Results 11 to 20 of about 266 (143)
The Reeb Graph Edit Distance is Universal [PDF]
Foundations of Computational Mathematics, 2020 AbstractWe consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to ...
Ulrich Bauer +2 more
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A reeb graph approach to tractography [PDF]
Proceedings of the 23rd SIGSPATIAL International Conference on Advances in Geographic Information Systems, 2015 We propose an efficient algorithm for discovering the high-level topological structure of a collection of 3-dimensional trajectories. Our algorithm computes a sparse graph representing the latent "bundling" and "unbundling" structure of the trajectory data.
Jonathan Sun +3 more
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Loops in reeb graphs of 2-manifolds [PDF]
Proceedings of the nineteenth annual symposium on Computational geometry, 2003 Let \(N\) be a compact connected surface of genus \(g\) with \(h\) boundary components and let \(f\) be a Morse function on \(N\). The Reeb graph of \(f\) is obtained from \(N\) by contracting the connected components of the level sets to points. The authors obtain sharp upper and lower bounds for the number of loops in the Reeb graph that depend on ...
Kree Cole-McLaughlin +4 more
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Tight quasi-universality of Reeb graph distances. [PDF]
J Appl Comput TopolAbstract We establish tight bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance.
Bauer U, Bjerkevik HB, Fluhr B.
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The Edit Distance for Reeb Graphs of Surfaces [PDF]
Discrete & Computational Geometry, 2016 An extended abstract of this work appeared in: E. Barcucci et al. (Eds.): DGCI 2014, LNCS 8668, pp.
DI FABIO, Barbara, LANDI, Claudia
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Quasi-Universality of Reeb Graph Distances.
CoRR, 2021 We establish bi-Lipschitz bounds certifying quasi-universality (universality up to a constant factor) for various distances between Reeb graphs: the interleaving distance, the functional distortion distance, and the functional contortion distance. The definition of the latter distance is a novel contribution, and for the special case of contour trees ...
Ulrich Bauer +2 more
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On combinatorial invariant of pseudo-harmonic function defined on k-connected closed domain
Pracì Mìžnarodnogo Geometričnogo Centru, 2015 Let f be a pseudo-harmonic function defined on k-connected oriented closed domain D whose boundary consists of finitely many closedJordancurves. We remind that this class of functions coincides with continuous functions which have finitely many number
Ірина Аркадіївна Юрчук
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IEEE Access, 2019 Neural somas perform most of the metabolic activities in the neuron and support the chemical process that generates the basic elements of the synapses, and consequently the brain activity.
Sergio Luengo-Sanchez +2 more
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An edit distance for Reeb graphs
, 2016 We consider the problem of assessing the similarity of 3D shapes using Reeb graphs from the standpoint of robustness under perturbations. For this purpose, 3D objects are viewed as spaces endowed with real-valued functions, while the similarity between the resulting Reeb graphs is addressed through a graph edit distance.
Ulrich Bauer +2 more
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Measuring Distance between Reeb Graphs [PDF]
Proceedings of the thirtieth annual symposium on Computational geometry, 2014 Updated to match the modified definitions of the conference version. Improved and simplified bounds for the Gromov-Hausdorff distance. New section on interleaving distance for merge trees.
Ulrich Bauer, Xiaoyin Ge, Yusu Wang 0001
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