Stability of Reeb Graphs under function perturbations: the case of closed curves

Di Fabio, Barbara ; Landi, Claudia (2010) Stability of Reeb Graphs under function perturbations: the case of closed curves. p. 23. DOI 10.6092/unibo/amsacta/2759.

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Reeb graphs provide a method for studying the shape of a manifold by encoding the evolution and arrangement of level sets of a simple Morse function defined on the manifold. Since their introduction in computer graphics they have been gaining popularity as an effective tool for shape analysis and matching. In this context one question deserving attention is whether Reeb graphs are robust against function perturbations. Focusing on 1-dimensional manifolds, we define an editing distance between Reeb graphs of curves, in terms of the cost necessary to transform one graph into another. Our main result is that changes in Morse functions induce smaller changes in the editing distance between Reeb graphs of curves, implying stability of Reeb graphs under function perturbations.

Document type
Monograph (Technical Report)
Di Fabio, Barbara
Landi, Claudia
shape similarity, editing distance, Morse function, natural stratification, natural pseudo-distance.
Deposit date
25 Mar 2010 09:57
Last modified
16 May 2011 12:13

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