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A Variational Loop Shrinking Analogy for Handle and Tunnel Detection and Reeb Graph Construction on Surfaces [article]

Alexander Weinrauch, Hans-Peter Seidel, Daniel Mlakar, Markus Steinberger, Rhaleb Zayer
2021 arXiv   pre-print
This is particularly true in the context of detecting relevant non-contractible loops on surfaces where elaborate homological and/or graph theoretical constructs are favored in algorithmic solutions.  ...  As a byproduct, our approach can be used to construct Reeb graphs by diffusion thus avoiding commonly encountered issues when using Morse functions.  ...  intermediate structures relying on persistence homology and Reeb graphs.  ... 
arXiv:2105.13168v1 fatcat:jlznioywrbg3daqgncsqzk6qum

GRAPH MATCHING A SKELETONIZED THEORETICAL MORPHOSPACE WITH A CLADOGRAM FOR GOMPHONEMOID-CYMBELLOID DIATOMS (BACILLARIOPHYTA)

JANICE L. PAPPAS
2011 Journal of biological systems  
A three-dimensional (3D) theoretical morphospace of gomphonemoid and cymbelloid diatoms was skeletonized using concepts from extended Reeb graph analysis and Morse theory.  ...  From this, an unweighted path matrix based on the number of branches between leaf nodes was ordinated to determine degree of matched tree structures.  ...  Pascucci V, Scorzelli G, Bremer P-T, Mascarenhas A, Robust on-line computation of Reeb graphs: simplicity and speed, ACM Trans Graphics 26:58-1-58-9, 2007. 50.  ... 
doi:10.1142/s0218339011003816 fatcat:mcojo24qdnd6vl2achgzz6cj7a

Graph Reconstruction by Discrete Morse Theory [article]

Tamal K. Dey and Jiayuan Wang and Yusu Wang
2018 arXiv   pre-print
as the hidden ground-truth graph, and is also geometrically close.  ...  We then introduce a simple and natural noise model and show that the aforementioned framework can correctly reconstruct a graph under this noise model, in the sense that it has the same loop structure  ...  This work is supported by National Science Foundation under grants CCF-1526513, CCF-1618247, and CCF-1740761, and by National Institute of Health under grant R01EB022899.  ... 
arXiv:1803.05093v1 fatcat:a47qxpyd2jemjftki4v4sh4uny

Unfolding Kernel embeddings of graphs: Enhancing class separation through manifold learning

Luca Rossi, Andrea Torsello, Edwin R. Hancock
2015 Pattern Recognition  
Hence, we propose to use a number of manifold learning techniques to compute a low-dimensional embedding of the graphs in an attempt to unfold the embedding manifold, and increase the class separation.  ...  We perform an extensive experimental evaluation on a number of standard graph datasets using the shortest-path [1], graphlet [2], random walk [3] and Weisfeiler-Lehman [4] kernels.  ...  Reeb: The Reeb dataset consists of a set of adjacency matrices associated to the computation of reeb graphs of 3D shapes [43] .  ... 
doi:10.1016/j.patcog.2015.03.018 fatcat:bkwwxpwbcfdx7bd446yzbngmoe

Shape-based retrieval and analysis of 3D models

Thomas Funkhouser, Michael Kazhdan
2004 Proceedings of the conference on SIGGRAPH 2004 course notes - GRAPH '04  
After an introduction to shape retrieval and analysis applications, the course will focus on computational representations of shape (shape descriptors).  ...  As the number of 3D models grows, there is an increasing need for computer algorithms to help people find the interesting ones and discover relationships between them.  ...  We thank Patrick Min for his valuable comments on a draft of this paper and the reviewers for their useful suggestions.  ... 
doi:10.1145/1103900.1103916 dblp:conf/siggraph/FunkhouserK04 fatcat:6shgctdwxzbhjnnwpznch2bfcu

Interactive Quadrangulation with Reeb Atlases and Connectivity Textures

Julien Tierny, Joel Daniels II, Luis Gustavo Nonato, Valerio Pascucci, Claudio T. Silva
2012 IEEE Transactions on Visualization and Computer Graphics  
Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with  ...  quality criteria on the output quad mesh, at interactive rates.  ...  We also thank the authors of the following papers [21] , [6] , [36] , [13] , [47] , who kindly provided their data-sets.  ... 
doi:10.1109/tvcg.2011.270 pmid:22025751 fatcat:muwl2xcywndaxlp34jitw4khj4

Trajectory Grouping Structure [chapter]

Kevin Buchin, Maike Buchin, Marc van Kreveld, Bettina Speckmann, Frank Staals
2013 Lecture Notes in Computer Science  
Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology.  ...  We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently.  ...  They use a proximity graph on the input points to build a simplicial complex from which they compute the Reeb graph.  ... 
doi:10.1007/978-3-642-40104-6_19 fatcat:724bov2ggvd5fefbvow3xik3uu

Trajectory Grouping Structure

Kevin Buchin, Maike Buchin, Marc van Kreveld, Bettina Speckmann, Frank Staals
2014 Annual Symposium on Computational Geometry - SOCG'14  
Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology.  ...  We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently.  ...  They use a proximity graph on the input points to build a simplicial complex from which they compute the Reeb graph.  ... 
doi:10.1145/2582112.2595646 dblp:conf/compgeom/BuchinBKSS14 fatcat:r4o3nkjj4fcwdd2xbwyedbuysi

Trajectory Grouping Structures [article]

Kevin Buchin, Maike Buchin, Marc van Kreveld, Bettina Speckmann, Frank Staals
2013 arXiv   pre-print
Given the trajectories of these entities, we define and model a structure that captures all of such changes using the Reeb graph, a concept from topology.  ...  We prove complexity bounds on the maximum number of maximal groups that can be present, and give algorithms to compute the grouping structure efficiently.  ...  They use a proximity graph on the input points to build a simplicial complex from which they compute the Reeb graph.  ... 
arXiv:1303.6127v1 fatcat:kt457cgx75gstn53ahqmygjpju

A graph-based technique for semi-supervised segmentation of 3D surfaces

Filippo Bergamasco, Andrea Albarelli, Andrea Torsello
2012 Pattern Recognition Letters  
Still, despite its simplicity, tests made on a standard database of scanned 3D objects show its effectiveness even with moderate user supervision.  ...  In our framework segmentation happens by propagating part labels over a weighted graph representation of the surface directly derived from its triangulated mesh.  ...  More recently Berretti et al. (2009) introduced an approach based on Reeb graphs that is motivated by perceptual principles and supports identification of salient object protrusions.  ... 
doi:10.1016/j.patrec.2012.03.015 fatcat:yqhaiahl3jhirmmqzjhoqx3rpu

Multivariate topology simplification

Amit Chattopadhyay, Hamish Carr, David Duke, Zhao Geng, Osamu Saeki
2016 Computational geometry  
Computationally, we show how to compute Jacobi structure, Reeb skeleton, range and geometric measures in the Joint Contour Net (an approximation of the Reeb space) and that these can be used for visualisation  ...  We propose a robust multivariate topology simplification method based on "lip"-pruning from the Reeb space.  ...  Our thanks also to the anonymous reviewers for their constructive comments on how to improve the paper.  ... 
doi:10.1016/j.comgeo.2016.05.006 fatcat:tvr6ithqtbhrdevtzkfmnjnv6u

Feature-Preserving Reconstruction of Singular Surfaces

T. K. Dey, X. Ge, Q. Que, I. Safa, L. Wang, Y. Wang
2012 Computer graphics forum (Print)  
The identification and reconstruction of feature curves are achieved by a novel combination of the Gaussian weighted graph Laplacian and the Reeb graphs.  ...  It becomes challenging in presence of 'singularities' such as boundaries, sharp features, and non-manifolds.  ...  Our current implementation uses a kd-tree to speed up computation of proximity graph.  ... 
doi:10.1111/j.1467-8659.2012.03183.x fatcat:vhc3gimrlra2bfxnwddfnouery

Multivariate Topology Simplification [article]

Amit Chattopadhyay, Hamish Carr, David Duke, Zhao Geng, Osamu Saeki
2015 arXiv   pre-print
Computationally, we show how to compute Jacobi Structure, Reeb Skeleton, Range and Geometric Measures in the Joint Contour Net (an approximation of the Reeb Space) and that these can be used for visualisation  ...  We propose a robust multivariate topology simplification method based on "lip"-pruning from the Reeb Space.  ...  This algorithm is stated recursively for simplicity, but can also be implemented with queue processing for speed.  ... 
arXiv:1509.04465v1 fatcat:xs2msbq3fzhbbezg2mzdqhcnve

Neutral surface topology

Geoffrey J. Stanley
2019 Ocean Modelling  
Cycles in the Reeb graph are created by islands and other holes in the neutral surface.  ...  The regions are represented by arcs of the Reeb graph of ∼p. The regions meet at saddles of ∼p which are represented by internal nodes of the Reeb graph. Leaf nodes represent extrema of ∼p.  ...  Acknowledgements The author thanks Chris Hughes and David Marshall for helpful discussions, Trevor McDougall for early en-  ... 
doi:10.1016/j.ocemod.2019.01.008 fatcat:5eveod5t5zdspagna7idfa26ve

SLICE: Enabling Greedy Routing in High Genus 3-D WSNs With General Topologies

Chen Wang, Hongbo Jiang, Tianlong Yu, John C. S. Lui
2016 IEEE/ACM Transactions on Networking  
Compared to previous 3-D greedy embedding techniques, SLICE improves both the robustness and applicability. 1) It achieves a smaller distance distortion and a lower routing stretch with guaranteed delivery  ...  We first slice the surface network to a genus-0 open surface with exactly one boundary.  ...  Corollary 2: Each loop in the Reeb graph of corresponds to one loop-end arc.  ... 
doi:10.1109/tnet.2015.2464312 fatcat:iwefmc4mtzezhke47qlwnxwbde
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