Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
Book cover

Joint IAPR International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (SSPR)

SSPR /SPR 2012: Structural, Syntactic, and Statistical Pattern Recognition pp 162–170Cite as

  1. Home
  2. Structural, Syntactic, and Statistical Pattern Recognition
  3. Conference paper
Laplacian Eigenimages in Discrete Scale Space

Laplacian Eigenimages in Discrete Scale Space

  • Martin Tschirsich24 &
  • Arjan Kuijper24,25 
  • Conference paper
  • 2385 Accesses

  • 2 Citations

Part of the Lecture Notes in Computer Science book series (LNIP,volume 7626)

Abstract

Linear or Gaussian scale space is a well known multi-scale representation for continuous signals. However, implementational issues arise, caused by discretization and quantization errors. In order to develop more robust scale space based algorithms, the discrete nature of computer processed signals has to be taken into account. Aiming at a computationally practicable implementation of the discrete scale space framework we used suitable neighborhoods, boundary conditions and sampling methods. In analogy to prevalent approaches, a discretized diffusion equation is derived from the continuous scale space axioms adapted to discrete two-dimensional images or signals, including requirements imposed by the chosen neighborhood and boundary condition. The resulting discrete scale space respects important topological invariants such as the Euler number, a key criterion for the successful implementation of algorithms operating on its deep structure. In this paper, relevant and promising properties of the discrete diffusion equation and the eigenvalue decomposition of its Laplacian kernel are discussed and a fast and robust sampling method is proposed. One of the properties leads to Laplacian eigenimages in scale space: Taking a reduced set of images can be considered as a way of applying a discrete Gaussian scale space.

Keywords

  • Diffusion Equation
  • Heat Kernel
  • Scale Space
  • Laplacian Matrix
  • Euler Number

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.

Download conference paper PDF

References

  1. Viola, P., Jones, M.: Robust real-time object detection. IJCV (2001)

    Google Scholar 

  2. Kuijper, A.: Exploring and exploiting the structure of saddle points in gaussian scale space. Computer Vision and Image Understanding 112(3), 337–349 (2008)

    CrossRef  Google Scholar 

  3. Lindeberg, T.: Discrete Scale-Space Theory and the Scale-Space Primal Sketch. PhD thesis, Royal Institute of Technology (1991)

    Google Scholar 

  4. Kuijper, A.: On detecting all saddle points in 2D images. Pattern Recognition Letters 25(15), 1665–1672 (2004)

    CrossRef  Google Scholar 

  5. Kuijper, A., Florack, L.M.J.: Understanding and Modeling the Evolution of Critical Points under Gaussian Blurring. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part I. LNCS, vol. 2350, pp. 143–157. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  6. Kuijper, A., Florack, L.M.J.: The Relevance of Non-generic Events in Scale Space Models. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002, Part I. LNCS, vol. 2350, pp. 190–204. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  7. Tschirsich, M., Kuijper, A.: A Discrete Scale Space Neighborhood for Robust Deep Structure Extraction. In: S+SSPR 2012, vol. 7626, pp. 124–132. Springer, Heidelberg (2012)

    Google Scholar 

  8. Witkin, A.P.: Scale-space filtering. In: Proc. 8th Int. Joint Conf. Art. Intell., pp. 1019–1022. Karlsruhe, Germany (August 1983)

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Weickert, J., Ishikawa, S., Imiya, A.: Scale-space has been discovered in Japan. Technical report, Department of Computer Science, University of Copenhagen (August 1997)

    Google Scholar 

  11. Iijima, T.: Basic theory on normalization of a pattern (in case of typical one-dimensional pattern). Bulletin of Electrical Laboratory, 368–388 (1962)

    Google Scholar 

  12. Tschirsich, M.: The discrete scale space as a base for robust scale space algorithms. Technical report, Department of Computer Science, Technical University of Darmstadt (June 2012)

    Google Scholar 

  13. Hancock, E.R., Wilson, R.C.: Pattern analysis with graphs: Parallel work at Bern and York. Pattern Recognition Letters 33(7), 833–841 (2012)

    CrossRef  Google Scholar 

  14. Xiao, B., Hancock, E.R., Wilson, R.C.: Geometric characterization and clustering of graphs using heat kernel embeddings. Image Vision Comput. 28(6), 1003–1021 (2010)

    CrossRef  MATH  Google Scholar 

  15. Xiao, B., Hancock, E.R., Wilson, R.C.: Graph characteristics from the heat kernel trace. Pattern Recognition 42(11), 2589–2606 (2009)

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Darmstadt, Germany

    Martin Tschirsich & Arjan Kuijper

  2. Fraunhofer IGD, Darmstadt, Germany

    Arjan Kuijper

Authors
  1. Martin Tschirsich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arjan Kuijper
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Auckland, Private Bag 92019, 1142, Auckland, New Zealand

    Georgy Gimel’farb

  2. Department of Computer Science, University of York, Deramore Lane, YO10 5GH, York, UK

    Edwin Hancock

  3. Institute of Media and Information Technology, Chiba University, Yayoi-cho 1-33, 263-8522, Inage-ku, Chiba, Japan

    Atsushi Imiya

  4. Technische Universität/Fraunhofer IGD, Fraunhoferstraße 5, 64283, Darmstadt, Germany

    Arjan Kuijper

  5. Graduate School of Information Science and Technology, Hokkaido University, 060-0814, Sapporo, Japan

    Mineichi Kudo

  6. Graduate School of Engineering, Tohoku University, 6-6-05 Aoba, Aramaki, Aoba-ku, 980-8579, Sendai, Miyagi, Japan

    Shinichiro Omachi

  7. Centre for Vision, Speech and Signal Processing, University of Surrey, GU2 7XH, Guildford, Surrey, UK

    Terry Windeatt

  8. C&C Innovation Research Laboratories, NEC Corporation, 8916-47 Takayama-cho, Ikoma-Shi, Nara, Japan

    Keiji Yamada

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tschirsich, M., Kuijper, A. (2012). Laplacian Eigenimages in Discrete Scale Space. In: Gimel’farb, G., et al. Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2012. Lecture Notes in Computer Science, vol 7626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34166-3_18

Download citation

  • .RIS
  • .ENW
  • .BIB
  • DOI: https://doi.org/10.1007/978-3-642-34166-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34165-6

  • Online ISBN: 978-3-642-34166-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • The International Association for Pattern Recognition

    Published in cooperation with

    http://www.iapr.org/

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature