Morphological Perceptrons: Geometry and Training Algorithms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10225)


Neural networks have traditionally relied on mostly linear models, such as the multiply-accumulate architecture of a linear perceptron that remains the dominant paradigm of neuronal computation. However, from a biological standpoint, neuron activity may as well involve inherently nonlinear and competitive operations. Mathematical morphology and minimax algebra provide the necessary background in the study of neural networks made up from these kinds of nonlinear units. This paper deals with such a model, called the morphological perceptron. We study some of its geometrical properties and introduce a training algorithm for binary classification. We point out the relationship between morphological classifiers and the recent field of tropical geometry, which enables us to obtain a precise bound on the number of linear regions of the maxout unit, a popular choice for deep neural networks introduced recently. Finally, we present some relevant numerical results.


Mathematical morphology Neural networks Machine learning Tropical geometry Optimization 



This work was partially supported by the European Union under the projects BabyRobot with grant H2020-687831 and I-SUPPORT with grant H2020-643666.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of ECENational Technical University of AthensAthensGreece

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