2010/03/24 by Barbara Di Fabio, Di Fabio, Barbara, Claudia Landi +1
Computer Science · Mathematics · #05C10 #57R99 #Computational Geometry (cs.CG) #Data Visualization and Analytics #FOS: Computer and information sciences #I.3.5 #Morphological variations and asymmetry #Primary 68U05 #Secondary 68T10 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1003.4610
openalex publication_date 2010/03/24 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
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.