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Line Voronoi Diagrams Using Elliptical Distances

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Structural, Syntactic, and Statistical Pattern Recognition (S+SSPR 2018)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11004))

Abstract

The paper introduces an Elliptical Line Voronoi diagram. In contrast to the classical approaches, it represents the line segment by its end points, and computes the distance from point to line segment using the Confocal Ellipse-based Distance. The proposed representation offers specific mathematical properties, prioritizes the sites of the greater length and corners with the obtuse angles without using an additional weighting scheme. The above characteristics are suitable for the practical applications such as skeletonization and shape smoothing.

A. Gabdulkhakova—Supported by the Austrian Agency for International Cooperation in Education and Research (OeAD) within the OeAD Sonderstipendien program, and by the Faculty of Informatics.

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Notes

  1. 1.

    If for several ellipses the focal points are the same, we denote it as E(a).

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Authors and Affiliations

  1. Pattern Recognition and Image Processing Group, 193-03 Institute of Visual Computing and Human-Centered Technology, Technische Universität Wien, Favoritenstrasse 9-11, Vienna, Austria

    Aysylu Gabdulkhakova, Maximilian Langer, Bernhard W. Langer & Walter G. Kropatsch

Authors
  1. Aysylu Gabdulkhakova
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  2. Maximilian Langer
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  3. Bernhard W. Langer
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  4. Walter G. Kropatsch
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Corresponding author

Correspondence to Aysylu Gabdulkhakova .

Editor information

Editors and Affiliations

  1. Beihang University, Beijing, China

    Xiao Bai

  2. University of York, York, United Kingdom

    Edwin R. Hancock

  3. IBM Research – Thomas J. Watson Research, Yorktown Heights, New York, USA

    Tin Kam Ho

  4. University of York, Heslington, York, United Kingdom

    Richard C. Wilson

  5. University of Cagliari, Cagliari, Italy

    Battista Biggio

  6. Data 61 - CSIRO, Canberra, Aust Capital Terr, Australia

    Antonio Robles-Kelly

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Gabdulkhakova, A., Langer, M., Langer, B.W., Kropatsch, W.G. (2018). Line Voronoi Diagrams Using Elliptical Distances. In: Bai, X., Hancock, E., Ho, T., Wilson, R., Biggio, B., Robles-Kelly, A. (eds) Structural, Syntactic, and Statistical Pattern Recognition. S+SSPR 2018. Lecture Notes in Computer Science(), vol 11004. Springer, Cham. https://doi.org/10.1007/978-3-319-97785-0_25

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  • DOI: https://doi.org/10.1007/978-3-319-97785-0_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-97784-3

  • Online ISBN: 978-3-319-97785-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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