Counting objects via Mathematical Morphology

• Grant number: 24/23600-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: May 01, 2025
• End date: April 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Benito Frazao Pires
• Grantee: Rafael Ribeiro dos Santos
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

In this research proposal, one studies the mathematics behind algorithms that count objects in images. The mathematical approach is denominated Mathematical Morphology. The proposal includes both the theoretical part (binary matrices, adjacency matrices, graphs, connected components and spectral theory of matrices) as well as the applied part (digitalization of images, representation of images as binary matrices, implementation of an algorithm in Python to count objects in images).