Topological coding of surfaces with boundary using Reeb graphs

Morse theory provides the theoretical framework for defining several shape descriptors related to the evolution on the surface of its contour levels. For example, the Reeb graph gives a conceptual sketch of the surface, which can be used to transmit/code abstract descriptions of the whole data set and to compose the object signatures instead of the whole models. In this paper, the basic concepts related to Reeb graphs are adapted and extended to generic surfaces with boundary.