  Integrating mathematical morphology operations within deep neural networks
has been subject to increasing attention lately. However, replacing standard
convolution layers with erosions or dilations is particularly challenging
because the min and max operations are not differentiable. Relying on the
asymptotic behavior of the counter-harmonic mean, p-convolutional layers were
proposed as a possible workaround to this issue since they can perform
pseudo-dilation or pseudo-erosion operations (depending on the value of their
inner parameter p), and very promising results were reported. In this work, we
present two new morphological layers based on the same principle as the
p-convolutional layer while circumventing its principal drawbacks, and
demonstrate their potential interest in further implementations within deep
convolutional neural network architectures.
