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In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials.
Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode
Zernike von F · 1934
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A proof of the hairy ball theorem
Murray Eisenberg and Robert Guy · 1979
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Discrete differential-geometry operators for triangulated 2-manifolds
Mark Meyer, Mathieu Desbrun, Peter Schröder, and Alan H Barr · 2003
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Jia Lu, Xianlian Zhou, and Madhavan L Raghavan · 2007
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Spectral mesh deformation
Guodong Rong, Yan Cao, and Xiaohu Guo · 2008
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Inverse method of stress analysis for cerebral aneurysms
Jia Lu, Xianlian Zhou, and Madhavan L Raghavan · 2008
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Segmentation of 3d lidar data in non-flat urban environments using a local convexity criterion
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Surface feature detection and description with applications to mesh matching
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Spectral mesh processing
Bruno Lévy and Hao (Richard) Zhang · 2010
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Blended intrinsic maps
Vladimir G Kim, Yaron Lipman, and Thomas Funkhouser · 2011
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Geodesic polar coordinates on polygonal meshes
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Functional maps: A flexible representation of maps between shapes
Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas Guibas · 2012
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Parametric human body shape modeling framework for human-centered product design
Seung-Yeob Baek and Kunwoo Lee · 2012
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Detecting global and local hippocampal shape changes in alzheimer’s disease using statistical shape models
Kai-kai Shen, Jurgen Fripp, Fabrice Mériaudeau, Gaël Chételat, Olivier Salvado, Pierrick Bourgeat, Alzheimer’s Disease Neuroimaging Initiative, et al · 2012
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Lie bodies: A manifold representation of 3D human shape
Oren Freifeld and Michael J. Black · 2012
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Spectral networks and locally connected networks on graphs
Joan Bruna, Wojciech Zaremba, Arthur Szlam, and Yann LeCun · 2013
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Automated bone landmarks prediction on the femur using anatomical deformation technique
Seung-Yeob Baek, Joon Ho Wang, Insub Song, Kunwoo Lee, Jehee Lee, and Seungbum Koo · 2013
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Emanuele Rodolà, Samuel Rota Bulo, Thomas Windheuser, Matthias Vestner, and Daniel Cremers · 2014
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Federica Bogo, Javier Romero, Matthew Loper, and Michael J. Black · 2014
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Zhiyu Sun, Yusen He, Andrey Gritsenko, Amaury Lendasse, and Stephen Baek · 2017
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Geometric deep learning: going beyond euclidean data
Michael M Bronstein, Joan Bruna, Yann LeCun, Arthur Szlam, and Pierre Vandergheynst · 2017
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SyncSpecCNN: Synchronized spectral CNN for 3D shape segmentation
Li Yi, Hao Su, Xingwen Guo, and Leonidas J Guibas · 2017
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Mikael Henaff, Joan Bruna, and Yann LeCun · 2015
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Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks
Davide Boscaini, Jonathan Masci, Simone Melzi, Michael M Bronstein, Umberto Castellani, and Pierre Vandergheynst · 2015
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Convolutional networks on graphs for learning molecular fingerprints
David K Duvenaud, Dougal Maclaurin, Jorge Iparraguirre, Rafael Bombarell, Timothy Hirzel, Alán Aspuru-Guzik, and Ryan P Adams · 2015
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Michaël Defferrard, Xavier Bresson, and Pierre Vandergheynst · 2016
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Thomas N Kipf and Max Welling · 2016
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The heat method for distance computation
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Convolutional neural networks on surfaces via seamless toric covers
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Pointnet++: Deep hierarchical feature learning on point sets in a metric space
Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas · 2017
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Building statistical shape spaces for 3d human modeling
Leonid Pishchulin, Stefanie Wuhrer, Thomas Helten, Christian Theobalt, and Bernt Schiele · 2017
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