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

EasyChair Preprint no. 5250

10 pagesDate: March 30, 2021


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 linear dilation-erosion perceptron (l-DEP), which is given by applying linear transformations before computing a dilation and an erosion. The decision function of the l-DEP model is defined by adding a dilation and an erosion. Furthermore, training an l-DEP can be formulated as a convex-concave optimization problem. We compare the performance of the l-DEP model with other machine learning techniques using several classification problems. The computational experiments support the potential application of the proposed l-DEP model for binary classification tasks.

Keyphrases: binary classification, concave-convex optimization, continuous piece-wise linear function., Dilation-Erosion Perceptron, mathematical morphology, Maxout Network, neural network

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Angélica Lourenço Oliveira and Marcos Eduardo Valle},
  title = {Linear Dilation-Erosion Perceptron Trained Using a Convex-Concave Procedure},
  howpublished = {EasyChair Preprint no. 5250},

  year = {EasyChair, 2021}}
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