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

TL;DR

This paper introduces a novel morphological neural network model called the linear dilation-erosion perceptron (ℓ-DEP), trained via a convex-concave procedure, demonstrating promising results in binary classification tasks.

Contribution

The paper proposes the ℓ-DEP model that combines linear transformations with morphological operators and formulates its training as a convex-concave optimization problem.

Findings

Supports binary classification with promising performance

Outperforms some existing machine learning techniques

Effective for various classification problems

Abstract

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