Séance Séminaire

Analyse Topologique des Données

An introduction to Discrete Morse Theory

The Discrete Morse Theory (DMT) introduced by Robin Forman in the early 2000s greatly contributed in the recent years to improve the robustness of Topological Data Analysis (TDA) algorithms, in particular for the problem of Morse-Smale complex computation in low dimensions as well as, more recently, for topology inference problems in high dimensions. In this talk, I will give an introductory tutorial on Discrete Morse theory. I will first motivate it from a computer science point of view, by discussing the limitations of the traditional piecewise linear (PL) Morse theory setting, in particular for the problem of Morse-Smale complex computation. Next, I will present the key notions illustrated with toy examples and I will discuss connections between the PL and Discrete settings. Finally, I will illustrate practical real-life applications where DMT plays a crucial role, in chemistry, biology, imaging, geometry processing and machine learning.