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BY 4.0 license Open Access Published by De Gruyter Open Access August 21, 2020

Approximating morphological operators with part-based representations learned by asymmetric auto-encoders

Samy Blusseau, Bastien Ponchon, Santiago Velasco-Forero, Jesús Angulo and Isabelle Bloch


This paper addresses the issue of building a part-based representation of a dataset of images. More precisely, we look for a non-negative, sparse decomposition of the images on a reduced set of atoms, in order to unveil a morphological and explainable structure of the data. Additionally, we want this decomposition to be computed online for any new sample that is not part of the initial dataset. Therefore, our solution relies on a sparse, non-negative auto-encoder, where the encoder is deep (for accuracy) and the decoder shallow (for explainability). This method compares favorably to the state-of-the-art online methods on two benchmark datasets (MNIST and Fashion MNIST) and on a hyperspectral image, according to classical evaluation measures and to a new one we introduce, based on the equivariance of the representation to morphological operators.

MSC 2010: 06-08; 15A23; 5A80; 68T07; 68T09; 68U10


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Received: 2019-11-11
Accepted: 2020-07-17
Published Online: 2020-08-21
Published in Print: 2020-01-01

© 2020 Samy Blusseau et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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