Skip to main content
SpringerLink
Log in

GET: The Connection Between Monogenic Scale-Space and Gaussian Derivatives

  • Conference paper
Scale Space and PDE Methods in Computer Vision (Scale-Space 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3459))

Included in the following conference series:

Abstract

In this paper we propose a new operator which combines advantages of monogenic scale-space and Gaussian scale-space, of the monogenic signal and the structure tensor. The gradient energy tensor (GET) defined in this paper is based on Gaussian derivatives up to third order using different scales. These filters are commonly available, separable, and have an optimal uncertainty. The response of this new operator can be used like the monogenic signal to estimate the local amplitude, the local phase, and the local orientation of an image, but it also allows to measure the coherence of image regions as in the case of the structure tensor. Both theoretically and in experiments the new approach compares favourably with existing methods.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Felsberg, M., Sommer, G.: The monogenic scale-space: A unifying approach to phase-based image processing in scale-space. JMIV 21, 5–26 (2004)

    Article  MathSciNet  Google Scholar 

  2. Koenderink, J.J.: The structure of images. Biol. Cybernetics 50, 363–370 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  3. Mechler, F., Reich, D.S., Victor, J.D.: Detection and discrimination of relative spatial phase by V1 neurons. Journal of Neuroscience 22, 6129–6157 (2002)

    Google Scholar 

  4. Oppenheim, A., Lim, J.: The importance of phase in signals. Proc. of the IEEE 69, 529–541 (1981)

    Article  Google Scholar 

  5. Hurt, N.E.: Phase Retrieval and Zero Crossings. Kluwer Academic, Dordrecht (1989)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Krieger, G., Zetzsche, C.: Nonlinear image operators for the evaluation of local intrinsic dimensionality. IEEE Trans. on Image Processing 5, 1026–1041 (1996)

    Article  Google Scholar 

  8. Granlund, G.H., Knutsson, H.: Signal Processing for Computer Vision. Kluwer Academic Publishers, Dordrecht (1995)

    Google Scholar 

  9. Felsberg, M.: On the design of two-dimensional polar separable filters. In: 12th European Signal Processing Conference, Vienna, Austria (2004)

    Google Scholar 

  10. Felsberg, M.: Low-Level Image Processing with the Structure Multivector. PhD thesis, Christian-Albrechts-University of Kiel, TR no. 0203 (2002)

    Google Scholar 

  11. Felsberg, M., Duits, R., Florack, L.: The monogenic scale space on a rectangular domain and its features. IJCV (2004); accepted publ. in future issue

    Google Scholar 

  12. Maragos, P., Bovik, A.C., Quartieri, J.F.: A multi-dimensional energy operator for image processing. In: SPIE Conference on Visual Communications and Image Processing, Boston, MA, pp. 177–186 (1992)

    Google Scholar 

  13. Felsberg, M., Granlund, G.: POI detection using channel clustering and the 2D energy tensor. In: Rasmussen, C.E., Bülthoff, H.H., Schölkopf, B., Giese, M.A. (eds.) DAGM 2004. LNCS, vol. 3175, pp. 103–110. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. Förstner, W., Gülch, E.: A fast operator for detection and precise location of distinct points, corners and centres of circular features. In: ISPRS Intercommission Workshop, Interlaken, pp. 149–155 (1987)

    Google Scholar 

  15. Bigün, J., Granlund, G.H.: Optimal orientation detection of linear symmetry. In: Proc. IEEE First International Conference on Computer Vision, pp. 433–438 (1987)

    Google Scholar 

  16. Nordberg, K.: Signal Representation and Processing using Operator Groups. PhD thesis, Linköping University (1995), Dissertation No 366, ISBN 91-7871-476-1

    Google Scholar 

  17. Bigün, J., Granlund, G.H., Wiklund, J.: Multidimensional orientation estimation with applications to texture analysis and optical flow. PAMI 13, 775–790 (1991)

    Google Scholar 

  18. Larkin, K.G., Oldfield, M.A., Bone, D.J.: Demodulation and phase estimation of two-dimensional patterns. Australian patent AU 200110005 A1 (2001)

    Google Scholar 

  19. Jähne, B.: Digitale Bildverarbeitung. Springer, Berlin (1997)

    Google Scholar 

  20. Harris, C.G., Stephens, M.: A combined corner and edge detector. In: 4th Alvey Vision Conference, pp. 147–151 (1988)

    Google Scholar 

  21. Florack, L., Duits, R.: Regularity classes for locally orderless images. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 255–265. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  22. Köthe, U., Felsberg, M.: Riesz-transforms vs. derivatives: on the relationship between the boundary tensor and the energy tensor. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 179–191. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. Knutsson, H., Andersson, M.: Robust N-dimensional orientation estimation using quadrature filters and tensor whitening. In: Proceedings of IEEE International Conference on Acoustics, Speech, & Signal Processing, Adelaide, Australia (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Vision Laboratory, Linköping University, SE-58183, Linköping, Sweden

    Michael Felsberg

  2. Cognitive Systems Group, University of Hamburg, D-22527, Hamburg, Germany

    Ullrich Köthe

Authors
  1. Michael Felsberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ullrich Köthe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Ron Kimmel

  2. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Nir A. Sochen

  3. Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Building E1.1, 66041, Saarbrücken, Germany

    Joachim Weickert

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Felsberg, M., Köthe, U. (2005). GET: The Connection Between Monogenic Scale-Space and Gaussian Derivatives. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds) Scale Space and PDE Methods in Computer Vision. Scale-Space 2005. Lecture Notes in Computer Science, vol 3459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408031_17

Download citation

  • DOI: https://doi.org/10.1007/11408031_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25547-5

  • Online ISBN: 978-3-540-32012-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation