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Abstract: Reeb graphs provide a method for studying the shape of a manifold by encodingthe evolution and arrangement of level sets of a simple Morse function definedon the manifold. Since their introduction in computer graphics they have beengaining popularity as an effective tool for shape analysis and matching. Inthis context one question deserving attention is whether Reeb graphs are robustagainst function perturbations. Focusing on 1-dimensional manifolds, we definean editing distance between Reeb graphs of curves, in terms of the costnecessary to transform one graph into another. Our main result is that changesin Morse functions induce smaller changes in the editing distance between Reebgraphs of curves, implying stability of Reeb graphs under functionperturbations.



Author: Barbara Di Fabio, Claudia Landi

Source: https://arxiv.org/



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