On Some Associations Between Mathematical Morphology and Artificial Intelligence

From LRDE

Abstract

This paper aims at providing an overview of the use of mathematical morphology, in its algebraic setting, in several fields of artificial intelligence (AI). Three domains of AI will be covered. In the first domainmathematical morphology operators will be expressed in some logics (propositional, modal, description logics) to answer typical questions in knowledge representation and reasoning, such as revision, fusion, explanatory relations, satisfying usual postulates. In the second domain, spatial reasoning will benefit from spatial relations modeled using fuzzy sets and morphological operators, with applications in model-based image understanding. In the third domain, interactions between mathematical morphology and deep learning will be detailed. Morphological neural networks were introduced as an alternative to classical architectures, yielding a new geometry in decision surfaces. Deep networks were also trained to learn morphological operators and pipelinesand morphological algorithms were used as companion tools to machine learning, for pre/post processing or even regularization purposes. These ideas have known a large resurgence in the last few years and new ones are emerging.


Bibtex (lrde.bib)

@InProceedings{	  bloch.21.dgmm,
  doi		= {10.1007/978-3-030-76657-3_33},
  author	= {Isabelle Bloch and Samy Blusseau and Ram\'on {Pino
		  P\'erez} and \'Elodie Puybareau and Guillaume Tochon},
  editor	= {Lindblad, Joakim and Malmberg, Filip and Sladoje,
		  Nata{\v{s}}a},
  title		= {On Some Associations Between Mathematical Morphology and
		  Artificial Intelligence},
  booktitle	= {Discrete Geometry and Mathematical Morphology},
  year		= {2021},
  address	= {Uppsala, Sweden},
  publisher	= {Springer},
  pages		= {457--469},
  month		= may,
  abstract	= {This paper aims at providing an overview of the use of
		  mathematical morphology, in its algebraic setting, in
		  several fields of artificial intelligence (AI). Three
		  domains of AI will be covered. In the first domain,
		  mathematical morphology operators will be expressed in some
		  logics (propositional, modal, description logics) to answer
		  typical questions in knowledge representation and
		  reasoning, such as revision, fusion, explanatory relations,
		  satisfying usual postulates. In the second domain, spatial
		  reasoning will benefit from spatial relations modeled using
		  fuzzy sets and morphological operators, with applications
		  in model-based image understanding. In the third domain,
		  interactions between mathematical morphology and deep
		  learning will be detailed. Morphological neural networks
		  were introduced as an alternative to classical
		  architectures, yielding a new geometry in decision
		  surfaces. Deep networks were also trained to learn
		  morphological operators and pipelines, and morphological
		  algorithms were used as companion tools to machine
		  learning, for pre/post processing or even regularization
		  purposes. These ideas have known a large resurgence in the
		  last few years and new ones are emerging.}
}