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Reeb graphs are combinatorial signatures that capture shape\udproperties from the perspective of a chosen function. One of the most\udimportant questions is whether Reeb graphs are robust against function\udperturbations that may occur because of noise and approximation errors\udin the data acquisition process. In this work we tackle the problem of\udstability by providing an editing distance between Reeb graphs of orientable\udsurfaces in terms of the cost necessary to transform one graph\udinto another by edit operations. Our main result is that the editing distance\udbetween two Reeb graphs is upper bounded by the extent of the\uddifference of the associated functions, measured by the maximum norm.\udThis yields the stability property under function perturbations

Stable Shape Comparison of Surfaces via Reeb Graphs