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Computing the Component-Labeling and the Adjacency Tree of a Binary Digital Image in Near Logarithmic-Time

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Computational Topology in Image Context (CTIC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11382))

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Abstract

Connected component labeling (CCL) of binary images is one of the fundamental operations in real time applications. The adjacency tree (AdjT) of the connected components offers a region-based representation where each node represents a region which is surrounded by another region of the opposite color. In this paper, a fully parallel algorithm for computing the CCL and AdjT of a binary digital image is described and implemented, without the need of using any geometric information. The time complexity order for an image of \(m \times n\) pixels under the assumption that a processing element exists for each pixel is near \(O(log(m+n))\). Results for a multicore processor show a very good scalability until the so-called memory bandwidth bottleneck is reached. The inherent parallelism of our approach points to the direction that even better results will be obtained in other less classical computing architectures.

This work has been supported by the Spanish research projects MTM2016-81030-P (AEI/FEDER, UE) and TEC2012-37868-C04-02 of Ministerio de Economía y Competitividad and the VPPI of the University of Seville.

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Author information

Authors and Affiliations

  1. Department of Computer Architecture and Technology, University of Seville, Seville, Spain

    Fernando Díaz del Río

  2. Department of Applied Mathematics, University of Seville, Seville, Spain

    Helena Molina-Abril & Pedro Real

Authors
  1. Fernando Díaz del Río
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  2. Helena Molina-Abril
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  3. Pedro Real
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Corresponding author

Correspondence to Helena Molina-Abril .

Editor information

Editors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    Rebeca Marfil

  2. Universidad de Málaga, Málaga, Spain

    Mariletty Calderón

  3. University of Seville, Sevilla, Spain

    Fernando Díaz del Río

  4. University of Seville, Sevilla, Spain

    Pedro Real

  5. Universidad de Málaga, Málaga, Spain

    Antonio Bandera

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Díaz del Río, F., Molina-Abril, H., Real, P. (2019). Computing the Component-Labeling and the Adjacency Tree of a Binary Digital Image in Near Logarithmic-Time. In: Marfil, R., Calderón, M., Díaz del Río, F., Real, P., Bandera, A. (eds) Computational Topology in Image Context. CTIC 2019. Lecture Notes in Computer Science(), vol 11382. Springer, Cham. https://doi.org/10.1007/978-3-030-10828-1_7

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  • DOI: https://doi.org/10.1007/978-3-030-10828-1_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10827-4

  • Online ISBN: 978-3-030-10828-1

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