Mapping representations between different domains and subspaces using geometric deep learning

• Grant number: 20/16475-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2021
• End date: July 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
• Principal Investigator: Moacir Antonelli Ponti
• Grantee: Matheus da Silva Araujo
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision, AP.TEM

Abstract

In computer vision, the mapping between data on distinct domains remains as an open problem. For example, it's a challenge to recognize the identity of a person in different representations, such as photos, hand-drawn sketches and 3D scanned models. Most methods don't explore the non-Euclidean geometry of manifolds, which models curves and surfaces such as the human face. A geometric approach for this task would allow to extract relevant information from both domains. This project aims to investigate methods to learn geometric characteristics of manifolds, and use these characteristics to map data between distinct domains. Methods of geometric deep learning and representation learning will be considered, exploring the ability of geometric characteristics to map data between distinct domains, particularly on two- and three-dimensional spaces.