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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 126–134Cite as

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A Discrete Scale Space Neighborhood for Robust Deep Structure Extraction

A Discrete Scale Space Neighborhood for Robust Deep Structure Extraction

  • Martin Tschirsich24 &
  • Arjan Kuijper24,25 
  • Conference paper
  • 2388 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. The exploration of its so-called deep structure by tracing critical points over scale has various theoretical applications and allows for the construction of a scale space hierarchy tree. 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 investigated suitable neighborhoods, boundary conditions and sampling methods. We show that 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. We discuss promising properties of topological graphs under the influence of smoothing, setting the stage for more robust deep structure extraction algorithms.

Keywords

  • Deep Structure
  • Scale Space
  • Euler Number
  • Topological Graph
  • Discrete Signal

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.

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References

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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
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  2. Arjan Kuijper
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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

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© 2012 Springer-Verlag Berlin Heidelberg

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Cite this paper

Tschirsich, M., Kuijper, A. (2012). A Discrete Scale Space Neighborhood for Robust Deep Structure Extraction. 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_14

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  • DOI: https://doi.org/10.1007/978-3-642-34166-3_14

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  • Print ISBN: 978-3-642-34165-6

  • Online ISBN: 978-3-642-34166-3

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