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DeepOrder: Deep Ordering for Vector-Valued Mathematical Morphology and Neural Networks

Grant number: 23/03368-0
Support Opportunities:Regular Research Grants
Duration: February 01, 2024 - January 31, 2028
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Convênio/Acordo: ANR
Principal Investigator:Marcos Eduardo Ribeiro Do Valle Mesquita
Grantee:Marcos Eduardo Ribeiro Do Valle Mesquita
Principal researcher abroad: Santiago Velasco-Forero
Institution abroad: ParisTech, France
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated researchers:Joao Batista Florindo ; Peter Sussner

Abstract

Deep learning techniques achieved outstanding performance in various image processing and analysis tasks. Deep networks for vector-valued images represent an active research topic and include, for example, hypercomplex-valued neural networks. The nonlinearity played by some layers and activation functions in modern deep neural networks is closely related to mathematical morphology, a theory of image operators based on topological and geometrical. This research project aims to develop a mathematical framework encompassing mathematical morphology, hypercomplex algebras, and deep learning. As a result, we expect to devise powerful and robust machine-learning techniques for vector-valued image processing, taking into account topologic and geometric concepts. (AU)

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