Differential topology methods for shape description

Differential topology, and specifically Morse theory, provides a suitable setting for formalizing and solving several problems related to shape analysis. In this field, we discuss how a shape can be analyzed according to the properties of a real function defined on it (e.g., harmonic fields or Laplacian eigenfunctions), and how these properties can be stored in compact and informative descriptors. We refer to Reeb graphs, that encode the configuration of level sets and critical points of the function.