometric concept of curvature can help to deal with some important aspects of information processing in natural and artificial vision systems. The paper briefly reviews earlier results regarding the relationship between the notions of curvature, the processing of information, and the modelling of end-stopped neurons in the visual cortex. It then focuses on the difference between Gaussian curvature and the Riemann tensor and reveals the corresponding logical structures. Furthermore, it is shown how multidimensional deviations from flatness can be measured by two-dimensional curvature operators. In the context of image-sequence analysis, a new relationship between the Riemann tensor components and the computation of the optical flow is found.

Keywords

Information Processing Visual Information Visual Cortex Optical Flow Gaussian Curvature 
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.

Bibliography

  1. 1.
    Attneave F., Psychological Review 61, 183 (1954).Google Scholar
  2. 2.
    Barlow H. B., Neural Computation 1, 295 (1989).Google Scholar
  3. 3.
    Barth E., T. Caelli, and C. Zetzsche, CVGIP: Graphical Models and Image Processing 55(6), 428 (1993).Google Scholar
  4. 4.
    Barth E., M. Ferraro, C. Zetzsche, and I. Rentschler, OSA Annual Meeting Technical Digest 16, 186 (1993).Google Scholar
  5. 5.
    Barth, E., C. Zetzsche, M. Ferraro, and I. Rentschler, Geometric Methods in Computer Vision III, ed. B. Vemuri, vol. SPIE 2031, p. 87, (1993).Google Scholar
  6. 6.
    Barth E., C. Zetzsche, and G. Krieger, Proceedings of the 4th Conference on Theoretical Physics, General Relativity and Gravitation, vol. 4–5, p. 84, Bistrita, Romania, May 1994.Google Scholar
  7. 7.
    Biedermann I., CVGIP 32, 29 (1985).Google Scholar
  8. 8.
    Do Carmo M. P., Differential Geometry of Curves and Surfaces, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1976.Google Scholar
  9. 9.
    Efimov N. W., Flächenverbiegung im großen, Akademie-Verlag, Berlin, 1957.Google Scholar
  10. 10.
    Field D. J., Neural Computation 6, 559 (1994).Google Scholar
  11. 11.
    Haralick R. M., L. T. Watson, and T. J. Laffey, Journal of Robotic Research 2(1), 50 (1983).Google Scholar
  12. 12.
    Hubel D. H. and T. N. Wiesel, J. of Neurophysiology 28, 229 (1965).Google Scholar
  13. 13.
    Johansson G., Scientific American 232, 76 (1975).Google Scholar
  14. 14.
    Klotzek B., Einführung in die Differentialgeometrie, vol. 2, VEB Deutscher Verlag der Wissenschaften, Berlin, 1983.Google Scholar
  15. 15.
    Koenderink J. J., Biol. Cybern. 50, 363 (1984).Google Scholar
  16. 16.
    Koenderink J. J., Solid shape, MIT Press, Cambridge, Massachusetts, 1990.Google Scholar
  17. 17.
    Koenderink J. J. and A. J. van Doorn, Biol. Cybern. 55, 367 (1987).Google Scholar
  18. 18.
    Krieger G. and C. Zetzsche, IEEE Trans. Image Processing 5(6), 1026 (1996).Google Scholar
  19. 19.
    Krieger G., C. Zetzsche, and E. Barth, Perception 22(Suppl.), 143 (1993).Google Scholar
  20. 20.
    Mach E., Die Analyse der Empfindungen und das Verhältnis des Physischen zum Psychischen, Fischer, 9. edition, (1992).Google Scholar
  21. 21.
    Nagel H. H., Artificial Intelligence 33, 299 (1987).Google Scholar
  22. 22.
    Orban G. A., Neuronal operations in the visual cortex, Springer, Heidelberg, 1984.Google Scholar
  23. 23.
    Parker L. and S. M. Christensen, MathTensor: a system for doing tensor analysis by computer, MathSolutions, Inc., (1992).Google Scholar
  24. 24.
    Saito H., K. Tanaka, Y. Fukada, and H. Oyamada, Journal of Neuroscience 8, 1131 (1988).Google Scholar
  25. 25.
    Schutz B., Geometrical methods of mathematical physics, Cambridge University Press, Cambridge, (1980).Google Scholar
  26. 26.
    Spivak M., A Comprehensive Introduction to Differential Geometry, vol. 1–5, Publish or Perish, Boston, MA, 1970/75.Google Scholar
  27. 27.
    Stoker J., Differential Geometry, Wiley and Sons, 1969.Google Scholar
  28. 28.
    Weinberg S., Gravitation and Cosmology, Wiley and Sons, New York, (1972).Google Scholar
  29. 29.
    Wolfram S., Mathematica: a system for doing mathematics by computer, Adison-Wesley Publishing Co., Redwood City, CA, 2 edition, (1991).Google Scholar
  30. 30.
    Yuille A. and T. Poggio, IEEE PAMI 8, 15 (1986).Google Scholar
  31. 31.
    Zetzsche C. and E. Barth, Vision Research 30, 1111 (1990).Google Scholar
  32. 32.
    Zetzsche C. and E. Barth, Human Vision and Electronic Imaging: Models, Methods, and Applications, in: B. Rogowitz ed., vol. SPIE 1249, p. 160, 1990.Google Scholar
  33. 33.
    Zetzsche C. and E. Barth, Pattern Recognition Letters 12, 771 (1991).Google Scholar
  34. 34.
    Zetzsche C., E. Barth, and J. Berkmann, Geometric Methods in Computer Vision, in B. Vemuri ed., vol. SPIE 1590, P. 337, 1991.Google Scholar
  35. 35.
    Zetzsche C., E. Barth, and B. Wegmann, Digital images and human vision, A. B. Watson ed., p. 109, MIT Press, Cambridge, MA, 1993.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Erhardt Barth
    • 1
  • Christoph Zetzsche
    • 1
  • Gerhard Krieger
    • 1
  1. 1.Institut für Medizinische PsychologieMünchenGermany

Personalised recommendations