Going Beyond p-convolutions to Learn Grayscale Morphological Operators

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 are not differentiable. Relying on asymptotic behavior of counter-harmonic mean, p-convolutional were proposed as a possible workaround this issue since they can perform pseudo-dilation pseudo-erosion (depending value their inner parameter p), very promising results reported. In work, we present two new morphological based same principle layer while circumventing its principal drawbacks, demonstrate potential interest in further implementations convolutional network architectures.