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Stable Shape Comparison of Surfaces via Reeb Graphs [chapter]

Barbara Di Fabio, Claudia Landi
2014 Lecture Notes in Computer Science  
Reeb graphs are combinatorial signatures that capture shape properties from the perspective of a chosen function.  ...  In this work we tackle the problem of stability by providing an editing distance between Reeb graphs of orientable surfaces in terms of the cost necessary to transform one graph into another by edit operations  ...  In conclusion, the novelty of this paper is the announcement of a new combinatorial method to compare Reeb graphs in a stable way when shapes can be modeled as surfaces.  ... 
doi:10.1007/978-3-319-09955-2_17 fatcat:ftah4gfr4je45fqvgwwxm5hsze

Simplified Reeb Graph as Effective Shape Descriptor for the Striatum [chapter]

Antonietta Pepe, Laura Brandolini, Marco Piastra, Juha Koikkalainen, Jarmo Hietala, Jussi Tohka
2012 Lecture Notes in Computer Science  
Experimental results showed that simplified Reeb graphs, as obtained by our pipeline, provide an intrinsic, effective, and stable descriptor of striatal shapes to be used as an automatic tool for inter-subject  ...  The quality of the inter-subject mesh registration obtained by the use of simplified Reeb graphs slightly outperformed the one obtained by surface-based registration techniques.  ...  This work was supported by the Academy of Finland grant number 130275 and 129657.  ... 
doi:10.1007/978-3-642-33463-4_14 fatcat:ywknxpllirexfggs2chfdmouby

An Edit Distance for Reeb Graphs [article]

Ulrich Bauer, Barbara Di Fabio, Claudia Landi
2016 Eurographics Workshop on 3D Object Retrieval, EG 3DOR  
We consider the problem of assessing the similarity of 3D shapes using Reeb graphs from the standpoint of robustness under perturbations.  ...  The main contribution of this paper is the introduction of a general edit distance suitable for comparing Reeb graphs in these settings.  ...  The stability of labeled Reeb graphs of curves via an edit distance has been proven in [DFL12] , that of surfaces in [DFL16] .  ... 
doi:10.2312/3dor.20161084 fatcat:fe5fvjihw5c65ho5nleiok4tta

3D Shape Description and Matching Based on Properties of Real Functions [article]

Silvia Biasotti, Bianca Falcidieno, Patrizio Frosini, Daniela Giorgi, Claudia Landi, Simone Marini, Giuseppe Patané, Michela Spagnuolo
2007 Eurographics State of the Art Reports  
the mapping function, shape description, via the construction of a signature, and comparison, via the definition of a distance measure.  ...  The methods are discussed following an abstract conceptual framework that distinguishes among the three main components of these class of shape matching methods: shape analysis, via the application of  ...  Acknowledgements This work has been partially supported by the EC-IST FP6 Network of Excellence AIM@SHAPE. Models are courtesy of the AIM@SHAPE repository http://www.aimatshape.net.  ... 
doi:10.2312/egt.20071071 fatcat:kunadx2snzhwzncsxyla675kfy

Reeb graph path dissimilarity for 3D object matching and retrieval

Waleed Mohamed, A. Ben Hamza
2011 The Visual Computer  
Experimental results demonstrate the feasibility of the proposed topological Reeb graph as a shape signature for 3D object matching and retrieval.  ...  The proposed skeletonization algorithm encodes a 3D shape into a topological Reeb graph using a normalized mixture distance function.  ...  Reeb graph of a 3D shape, we assign three features to each endpoint of the skeleton.  ... 
doi:10.1007/s00371-011-0640-5 fatcat:nifvy5ehpzbxxme2pswagx3vby

A functional-based segmentation of human body scans in arbitrary postures

N. Werghi, Yijun Xiao, J.P. Siebert
2006 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
Index Terms-Human body shape analysis, Reeb graph, scattered 3-D range data segmentation, 3-D surface topology, 3-D whole-body scanners.  ...  Although whole human body scanners are now capable of routinely capturing the shape of the whole body in machine readable format, they have not yet realized their potential to provide automatic extraction  ...  Digital Object Identifier 10.1109/TSMCB.2005.854503 Fig. 1 . 1 (a) Reeb graph of a torus. (b) Reeb graph of a HB shape. (c) Discrete Reeb graph.  ... 
doi:10.1109/tsmcb.2005.854503 pmid:16468574 fatcat:5p2y4zl3azflpa57yhkvsaikpm

Describing shapes by geometrical-topological properties of real functions

S. Biasotti, L. De Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, M. Spagnuolo
2008 ACM Computing Surveys  
The methods proposed range from approaches which use the configuration of contours for encoding topographic surfaces to more recent work on size theory and persistent homology.  ...  The fundamental idea behind Morse theory is that of combining the topological exploration of a shape with quantitative measurement of geometrical properties provided by a real function defined on the shape  ...  This work has been developed within the CNR research activities ICT-P03 and DG.RSTL.050.004, and with the support of the EU FP6 Network of Excellence AIM@SHAPE, contract number 506766, by the Italian National  ... 
doi:10.1145/1391729.1391731 fatcat:yg6k2lwerfd63nuhhxxypcnzju

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  ...  Creating high-quality quad meshes from triangulated surfaces is a highly non trivial task that necessitates consideration of various application specific metrics of quality.  ...  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

The edit distance for Reeb graphs of surfaces [article]

Barbara Di Fabio, Claudia Landi
2014 arXiv   pre-print
Reeb graphs are structural descriptors that capture shape properties of a topological space from the perspective of a chosen function.  ...  In this work we define a combinatorial metric for Reeb graphs of orientable surfaces in terms of the cost necessary to transform one graph into another by edit operations.  ...  Sharko for his clarifications on the uniqueness property of Reeb graphs of surfaces and for indicating the reference [15] .  ... 
arXiv:1411.1544v1 fatcat:dyav3pa4nbb7jjzold3r23tnre

3D Mesh decomposition using Reeb graphs

Stefano Berretti, Alberto Del Bimbo, Pietro Pala
2009 Image and Vision Computing  
In this paper, an approach is proposed for decomposition of 3D objects based on Reeb-graphs.  ...  by manual decomposition of 3D objects.  ...  Surface Topology and Reeb-graphs Topology is the study of the properties of a shape that do not change under deformation.  ... 
doi:10.1016/j.imavis.2009.02.004 fatcat:vd7dbuablzfjxlw2wf6y32esqm

Analyzing and Tracking Burning Structures in Lean Premixed Hydrogen Flames

P.-T. Bremer, G.H. Weber, V. Pascucci, M. Day, J.B. Bell
2010 IEEE Transactions on Visualization and Computer Graphics  
Third, for a given parameter selection we create detailed tracking graphs representing the complete evolution of all features in a combustion simulation over several hundred time steps.  ...  We demonstrate our approach by analyzing three numerical simulations of lean hydrogen flames subject to different levels of turbulence.  ...  Later in the process cells will be tracked by computing the Reeb graph of the final space-time isosurface. The Reeb graph, however, only depends on the connectivity of the surface not its geometry.  ... 
doi:10.1109/tvcg.2009.69 pmid:20075485 fatcat:g2vbm4mkdfhv7likxtotfjquve

Shape approximation by differential properties of scalar functions

Silvia Biasotti, Giuseppe Patanè, Michela Spagnuolo, Bianca Falcidieno, Gill Barequet
2010 Computers & graphics  
The method is geometry-aware by definition, as the nodes of the Reeb graph are representative of the main shape features, which belong to the approximated shape already at the initial iteration steps.  ...  This paper presents a method of shape chartification suitable for surface approximation.  ...  Acknowledgments The authors would like to thank all the members of the Shape Modeling Group at CNR-IMATI for their valuable support.  ... 
doi:10.1016/j.cag.2010.03.013 fatcat:ewhm7hcxtvdz3ik33bsehbuog4

Neutral surface topology

Geoffrey J. Stanley
2019 Ocean Modelling  
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.  ...  Cycles in the Reeb graph are created by islands and other holes in the neutral surface.  ...  The only way path-dependence can affect (20) is via cycles in the Reeb graph. To see this, suppose the Reeb graph has no cycles (a tree), and consider any two nodes.  ... 
doi:10.1016/j.ocemod.2019.01.008 fatcat:5eveod5t5zdspagna7idfa26ve

Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis

Martin Reuter, Franz-Erich Wolter, Martha Shenton, Marc Niethammer
2009 Computer-Aided Design  
Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable  ...  This paper proposes the use of the surface-based Laplace-Beltrami and the volumetric Laplace eigenvalues and eigenfunctions as shape descriptors for the comparison and analysis of shapes.  ...  In addition to the eigenvalues (allowing only global shape comparisons), new eigenfunction analyses are introduced employing the Morse-Smale complex and Reeb graph to shed light on the behavior of the  ... 
doi:10.1016/j.cad.2009.02.007 pmid:20161035 pmcid:PMC2753296 fatcat:ufbzmuiy5jbdjjeitudukalxrq

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

Tripti Agarwal, Amit Chattopadhyay, Vijay Natarajan
2019 arXiv   pre-print
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields.  ...  Topological feature search of such data aims to reveal important properties useful to the domain scientists.  ...  We would like to thank all authors of the paper [13] for sharing the nuclear scission data. We also thank Prof.  ... 
arXiv:1911.00687v1 fatcat:3vghddqbyjghzdllip24vtlqay
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