Improving Morphological Networks for Learning Image-to-Image Transforms

Antoine Bottenmuller, Guillaume Tochon, Romain Hermary, Elodie Puybareau, Jesus Angulo

Abstract: Replacing convolution with morphological operations in trainable layers has received significant attention lately. Among the various strategies that have emerged, smooth morphological layers have shown strong potential and flexibility, as a single layer can behave either like a (pseudo-)erosion or a (pseudo-)dilation depending on the sign and value of its trainable control parameter. In this work, we build upon the so-called SMorph layer by introducing a harmonized formulation that addresses previously identified asymptotic limitations when learning grayscale erosion and dilation. We also investigate and compare two strategies (a novel penalty term in the training loss and shared-weight layers) to improve the learning of grayscale opening and closing operations in two-layer networks. Finally, we evaluate the performance of this improved SMorph layer on a salt-and-pepper denoising task in a four-layer network architecture, and compare it with other morphological and convolutional networks.