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Shape Preservation during Digitization: Tight Bounds Based on the Morphing Distance

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Pattern Recognition (DAGM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2781))

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Abstract

We define strongr-similarity and the morphing distance to bound geometric distortions between shapes of equal topology. We then derive a necessary and sufficient condition for a set and its digitizations to be r-similar, regardless of the sampling grid. We also extend these results to certain gray scale images. Our findings are steps towards a theory of shape digitization for real optical systems.

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References

  1. Köthe, U., Stelldinger, P.: Shape Preserving Digitization of Ideal and Blurred Binary Shapes, Univ. Hamburg, Informatics Dept., Tech. Rep. FBI-HH-M-325/03 (2003)

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Author information

Authors and Affiliations

  1. Cognitive Systems Group, University of Hamburg, Vogt-Köln-Str. 30, D-22527, Hamburg, Germany

    Peer Stelldinger & Ullrich Köthe

Authors
  1. Peer Stelldinger
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  2. Ullrich Köthe
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Editor information

Editors and Affiliations

  1. Otto-von-Guericke University, 39106, Magdeburg, Germany

    Bernd Michaelis

  2. Institute for Electronics, Signal Processing and Communications (IESK), Otto-von-Guericke-University Magdeburg, P.O. Box 4120, D-39016, Magdeburg, Germany

    Gerald Krell

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© 2003 Springer-Verlag Berlin Heidelberg

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Stelldinger, P., Köthe, U. (2003). Shape Preservation during Digitization: Tight Bounds Based on the Morphing Distance. In: Michaelis, B., Krell, G. (eds) Pattern Recognition. DAGM 2003. Lecture Notes in Computer Science, vol 2781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45243-0_15

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  • DOI: https://doi.org/10.1007/978-3-540-45243-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40861-1

  • Online ISBN: 978-3-540-45243-0

  • eBook Packages: Springer Book Archive

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