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Exact Linear Time Euclidean Distance Transforms of Grid Line Sampled Shapes

  • Conference paper
Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9082))

Abstract

We propose a method for computing, in linear time, the exact Euclidean distance transform of sets of points s.t. one coordinate of a point can be assigned any real value, whereas other coordinates are restricted to discrete sets of values. The proposed distance transform is applicable to objects represented by grid line sampling, and readily provides sub-pixel precise distance values. The algorithm is easy to implement; we present complete pseudo code. The method is easy to parallelize and extend to higher dimensional data. We present two ways of obtaining approximate grid line sampled representations, and evaluate the proposed EDT on synthetic examples. The method is competitive w.r.t. state-of-the-art methods for sub-pixel precise distance evaluation.

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Author information

Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Joakim Lindblad

  2. Centre for Image Analysis, Uppsala University, Uppsala, Sweden

    Nataša Sladoje

  3. Mathematical Institute, Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Nataša Sladoje

Authors
  1. Joakim Lindblad
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  2. Nataša Sladoje
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Corresponding author

Correspondence to Joakim Lindblad .

Editor information

Editors and Affiliations

  1. University of Iceland, Reykjavik, Iceland

    Jón Atli Benediktsson

  2. Université de Grenoble Alpes, Grenoble, France

    Jocelyn Chanussot

  3. ESIEE Paris, Noisy-le-Grand Cedex, France

    Laurent Najman

  4. ESIEE Paris, Noisy-le-Grand Cedex, France

    Hugues Talbot

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Lindblad, J., Sladoje, N. (2015). Exact Linear Time Euclidean Distance Transforms of Grid Line Sampled Shapes. In: Benediktsson, J., Chanussot, J., Najman, L., Talbot, H. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2015. Lecture Notes in Computer Science(), vol 9082. Springer, Cham. https://doi.org/10.1007/978-3-319-18720-4_54

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  • DOI: https://doi.org/10.1007/978-3-319-18720-4_54

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18719-8

  • Online ISBN: 978-3-319-18720-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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