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International Workshop on Combinatorial Image Analysis

IWCIA 2012: Combinatorial Image Analaysis pp 249–262Cite as

Novel Morphological Algorithms for Dominating Sets on Graphs with Applications to Image Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7655))

Abstract

In this paper, we extend the morphological operators defined for graphs by Cousty et al. to use structuring elements. We then apply these extended operators to develop algorithms for Minimum Dominating Set (MDS) and Minimum Independent Dominating Set (MIDS) on incomplete grid graphs which correspond to binary images with 4-connected neighbourhoods. We show that our algorithm performs as well as the best known heuristic for Minimum Independent Dominating Set. We apply the extended morphological graph operators and algorithms to various image analysis tasks such as distance transforms, skeletons and clustering. In particular, we propose a novel MIDS Skeleton that may potentially reduce the time for reconstructing the original objects. A hierarchical clustering algorithm (also using MIDS) is proposed. This algorithm is analogous to the conventional algorithms that use a distance threshold for clustering. We illustrate the proposed algorithms on several example images and conclude that they are useful in image analysis.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Sciences, University of Hyderabad, Hyderabad, India

    Anupama Potluri & Chakravarthy Bhagvati

Authors
  1. Anupama Potluri
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  2. Chakravarthy Bhagvati
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Editor information

Editors and Affiliations

  1. Department of Computer and Information Sciences, State University of New York at Fredonia, 280 Central Ave, 14063, Fredonia, NY, USA

    Reneta P. Barneva

  2. Mathematics Department, SUNY Buffalo State College, 1300Elmwood Ave, 14222, Buffalo, NY, USA

    Valentin E. Brimkov

  3. Department of Electrical and Computer Engineering, University of Texas at Austin, 1 University Station C0803, 78712-0240 TX, Austin, USA

    Jake K. Aggarwal

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© 2012 Springer-Verlag Berlin Heidelberg

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Potluri, A., Bhagvati, C. (2012). Novel Morphological Algorithms for Dominating Sets on Graphs with Applications to Image Analysis. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds) Combinatorial Image Analaysis. IWCIA 2012. Lecture Notes in Computer Science, vol 7655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34732-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-34732-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34731-3

  • Online ISBN: 978-3-642-34732-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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