Computational Topology in Imaging

Monday, May 28 - h 14:15 - aula Vitali (ground floor)

If one has to analyze, classify, retrieve images of mechanical pieces, vehicles, rigid objects, then geometry fulfills all needs. The scene changes if the depicted objects are of natural origin: the rigidity of geometry becomes an obstacle. Recognizing the resemblance between a sitting and a standing man is difficult. The challenge is even harder when it comes to biomedical data and when the context is essential for the understanding of data.

It's here that topology comes into play. In particular, algebraic topology offers invariants which capture qualitative aspects in a formal, computable way. Computational topology faces two main problems related to this project:

1. the computational burden might be overwhelming, so special algorithms have to be conceived;
2. if geometry is too rigid, topology is too free: it considers as equivalent some objects that common sense sees as very different; a way out is suggested by “persistence”, the study of filtered topological spaces, where the filtration conveys a more natural idea of shape.

Invited lecture:

Dr. Daniela Giorgi CNR - Istituto di Scienza e Tecnologie dell’Informazione “A. Faedo”, Pisa (Italy)

"Geometry and topology for 3D data analysis"

Introduction:

Prof. Massimo Ferri

"Topology for computer vision and pattern recognition in Bologna"

Program:

14.15 M. Ferri

14.40 D. Giorgi

16.00 Coffee break

16.20 D. Giorgi

16.50 Questions and comments