Reeb graphs for Shape Analysis and Synthesis
by
Silvia Biasotti
CNR - IMATI - GE
Coauthors: Daniela Giorgi, Michela Spagnuolo and Bianca Falcidieno

Reeb graphs are compact shape descriptions that convey topological information by analysing the evolution of the level sets of a function defined on the shape.

Their definition dates back to 1946, and finds its root in Morse theory. Reeb graphs have been proposed as shape descriptors to solve different problems arising in Computer Graphics, and nowadays they play a fundamental role in the field of computational topology for shape analysis.

This talk provides an overview of the mathematical properties of Reeb graphs and reconstructs their history in the Computer Graphics context. We will also discuss the enrichment of the Reeb graph with geometrical information about the shape, which give an abstraction of the main shape features. Finally, directions of future research will be discussed.

Date received: May 21, 2008