Learning Grayscale Mathematical Morphology with Smooth Morphological Layers

From LRDE

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 drawbacksand 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.

Documents

Bibtex (lrde.bib)

@Article{	  hermary.22.jmiv,
  author	= {Romain Hermary and Guillaume Tochon and \'Elodie Puybareau
		  and Alexandre Kirszenberg and Jes\'us Angulo},
  title		= {Learning Grayscale Mathematical Morphology with Smooth
		  Morphological Layers},
  journal	= {Journal of Mathematical Imaging and Vision},
  month		= apr,
  year		= {2022},
  doi		= {10.1007/s10851-022-01091-1},
  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.}
}