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

• 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
• 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)