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Learning Grayscale Mathematical Morphology with Smooth Morphological Layers

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Abstract

The integration of mathematical morphology operations within convolutional neural network architectures has received an increasing attention lately. However, replacing standard convolution layers by morphological layers performing erosions or dilations is particularly challenging because the \(\min \) and \(\max \) operations are not differentiable. P-convolution layers were proposed as a possible solution to this issue since they can act as smooth differentiable approximation of \(\min \) and \(\max \) operations, yielding pseudo-dilation or pseudo-erosion layers. In a recent work, we proposed two novel morphological layers based on the same principle as the p-convolution, while circumventing its principal drawbacks, and showcased their capacity to efficiently learn grayscale morphological operators while raising several edge cases. In this work, we complete those previous results by thoroughly analyzing the behavior of the proposed layers and by investigating and settling the reported edge cases. We also demonstrate the compatibility of one of the proposed morphological layers with binary morphological frameworks.

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Authors and Affiliations

  1. EPITA Research and Development Laboratory (LRDE), Le Kremlin-Bicêtre, France

    Romain Hermary, Guillaume Tochon, Élodie Puybareau & Alexandre Kirszenberg

  2. Centre for Mathematical Morphology, Mines ParisTech, PSL Research University, Fontainebleau, France

    Jesús Angulo

Authors
  1. Romain Hermary
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  2. Guillaume Tochon
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  3. Élodie Puybareau
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  4. Alexandre Kirszenberg
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  5. Jesús Angulo
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Correspondence to Guillaume Tochon.

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Hermary, R., Tochon, G., Puybareau, É. et al. Learning Grayscale Mathematical Morphology with Smooth Morphological Layers. J Math Imaging Vis 64, 736–753 (2022). https://doi.org/10.1007/s10851-022-01091-1

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  • DOI: https://doi.org/10.1007/s10851-022-01091-1

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