  This paper analyses both nonlinear activation functions and spatial
max-pooling for Deep Convolutional Neural Networks (DCNNs) by means of the
algebraic basis of mathematical morphology. Additionally, a general family of
activation functions is proposed by considering both max-pooling and nonlinear
operators in the context of morphological representations. Experimental section
validates the goodness of our approach on classical benchmarks for supervised
learning by DCNN.
