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A Novel Approach for Computation of Morphological Operations Using the Number Theoretic Transform

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Discrete Geometry and Mathematical Morphology (DGMM 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13493))

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Abstract

The fundamental operations of mathematical morphology are dilation and erosion. They are often implemented using a sliding window with the purpose to compute maximum respectively minimum of pixel values within the corresponding mask.

We reformulate the problem of morphological dilation respectively erosion of an image with a non-flat filter as a convolution of their umbras. To this end, we propose to make use of the number theoretic transform to compute the convolution in this setting. In contrast to other possible schemes, this transform represents a completely discrete computational approach. It allows exact convolution of sequences made up of integers. Therefore we propose by the combination of umbra framework and number theoretic transform a well-engineered combination.

There is no restriction on size or shape of the structuring element, and also flat and non-flat filters can be realised.

The current work was supported by the European Regional Development Fund (EFRE 85037495). Furthermore, the authors acknowledge the support by BTU Graduate Research School (STIBET short-term scholarship for international PhD Students sponsored by the German Academic Exchange Service (DAAD) with funds of the German Federal Foreign Office).

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Acknowledgements

The current work was supported by the European Regional Development Fund (EFRE 85037495). Furthermore, the authors acknowledge the support by BTU Graduate Research School (STIBET short-term scholarship for international PhD Students sponsored by the German Academic Exchange Service (DAAD) with funds of the German Federal Foreign Office).

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Authors and Affiliations

  1. Institute for Mathematics, Brandenburg Technical University, Platz der Deutschen Einheit 1, 03046, Cottbus, Germany

    Vivek Sridhar & Michael Breuß

Authors
  1. Vivek Sridhar
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  2. Michael Breuß
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Correspondence to Vivek Sridhar .

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Editors and Affiliations

  1. University of Strasbourg, Strasbourg, France

    Étienne Baudrier

  2. University of Strasbourg, Strasbourg, France

    Benoît Naegel

  3. University of Strasbourg, Strasbourg, France

    Adrien Krähenbühl

  4. University of Strasbourg, Strasbourg, France

    Mohamed Tajine

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Sridhar, V., Breuß, M. (2022). A Novel Approach for Computation of Morphological Operations Using the Number Theoretic Transform. In: Baudrier, É., Naegel, B., Krähenbühl, A., Tajine, M. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2022. Lecture Notes in Computer Science, vol 13493. Springer, Cham. https://doi.org/10.1007/978-3-031-19897-7_15

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  • DOI: https://doi.org/10.1007/978-3-031-19897-7_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-19896-0

  • Online ISBN: 978-3-031-19897-7

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