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Mathematical morphology (MM) is a theory of non-linear operators used for theprocessing and analysis of images. Morphological neural networks (MNNs) areneural networks whose neurons compute morphological operators. Dilations anderosions are the elementary operators of MM. From an algebraic point of view, adilation and an erosion are operators that commute respectively with thesupremum and infimum operations. In this paper, we present the \textit{lineardilation-erosion perceptron} ($\ell$-DEP), which is given by applying lineartransformations before computing a dilation and an erosion. The decisionfunction of the $\ell$-DEP model is defined by adding a dilation and anerosion. Furthermore, training a $\ell$-DEP can be formulated as aconvex-concave optimization problem. We compare the performance of the$\ell$-DEP model with other machine learning techniques using severalclassification problems. The computational experiments support the potentialapplication of the proposed $\ell$-DEP model for binary classification tasks.

Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure