Integrating mathematical morphology operations within deep neural networks has been subject to increasing attention lately. However, replacing standard convolution layers with erosions or dilations is particularly challenging because the \(\min \) and \(\max are not differentiable. Relying on asymptotic behavior of counter-harmonic mean, p-convolutional were proposed as a possible workaround th...

Bartovský, J. Hardware Architectures for Morphological Filters with Large Structuring Elements. University Paris-Est, University of West Bohemia. Directors: Mohamed Akil, Vjačeslav Georgiev. This thesis is focused on implementation of fundamental morphological filters in the dedicated hardware. The main objective of this thesis is to provide a programmable and efficient implementation of basic ...

A mathematical morphology based approach for color image indexing is explored in this paper. Morphological signatures are powerful descriptions of the image content in the framework of mathematical morphology. A morphological signature (either a pattern spectrum or a differential morphological profile) is defined as a series of morphological operations (namely openings and closings) considering...

The aim of this paper is to propose efficient tools for analysing shape families using morphological operators. The developments include the definition of shape statistics (mean and variance of shapes, modes of shape variation) and the interpolation/extrapolation in shape geodesic paths. The main required ingredients for the operators and the algorithms here introduced are well known in mathema...

In this paper we introduce a neural network implementation of fuzzy mathematical morphology operators and apply it to image denoising. Using a supervised training method and differentiable equivalent representations for the fuzzy morphological operators, we derive efficient adaptation algorithms to optimize the structuring elements. We can then design fuzzy morphological filters for processing ...

Oriented textures are characterised by a dominant orientation at each point of the texture, and can be summarised by images encoding these dominant orientations. Because of the angular values in these images, standard morphological operators are not suited to their treatment. We discuss the application of the morphological circular centred operators to the analysis of oriented textures for the ...