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We use persistent homology along with the eigenfunctions of the Laplacian to study similarity amongst triangulated 2-manifolds.
Algebraic connectivity of graphs
Miroslav Fiedler · 1973
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A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory
Miroslav Fiedler · 1975
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Topological persistence and simplification
Herbert Edelsbrunner, David Letscher, and Afra J. Zomorodian · 2002
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On spectral clustering: Analysis and an algorithm
Andrew Y Ng, Michael I Jordan, and Yair Weiss · 2002
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Deformation transfer for triangle meshes
Robert W Sumner and Jovan Popović · 2004
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Streaming meshes
Martin Isenburg and Peter Lindstrom · 2005
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Sub-part correspondence by structural descriptors of 3d shapes
Silvia Biasotti, Simone Marini, Michela Spagnuolo, and Bianca Falcidieno · 2006
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Diffusion maps and coarse-graining: A unified framework for dimensionality reduction, graph partitioning, and data set parameterization
Stephane Lafon and Ann B Lee · 2006
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Laplace-beltrami eigenfunctions towards an algorithm that” understands” geometry
Bruno Levy · 2006
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Laplace-beltrami eigenfunctions towards an algorithm that understands geometry
Bruno Lévy · 2006
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Laplace–beltrami spectra as ‘shape-dna’of surfaces and solids
Martin Reuter, Franz-Erich Wolter, and Niklas Peinecke · 2006
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Laplace-beltrami eigenfunctions for deformation invariant shape representation
Raif M Rustamov · 2007
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Topological methods for the analysis of high dimensional data sets and 3d object recognition
Gurjeet Singh, Facundo Mémoli, and Gunnar E Carlsson · 2007
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Survey on 3d shape descriptors
Lisha Zhang, Manuel João da Fonseca, Alfredo Ferreira, and Combinando Realidade Aumentada e Recuperação · 2007
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Barcodes: The persistent topology of data
Robert Ghrist · 2008
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Visualizing data using t-SNE
Laurens van der Maaten and Geoffrey Hinton · 2008
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Gromov-hausdorff stable signatures for shapes using persistence
Frédéric Chazal, David Cohen-Steiner, Leonidas J Guibas, Facundo Mémoli, and Steve Y Oudot · 2009
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A survey on shape correspondence
Oliver Van Kaick, Hao Zhang, Ghassan Hamarneh, and Daniel Cohen-Or · 2011
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Topological analysis and visualization of cyclical behavior in memory reference traces
ANM Imroz Choudhury, Bei Wang, Paul Rosen, and Valerio Pascucci · 2012
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The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains
David I Shuman, Sunil K Narang, Pascal Frossard, Antonio Ortega, and Pierre Vandergheynst · 2013
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Registration of 3d point clouds and meshes: a survey from rigid to nonrigid
Gary KL Tam, Zhi-Quan Cheng, Yu-Kun Lai, Frank C Langbein, Yonghuai Liu, David Marshall, Ralph R Martin, Xian-Fang Sun, and Paul L Rosin · 2013
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Quantifying 3d shape similarity using maps: Recent trends, applications and perspectives
Silvia Biasotti, Andrea Cerri, Alexander M Bronstein, and Michael M Bronstein · 2014
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