Reeb graphs for shape analysis and applications

By Silvia Biasotti, Daniela Giorgi, Michela Spagnuolo, Bianca Falcidieno. Theoretical Computer Science, 2008

316 citations recorded by the source corpus.

Reeb graphs are compact shape descriptors which convey topological information related to 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 as shape descriptors have been proposed 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 paper provides an overview of the mathematical properties of Reeb graphs and reconstructs its history in the Computer Graphics context, with an eye towards directions of future research.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/575cf289eb5b7fe69c5d6f69d55a5e122832dd0e

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In Computational Theory and Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Visualizing High-Dimensional Data: Advances in the Past Decade (2017, unknown): “In both examples, regression is used as a post-processing step of the algorithms in order to present summaries of the extracted subsets of the data.”
Unsupervised co-segmentation of a set of shapes via descriptor-space spectral clustering (2011, background): “Nevertheless, our approach will naturally beneﬁt from incorporating more sophisticated descriptors, e.g., of a structural nature [Biasotti et al. 2008; Shapira et al. 2009].”
Realization of a graph as the Reeb graph of a Morse function on a manifold (2018, background): “Reeb graphs are widely applied in computer graphics and shape analysis (see [1]).”
Recent Trends, Applications, and Perspectives in 3D Shape Similarity Assessment (2016, background): “…in the graph with geometric attributes of the shape parts corresponding to nodes and arcs, the most popular being the augmented Multi-Resolution Reeb graph [TS04, TS05], the Extended Reeb graph [BMM*03] and the Discrete Reeb graph [XSW03], more details can be found in the survey paper [BGSF08a].”
A SMOOTH FUNCTION ON A MANIFOLD WITH GIVEN REEB GRAPH (2011, background): “) This object is very important in studying the shape of a surface both in Differential Topology and in Computer Graphics (see [4]–[9] and [2, 3], for example).”