| Grant number: | 23/03368-0 |
| Support Opportunities: | Regular Research Grants |
| Start date: | February 01, 2024 |
| End date: | January 31, 2028 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Applied Mathematics |
| Agreement: | 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 |
| City of the host institution: | Campinas |
| 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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