Skip to main content

A Multiscale Geometric Model of Human Vision

  • Chapter
The Perception of Visual Information

Abstract

A crucial factor in human perception is that we are able to move around in the three- dimensional world we live in. This induces continuous changes in the structure of the visual world as it is projected onto the retina. Much attention has been paid to the analysis of the “pictorial mode” of perception, the analysis of the retinal images as such. Gibson was one of the pioneers in this field, studying the behavior and perception of aircraft pilots during landing manoeuvres. He coined the term “ecological optics” for the study of the natural inflow of information, in which the deformation of structure due to relative movements of objects and observer (or the observer’s eyes) is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gibson J.J. The Perception of the Visual World. Boston: Houghton Mifflin; 1952.

    Google Scholar 

  2. Kay D.C. Tensor Calculus (Schaum’s Outline Series). New York: McGraw-Hill; 1988.

    Google Scholar 

  3. Gurevich B. Foundations of the Theory of Algebraic Invariants. Groningen: Noordhof; 1979.

    Google Scholar 

  4. Spivak M. A Comprehensive Introduction to Differential Geometry (Vols. I–V). Berkeley: Publish or Perish; 1970.

    Google Scholar 

  5. Young R.A. The Gaussian derivative model for machine vision: Visual cortex simulation. J. Opt. Soc. Am. 1985; A2(13): 39, 102.

    ADS  Google Scholar 

  6. Young R.A. Simulation of human retinal function with the Gaussian derivative model. Proc. IEEE Conf. Comput. Vision Patt. Recogn. 1986; 564–569.

    Google Scholar 

  7. Kanatani K. Group-Theoretical Methods in Image Understanding (Springer Series in Information Sciences, Vol. 20). Berlin: Springer; 1990.

    Book  MATH  Google Scholar 

  8. Ter Haar Romeny B.M., Florack L.M.J., Koenderink J.J., Viergerer M.A. Scale-space: its natural operators and differential invariants. In: Colchester A.C.F., Hawkes D.J., eds. Information Processing in Medical Imaging (Lecture Notes in Computer Science, 511), Berlin: Springer; 1991: 239–255.

    Google Scholar 

  9. Florack L.M.J., Ter Haar Romeny B.M., Koenderink J.J., Viergerer M.A. Scale and the differential structure of images. Image Vis. Comput. 1992; 10: 376–388.

    Article  Google Scholar 

  10. Florack L.M.J., Ter Haar Romeny B.M., Koenderink J.J., Viergerer M.A. Linear scale-space. J. Math. Imag. Vis. 1994; 4: 325–351.

    Article  Google Scholar 

  11. Weyl H. The Classical Groups, their Invariants and Representations. Princeton: Princeton University Press; 1946.

    MATH  Google Scholar 

  12. Ter Haar Romeny B.M., Florack L.M.J., Salden A.H., Viergerer M.A. Higher order differential structure of images. Image Vis. Comput. 1994; 12: 317–325.

    Article  Google Scholar 

  13. Witkin A.P. Scale space filtering. Proc. Int. Joint Conf. Artificial Intell. (Karlsruhe) 1983; 1019–1021.

    Google Scholar 

  14. Koenderink J.J. The structure of images. Biol. Cybern. 1984; 50: 363–370.

    Article  MathSciNet  MATH  Google Scholar 

  15. Babaud J., Witkin A., Duda R. Uniqueness of the Gaussian kernel for scale space filtering. IEEE Trans. Patt. Anal. Mach. Intell. 1986; PAMI-8: 26–33.

    Google Scholar 

  16. Korn A. Toward a symbolic representation of intensity changes in images. IEEE Trans. Patt. Anal. Mach. Intell. 1988; PAMI-10: 610–625.

    Google Scholar 

  17. Koenderink J.J. Geometrical structures determined by the functional order in nervous nets. Biol. Cybern. 1984; 50: 43–50.

    Article  MathSciNet  MATH  Google Scholar 

  18. Koenderink J.J., van Doom A.J. Representation of local geometry in the visual system. Biol. Cybern. 1987; 55: 367–375.

    Article  MATH  Google Scholar 

  19. Torre V., Poggio T.A. On edge detection. IEEE Trans. Patt. Anal. Mach. Intell. 1986; PAMI-8: 147–163.

    Google Scholar 

  20. Poggio T., Torre V., Koch C. Computational vision and regularization. Nature 1985; 317: 314–319.

    Article  ADS  Google Scholar 

  21. Koenderink J.J. Image structure. In: Viergever M.A., Todd-Pokropek A., eds. Mathematics and Computer Science in Medical Imaging (NATO ASI Series F39. Berlin: Springer; 1988: 67–104.

    Chapter  Google Scholar 

  22. Hubel D.H. Eye, Brain, and Vision (Scientific American Library Series 22). San Francisco: Freeman; 1988.

    Google Scholar 

  23. Hubel D.H., Wiesel T.N. Brain mechanisms of vision. Sci. Am. 1979; 241(3): 130–146.

    Google Scholar 

  24. Koenderink J.J., van Doom A.J. Receptive field families. Biol Cybern. 1990; 63: 291–298.

    Article  MATH  Google Scholar 

  25. Florack L.M.J., Ter Haar Romeny B.M., Koenderink J.J., Viergerer M.A. Cartesian differential invariants in scale-space. J. Math Imag. Vis. 1993; 3: 327–348.

    Article  Google Scholar 

  26. Marr D., Hildrecht E.C. Theory of edge detection. Proc. R. Soc. London 1980; 200: 269–294.

    Article  Google Scholar 

  27. Clark J.J. Authenticating edges produced by zero-crossing algorithms. IEEE Trans. Path. Anal. Mach. Intell. 1989; PAMI-11: 43–57.

    Google Scholar 

  28. Lindeberg T. Scale space for discrete signals. IEEE Trans. Patt. Anal. Mach. Intell. 1990; PAMI-12: 234–245.

    Google Scholar 

  29. Canny J. A computational approach to edge detection. IEEE Trans. Patt. Anal. Mach. Intell. 1987; PAMI-8: 679–698.

    Google Scholar 

  30. De Micheli E., Caprile B., Ottonello P., Torre V. Localization and noise in edge detection. IEEE Trans. Patt. Anal. Mach. Intell. 1989; PAMI-10: 1106–1117.

    Article  Google Scholar 

  31. Koenderink J.J., van Doom A.J. A description of the structure of visual images in terms of an ordered hierarchy of light and dark blobs. In: Jaeffe S.C., ed. Proc. 2nd IEEE Int. Conf. Vis. Psychophys. Med. Imag. (Cat. 81 CH 1676-6) New York: IEEE; 1981: 173–176.

    Google Scholar 

  32. Noble J.A. Finding corners. Image Vis. Comput. 1988; 6:121–128.

    Article  Google Scholar 

  33. Koenderink J.J. Solid Shape. Cambridge: MIT; 1990.

    Google Scholar 

  34. Lifshitz L.M., Pizer S.M. A multiresolution hierarchical approach to image segmentation based on intensity extrema. IEEE Trans. Patt. Anal. Mach. Intell. 1990; PAMI-12: 529–541.

    Article  Google Scholar 

  35. Betgholm F. Edge focusing. IEEE Trans. Patt. Anal. Mach. Intell. 1987; PAMI-9: 726–741.

    Google Scholar 

  36. Bovik A.C., Clark M., Geisler W.S. Multichannel texture analysis using localized spatial filters. IEEE Trans. Patt. Anal. Mach. Intell. 1990; PAMI-12: 55–73.

    Google Scholar 

  37. Mallat S.G. A theory for multiresolution signal decomposition: The wavelet representation. IEEETrans. Patt. Anal. Mach. Intell. 1989; PAMI-11: 674–694.

    Google Scholar 

  38. Ter Haar Romeny B.M., ed. Geometry-Driven Diffusion in Computer Vision. Dordrecht: Kluwer; 1994.

    MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Romeny, B.M.T.H., Florack, L. (1997). A Multiscale Geometric Model of Human Vision. In: Hendee, W.R., Wells, P.N.T. (eds) The Perception of Visual Information. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1836-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-1836-4_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7306-6

  • Online ISBN: 978-1-4612-1836-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics