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Time-varying reeb graphs for continuous space-time data

Herbert Edelsbrunner, John Harer, Ajith Mascarenhas, Valerio Pascucci
2004 Proceedings of the twentieth annual symposium on Computational geometry - SCG '04  
We study the evolution of the Reeb graph of a time-varying continuous function defined in three-dimensional space.  ...  While maintaining the Reeb graph, we compress the evolving sequence into a single, partially persistent data structure.  ...  Acknowledgments The third author would like to thank Jack Snoeyink for providing the start in working on this problem and for stimulating discussions.  ... 
doi:10.1145/997817.997872 dblp:conf/compgeom/EdelsbrunnerHMP04 fatcat:hewc6bx64bgrbh55643dhhgive

Time-varying Reeb graphs for continuous space–time data

Herbert Edelsbrunner, John Harer, Ajith Mascarenhas, Valerio Pascucci, Jack Snoeyink
2008 Computational geometry  
We study the evolution of the Reeb graph of a time-varying continuous function defined in three-dimensional space.  ...  While maintaining the Reeb graph, we compress the evolving sequence into a single, partially persistent data structure.  ...  Acknowledgments The third author would like to thank Jack Snoeyink for providing the start in working on this problem and for stimulating discussions.  ... 
doi:10.1016/j.comgeo.2007.11.001 fatcat:couqmd2senciditjx3rf3tmp4m

Isocontour based Visualization of Time-varying Scalar Fields [chapter]

Ajith Mascarenhas, Jack Snoeyink
2009 Mathematics and Visualization  
In this paper we survey isocontour based visualization techniques for time-varying scalar fields.  ...  A useful tool in interpreting the data is graphical visualization, often through level sets, or isocontours of a continuous function derived from the data.  ...  We thank the anonymous referees for their suggestions.  ... 
doi:10.1007/b106657_3 fatcat:nrwen6mzlvbh5izwlb4bimjk3m

Joint Contour Nets

Hamish Carr, David Duke
2014 IEEE Transactions on Visualization and Computer Graphics  
Contour Trees and Reeb Graphs are firmly embedded in scientific visualization for analysing univariate (scalar) fields.  ...  We generalize this analysis to multivariate fields with a data structure called the Joint Contour Net that quantizes the variation of multiple variables simultaneously.  ...  We expect that many of the techniques that work for the contour tree and Reeb graph will then extend to the JCN.  ... 
doi:10.1109/tvcg.2013.269 pmid:26357364 fatcat:tpbn4cppj5e57dci5zai7ihjsi

Topological Feature Search in Time-Varying Multifield Data [article]

Tripti Agarwal, Amit Chattopadhyay, Vijay Natarajan
2019 arXiv   pre-print
Given a time-varying multifield data, the method computes a metric plot for each pair of histograms at consecutive time stamps to understand the topological changes in the data over time.  ...  We validate the method using real and synthetic data.  ...  Brijesh Kumar Mishra, IIIT-Bangalore for his expert help in understanding the Pt-CO interaction data.  ... 
arXiv:1911.00687v1 fatcat:3vghddqbyjghzdllip24vtlqay

A Topological Similarity Measure between Multi-Field Data using Multi-Resolution Reeb Spaces [article]

Tripti Agarwal, Yashwanth Ramamurthi, Amit Chattopadhyay
2020 arXiv   pre-print
We demonstrate an application of the proposed similarity measure by detecting the nuclear scission point in a time-varying multi-field data from computational physics.  ...  Overall, our method consists of two steps: (i) building a multi-resolution Reeb space corresponding to each of the multi-fields and (ii) proposing a similarity measure for a list of matching pairs (of  ...  [16] present an edit distance based method between merge trees for feature visualization in time-varying scalar field data.  ... 
arXiv:2008.12567v1 fatcat:gghg6okpd5fo7krzquzmxa7a5e

Joint Contour Net Analysis for Feature Detection in Lattice Quantum Chromodynamics Data

Dean P. Thomas, Rita Borgo, Robert S. Laramee, Simon J. Hands
2019 Big Data Research  
In this paper we demonstrate the use of multivariate topological algorithms to analyse and interpret Lattice Quantum Chromodynamics (QCD) data.  ...  This enables them to focus upon the structure and distribution of the core observables by identifying them within the surrounding data.  ...  resources of the DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and Swansea University, and the DEISA Consortium (www.deisa.eu), funded through the EU FP7 project RI-222919, for  ... 
doi:10.1016/j.bdr.2019.02.003 fatcat:mdhwylmd5rcrpkll5nydhg3vz4

Real-Time Motion Planning in Changing Environments Using Topology-Based Encoding of Past Knowledge

Richard Fisher, Benjamin Rosman, Vladimir Ivan
2018 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)  
We evaluate DRM-connect with a Reeb graph on reaching tasks, and we compare it to state-of-the-art methods.  ...  Furthermore, we investigate using an approximate Reeb graph to capture the topologypersistent features of the past solutions of the problem utilising this sparsity.  ...  The number of bands can be varied depending on the volume of data points in the adjacency graph and the computational requirements.  ... 
doi:10.1109/iros.2018.8593879 dblp:conf/iros/FisherRI18 fatcat:kcmcfiepibhnhdrt53n3pih4uu

Topology analysis of time-dependent multi-fluid data using the Reeb graph

Fang Chen, Harald Obermaier, Hans Hagen, Bernd Hamann, Julien Tierny, Valerio Pascucci
2013 Computer Aided Geometric Design  
We present a topology-based approach to track the splitting and merging events of these regions using the Reeb graphs.  ...  Time is used as the third dimension in addition to two-dimensional (2D) point-based simulation data.  ...  Finally we carry out a topological analysis of the extracted time-varying level sets using the Reeb graph.  ... 
doi:10.1016/j.cagd.2012.03.019 fatcat:rm3fkyckf5a2ndz4tsly5i5xjm

A Deterministic $$O(m \log {m})$$ O ( m log m ) Time Algorithm for the Reeb Graph

Salman Parsa
2013 Discrete & Computational Geometry  
In addition, we reduce the offline graph connectivity problem to computing the Reeb graph.  ...  We present a deterministic algorithm to compute the Reeb graph of a PL real-valued function on a simplicial complex in O(m log m) time, where m is the size of the 2-skeleton.  ...  Acknowledgments The author thanks Herbert Edelsbrunner for support and valuable suggestions on the paper.  ... 
doi:10.1007/s00454-013-9511-3 fatcat:ft62phete5frll4ybzborq2eou

Topological Visualisation Techniques for Volume Multifield Data [chapter]

Dean P. Thomas, Rita Borgo, Robert S. Laramee, Simon J. Hands
2018 Computer Graphics and Imaging [Working Title]  
This survey paper provides an overview of topological visualisation techniques for scalar data sets.  ...  These can be visualised using graph drawing techniques or used as a method of seeding meshes of distinct objects existing in the data.  ...  Hamish Carr for his advice and assistance throughout the duration of this work.  ... 
doi:10.5772/intechopen.82185 fatcat:f4pgvn2dvzauxp4l6vmje47itm

Data Skeletonization via Reeb Graphs

Xiaoyin Ge, Issam Safa, Mikhail Belkin, Yusu Wang
2011 Neural Information Processing Systems  
In this paper, we develop a framework to extract, as well as to simplify, a one-dimensional "skeleton" from unorganized data using the Reeb graph.  ...  We believe that the simplicity and practicality of our algorithm will help to promote skeleton graphs as a data analysis tool for a broad range of applications.  ...  Ozertem for kindly providing their software and for help with using the software. This work was in part supported by the NSF under CCF-0747082, CCF-1048983, CCF-1116258, IIS-1117707, IIS-0643916.  ... 
dblp:conf/nips/GeSBW11 fatcat:72bc6ayohvdp5noeyopjt4oram

Feature Tracking Using Reeb Graphs [chapter]

Gunther Weber, Peer-Timo Bremer, Marcus Day, John Bell, Valerio Pascucci
2010 Mathematics and Visualization  
The Reeb graph of this boundary surface is the tracking graph for burning regions.  ...  Our approach tracks burning regions by extracting a temperature isovolume from the four-dimensional space-time temperature field.  ...  Since the Reeb graph ignores the embedding of the underlying manifold (the space-time surface) snapping the vertices to those of the isovolume leaves the Reeb graph unchanged.  ... 
doi:10.1007/978-3-642-15014-2_20 fatcat:m5zy4xfoajesbffmllqf3iyw6u

Propagate and Pair: A Single-Pass Approach to Critical Point Pairing in Reeb Graphs [article]

Junyi Tu, Mustafa Hajij, Paul Rosen
2019 arXiv   pre-print
With the popularization of Topological Data Analysis, the Reeb graph has found new applications as a summarization technique in the analysis and visualization of large and complex data, whose usefulness  ...  In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.  ...  Mesh data are provided by AIM@SHAPE Repository.  ... 
arXiv:1909.01513v2 fatcat:ncmbanvmwzeuhjjnymcf4kz75m

Algorithms for Dynamic Reeb Graphs [article]

Salman Parsa
2015 arXiv   pre-print
The algorithm updates the Reeb graph in O(l gn) worst-case deterministic time for each such interchange, where l is an upper bound on the size of the star of the involved vertices, and g(n) is a worst-case  ...  We present an algorithm for updating the Reeb graph under fully dynamic changes of the function values. The basic event is the interchange of two consecutive vertex values.  ...  For example, if we have a function that changes with time and we know the values of the function over a time interval. This case is called "time-varying Reeb graphs" in [5] .  ... 
arXiv:1402.2812v3 fatcat:ngrh7vnuovezfhgzwai45kkmxu
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