Image analysis using morse theory and homological persistence

• Grant number: 12/01002-4
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: May 01, 2012
• End date: November 30, 2012
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
• Principal Investigator: Hélio Pedrini
• Grantee: Ricardo Dutra da Silva
• Supervisor: Bernd Hamann
• Host Institution: Instituto de Computação (IC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of California, Davis (UC Davis), United States
• Associated to the scholarship: 09/10627-5 - Video Segmentation Based On Descriptors Extracted from Wavelet Transforms, BP.DR

Abstract

Even though topology has a long history of research and is the fundamental mathematics of shapes, difficulties arise when its concepts are applied to real situations. However, new researches considering topological concepts have been explored in the last decade. Among the new developments, persistent homology has effective applications on computer vision and image processing. Persistent homology allows obtaining different homological groups and importance information relative to structures as the number of connected components, holes and tunnels. The Morse complex provides a compact representation which connects the topology of an space with critical points such as maxima, minima and saddles. This work presents a new proposal based on persistent homology and Morse complex to acquire topological informations and use them for description and analysis of images and their regions. (AU)