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A common approach to define convolutions on meshes is to interpret them as a graph and apply graph convolutional networks (GCNs).
Spherical u-net on cortical surfaces: Methods and applications
Zhao, F., Xia, S., Wu, Z., Duan, D., Wang, L., Lin, W., Gilmore, J. H., Shen, D., and Li, G · 1904
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General E(2)-equivariant steerable CNNs
Weiler, M. and Cesa, G · 1911
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Quaternion equivariant capsule networks for 3d point clouds
Zhao, Y., Birdal, T., Lenssen, J. E., Menegatti, E., Guibas, L., and Tombari, F · 1912
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Linear representations of finite groups
Serre, J.-P · 1977
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Metric-driven rosy field design and remeshing
Lai, Y.-K., Jin, M., Xie, X., He, Y., Palacios, J., Zhang, E., Hu, S.-M., and Gu, X · 2009
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Trivial connections on discrete surfaces
Crane, K., Desbrun, M., and Schröder, P · 2010
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Unique signatures of histograms for local surface description
Tombari, F., Salti, S., and Di Stefano, L · 2010
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Digital geometry processing with discrete exterior calculus
Crane, K., de Goes, F., Desbrun, M., and Schröder, P · 2013
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Faust: Dataset and evaluation for 3d mesh registration
Bogo, F., Romero, J., Loper, M., and Black, M. J · 2014
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Geodesic convolutional neural networks on riemannian manifolds
Masci, J., Boscaini, D., Bronstein, M. M., and Vandergheynst, P · 2015
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3d shapenets: A deep representation for volumetric shapes
Wu, Z., Song, S., Khosla, A., Yu, F., Zhang, L., Tang, X., and Xiao, J · 2015
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Learning shape correspondence with anisotropic convolutional neural networks
Boscaini, D., Masci, J., Rodolà, E., and Bronstein, M. M · 2016
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Group equivariant convolutional networks
Cohen, T. and Welling, M · 2016
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Convolutional neural networks on graphs with fast localized spectral filtering
Defferrard, M., Bresson, X., and Vandergheynst, P · 2016
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Geometric deep learning on graphs and manifolds using mixture model cnns
Monti, F., Boscaini, D., Masci, J., Rodolà, E., Svoboda, J., and Bronstein, M. M · 2016
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Geometric deep learning: Going beyond Euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., and Vandergheynst, P · 2017
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Steerable CNNs
Cohen, T. S. and Welling, M · 2017
Cited alongside, same era.
Semi-Supervised Classification with Graph Convolutional Networks
Kipf, T. N. and Welling, M · 2017
Cited alongside, same era.
Convolutional neural networks on surfaces via seamless toric covers
Maron, H., Galun, M., Aigerman, N., Trope, M., Dym, N., Yumer, E., Kim, V. G., and Lipman, Y · 2017
Cited alongside, same era.
Octnet: Learning deep 3d representations at high resolutions
Riegler, G., Osman Ulusoy, A., and Geiger, A · 2017
Cited alongside, same era.
Segcloud: Semantic segmentation of 3d point clouds
Tchapmi, L., Choy, C., Armeni, I., Gwak, J., and Savarese, S · 2017
Cited alongside, same era.
Differential geometry: connections, curvature, and characteristic classes , volume 275
Tu, L. W · 2017
Cited alongside, same era.
Sun, Z., Rooke, E., Charton, J., He, Y., Lu, J., and Baek, S · 2018
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Tensor Field Networks: Rotation- and Translation-Equivariant Neural Networks for 3D Point Clouds
Thomas, N., Smidt, T., Kearnes, S., Yang, L., Li, L., Kohlhoff, K., and Riley, P · 2018
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Feastnet: Feature-steered graph convolutions for 3d shape analysis
Verma, N., Boyer, E., and Verbeek, J · 2018
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3D G-CNNs for pulmonary nodule detection
Winkels, M. and Cohen, T. S · 2018
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Cubenet: Equivariance to 3D rotation and translation
Worrall, D. E. and Brostow, G. J · 2018
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Harmonic Networks: Deep Translation and Rotation Equivariance
Worrall, D. E., Garbin, S. J., Turmukhambetov, D., and Brostow, G. J · 2017
Cited alongside, same era.
Roto-translation covariant convolutional networks for medical image analysis
Bekkers, E. J., Lafarge, M. W., Veta, M., Eppenhof, K. A., Pluim, J. P., and Duits, R · 2018
Cited alongside, same era.
Convolutional neural networks for mesh-based parcellation of the cerebral cortex
Cucurull, G., Wagstyl, K., Casanova, A., Veličković, P., Jakobsen, E., Drozdzal, M., Romero, A., Evans, A., and Bengio, Y · 2018
Cited alongside, same era.
Alignet: Partial-shape agnostic alignment via unsupervised learning
Hanocka, R., Fish, N., Wang, Z., Giryes, R., Fleishman, S., and Cohen-Or, D · 2018
Cited alongside, same era.
HexaConv
Hoogeboom, E., Peters, J. W. T., Cohen, T. S., and Welling, M · 2018
Cited alongside, same era.
Clebsch-gordan nets: a fully fourier space spherical convolutional neural network
Kondor, R., Lin, Z., and Trivedi, S · 2018
Cited alongside, same era.
Bouritsas, G., Bokhnyak, S., Ploumpis, S., Bronstein, M., and Zafeiriou, S · 2019
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Spiralnet++: A fast and highly efficient mesh convolution operator
Gong, S., Chen, L., Bronstein, M., and Zafeiriou, S · 2019
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Deepsphere: Efficient spherical convolutional neural network with healpix sampling for cosmological applications
Perraudin, N., Defferrard, M., Kacprzak, T., and Sgier, R · 2019
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Deep scale-spaces: Equivariance over scale
Worrall, D. and Welling, M · 2019
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Differential Geometry and Lie Groups: A Computational Perspective , volume 12
Gallier, J. and Quaintance, J · 2020
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A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels
Lang, L. and Weiler, M · 2020
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Scale-equivariant steerable networks
Sosnovik, I., Szmaja, M., and Smeulders, A · 2020
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CNNs on Surfaces using Rotation-Equivariant Features
Wiersma, R., Eisemann, E., and Hildebrandt, K · 2020
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Steerable partial differential operators for equivariant neural networks
Jenner, E. and Weiler, M · 2021
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Weiler, M., Forré, P., Verlinde, E., and Welling, M · 2021
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