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Group convolutional neural networks (G-CNNs) can be used to improve classical CNNs by equipping them with the geometric structure of groups.
Receptive fields of single neurones in the cat’s striate cortex
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Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex
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Engineering applications of noncommutative harmonic analysis: with emphasis on rotation and motion groups
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The neurogeometry of pinwheels as a sub-Riemannian contact structure
Jean Petitot · 2003
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Perceptual organization in image analysis
R. Duits · 2005
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A cortical based model of perceptual completion in the roto-translation space
Giovanna Citti and Alessandro Sarti · 2006
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M.A. Almsick, van · 2007
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Fast and accurate Gaussian derivatives based on B-splines
Henri Bouma, Anna Vilanova, Javier Oliván Bescós, Bart M ter Haar Romeny, and Frans A Gerritsen · 2007
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Scale spaces on Lie groups
Remco Duits and Bernhard Burgeth · 2007
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Enhancement of crossing elongated structures in images
Erik M Franken · 2008
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Crossing-preserving coherence-enhancing diffusion on invertible orientation scores
Erik Franken and Remco Duits · 2009
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Transforming auto-encoders
Geoffrey E Hinton, Alex Krizhevsky, and Sida D Wang · 2011
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Association fields via cuspless sub-Riemannian geodesics in SE (2)
Remco Duits, Ugo Boscain, Francesco Rossi, and Yuri Sachkov · 2014
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Deep symmetry networks
Robert Gens and Pedro M Domingos · 2014
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Spatial transformer networks
Max Jaderberg, Karen Simonyan, Andrew Zisserman, and others · 2015
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Deep Learning Face Attributes in the Wild
Ziwei Liu, Ping Luo, Xiaogang Wang, and Xiaoou Tang · 2015
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Deep roto-translation scattering for object classification
Edouard Oyallon and Stéphane Mallat · 2015
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New approximation of a scale space kernel on SE (3) and applications in neuroimaging
Jorg Portegies, Gonzalo Sanguinetti, Stephan Meesters, and Remco Duits · 2015
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Group equivariant convolutional networks
Taco S Cohen and Max Welling · 2016
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Exploiting cyclic symmetry in convolutional neural networks
Sander Dieleman, Jeffrey De Fauw, and Koray Kavukcuoglu · 2016
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Roto-Translation Covariant Convolutional Networks for Medical Image Analysis
Erik J Bekkers, Maxime W Lafarge, Mitko Veta, Koen A J Eppenhof, Josien P W Pluim, and Remco Duits · 2018
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Optimal Paths for Variants of the 2d and 3d Reeds–Shepp Car with Applications in Image Analysis
R. Duits, S. P. L. Meesters, J.-M. Mirebeau, and J. M. Portegies · 2018
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SplineCNN: Fast geometric deep learning with continuous B-spline kernels
Matthias Fey, Jan Eric Lenssen, Frank Weichert, and Heinrich Müller · 2018
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HexaConv
Emiel Hoogeboom, Jorn WT Peters, Taco S Cohen, and Max Welling · 2018
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On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
Risi Kondor and Shubhendu Trivedi · 2018
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Analysis of vessel connectivities in retinal images by cortically inspired spectral clustering
Marta Favali, Samaneh Abbasi-Sureshjani, Bart ter Haar Romeny, and Alessandro Sarti · 2016
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Multi-Scale Context Aggregation by Dilated Convolutions
Fisher Yu and Vladlen Koltun · 2016
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Template matching via densities on the roto-translation group
Erik J Bekkers, Marco Loog, Bart M ter Haar Romeny, and Remco Duits · 2017
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DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs
L. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. Yuille · 2017
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Babak Ehteshami Bejnordi, Mitko Veta, Paul Johannes van Diest, Bram van Ginneken, Nico Karssemeijer, Geert Litjens, Jeroen A. W. M. van der Laak, and and the CAMELYON16 Consortium · 2017
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Group equivariant capsule networks
Jan Eric Lenssen, Matthias Fey, and Pascal Libuschewski · 2018
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Scale equivariance in CNNs with vector fields
Diego Marcos, Benjamin Kellenberger, Sylvain Lobry, and Devis Tuia · 2018
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Tensor Field Networks: Rotation-and Translation-Equivariant Neural Networks for 3d Point Clouds
Nathaniel Thomas, Tess Smidt, Steven Kearnes, Lusann Yang, Li Li, Kai Kohlhoff, and Patrick Riley · 2018
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Rotation Equivariant CNNs for Digital Pathology
Bastiaan S. Veeling, Jasper Linmans, Jim Winkens, Taco Cohen, and Max Welling · 2018
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3d Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler, Mario Geiger, Max Welling, Wouter Boomsma, and Taco Cohen · 2018
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3d G-CNNs for Pulmonary Nodule Detection
Marysia Winkels and Taco S Cohen · 2018
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CubeNet: Equivariance to 3d Rotation and Translation
Daniel Worrall and Gabriel Brostow · 2018
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Exploring local rotation invariance in 3d {CNN}s with steerable filters
Vincent Andrearczyk, Julien Fageot, Valentin Oreiller, Xavier Montet, and Adrien Depeursinge · 2019
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Gauge Equivariant Convolutional Networks and the Icosahedral CNN
Taco Cohen, Maurice Weiler, Berkay Kicanaoglu, and Max Welling · 2019
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Noemi Montobbio, Giovanna Citti, and Alessandro Sarti · 2019
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Daniel E Worrall and Max Welling · 2019
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