Multi-scale representation and persistency for shape description

Extraction, organization and exploitation of topological features are emerging topics in computer vision and graphics. However, such kind of features often exhibits weak robustness with respect to small perturbations and it is often unclear how to distinguish truly topological features from topological noise. In this paper, we present an introduction to persistence theory, which aims at analyzing multi-scale representations from a topological point of view. Besides, we extend the ideas of persistency to a more general setting by defining a set of discrete invariants.