A Learning Framework for Morphological Operators using Counter-Harmonic   Mean
  We present a novel framework for learning morphological operators using counter-harmonic mean. It combines concepts from morphology and convolutional neural networks. A thorough experimental validation analyzes basic morphological operators dilation and erosion, opening and closing, as well as the much more complex top-hat transform, for which we report a real-world application from the steel industry. Using online learning and stochastic gradient descent, our system learns both the structuring element and the composition of operators. It scales well to large datasets and online settings. 
Jonathan Masci and Jes\'us Angulo and J\"urgen Schmidhuber
cs.CV