Skip to main content

Differential Geometry of Monogenic Signal Representations

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4931))

Abstract

This paper presents the fusion of monogenic signal processing and differential geometry to enable monogenic analyzing of local intrinsic 2D features of low level image data. New rotational invariant features such as structure and geometry (angle of intersection) of two superimposed intrinsic 1D signals will be extracted without the need of any steerable filters. These features are important for all kinds of low level image matching tasks in robot vision because they are invariant against local and global illumination changes and result from one unique framework within the monogenic scale-space.

We acknowledge funding by the German Research Foundation (DFG) under the projects SO 320/4-2 and We 2602/5-1.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baer, C.: Elementare Differentialgeometrie, de Gruyter, Berlin, New York, vol. 1 (2001)

    Google Scholar 

  2. Beyerer, J., Leon, F.P.: The Radon transform in digital image processing, Oldenbourg, vol 50, part 10, pp. 472–480, Automatisierungstechnik, Germany (2002)

    Google Scholar 

  3. Felsberg, M., Sommer, G.: The monogenic signal. IEEE Transactions on Signal Processing 49(12), 3136–3144 (2001)

    Article  MathSciNet  Google Scholar 

  4. Michael Felsberg, Low-Level Image Processing with the Structure Multivector, PhD Thesis, Kiel University (2002)

    Google Scholar 

  5. Felsberg, M., Sommer, G.: The monogenic scale-space: A unifying approach to phase-based image processing in scale-space, vol. 21, pp. 5–26. Kluwer Academic Publishers, Dordrecht (2004)

    Google Scholar 

  6. Stefan, L.: Hahn, Hilbert Transforms in Signal Processing, Artech House, Norwood, Maryland (1996)

    Google Scholar 

  7. Porteous, I.R.: Clifford Algebras and the Classical Groups, Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  8. Sobczyk, G., Erlebacher, G.: Hybrid matrix geometric algebra. In: Li, H., J. Olver, P., Sommer, G. (eds.) IWMM-GIAE 2004. LNCS, vol. 3519, pp. 191–206. Springer, Heidelberg (2005)

    Google Scholar 

  9. Stein, E.M.: Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series. Princeton University Press, Princeton (1970)

    Google Scholar 

  10. Stuke, I., et al.: Analysing superimposed oriented patterns. In: 6th IEEE Southwest Symposium on Image Analysis and Interpretation, Lake Tahoe, NV, pp. 133–137 (2004)

    Google Scholar 

  11. Toft, P.: The Radon Transform - Theory and Implementation, PhD Thesis, Department of Mathematical Modelling, Technical University of Denmark (1996)

    Google Scholar 

  12. Zang, D., Sommer, G.: Signal modeling for two-dimensional image structures. Journal of Visual Communication and Image Representation 18(1), 81–99 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gerald Sommer Reinhard Klette

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wietzke, L., Sommer, G., Schmaltz, C., Weickert, J. (2008). Differential Geometry of Monogenic Signal Representations. In: Sommer, G., Klette, R. (eds) Robot Vision. RobVis 2008. Lecture Notes in Computer Science, vol 4931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78157-8_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78157-8_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78156-1

  • Online ISBN: 978-3-540-78157-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics