Geodesic Convolutional Neural Networks on Riemannian Manifolds

By Jonathan Masci, Davide Boscaini, Michael M. Bronstein, Pierre Vandergheynst. 2015

789 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Geometry and Topology, Model Architectures

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Citations in the corpus

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, background): “This paper introduces the mathematical and computational foundations of such models, while future developments may consider to enhance the building blocks, namely graph filtering and coarsening.”
Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs (2016, methodology): “Such a construction allows to formulate previously proposed Geodesic CNN (GCNN) [32] and Anisotropic CNN (ACNN) [7] on manifolds or GCN [26] and DCNN [2] on graphs as particular instances of our approach.”
PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation (2016, background): “Spectral CNNs: Some latest works [4, 14] use spectral CNNs on meshes.”
PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space (2017, background): “In 3D metric space, other than point set, there are several popular representations for deep learning, including volumetric grids [21; 22; 29], and geometric graphs [3; 15; 33].”
RealPoint3D: Point Cloud Generation from a Single Image with Complex Background (2018, methodology): “Beside point clouds, many frameworks have been proposed for meshes representation, such as (Bronstein et al. 2016), spectral graph CNN (Yi et al. 2017) and Geodesic CNN (GCNN) (Masci et al. 2015).”
Molecular graph convolutions: moving beyond fingerprints (2016, methodology): “Convolutional networks on non-Euclidean mani-2 folds were described by Masci et al. (2015).”
SchNet: A continuous-filter convolutional neural network for modeling quantum interactions (2017, neutral): “, for graphs [29, 30] and 3d shapes[31].”
Cormorant: Covariant Molecular Neural Networks (2019, background): “Similar ideas underly generalizations of CNNs to manifolds [Masci et al., 2015, Monti et al., 2016, Bronstein et al., 2017] and graphs [Bruna et al., 2014, Henaff et al., 2015].”
Gauge Equivariant Convolutional Networks and the Icosahedral CNN (2019, methodology): “We also evaluate a model that uses only scalar-to-regular (S2R) convolution layers, followed by orientation pooling (a max over the 6 orientation channels of each regular feature, thus mapping a regular feature to a scalar), as in (Masci et al., 2015).”
Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network (2018, background): “The starting point for our Generalized Spherical CNNs is the Fourier space correlation formula (10).”
Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks (2017, background): “, 2016) techniques that can mathematically deal with graph-structured data, which arises in numerous applications, ranging from computer graphics and vision (Masci et al., 2015; Boscaini et al., 2015; 2016b;a; Monti et al., 2017) to chemistry (Duvenaud et al.”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “The purpose of this paper is to overview the problems arising in relation to geometric deep learning and present solutions existing today for this class of problems, as well as key difﬁculties and future research directions.”
Deep Learning on Lie Groups for Skeleton-Based Action Recognition (2016, methodology): “Moreover, recently some deep learning models have emerged [10, 7, 28, 25, 18, 21] that deal with data in a nonEuclidean domain.”
SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation (2016, background): “There have been some previous works studying graph CNN on more general graphs instead of 2D regular grids [3, 6, 8, 5], and [19, 1, 2] have a special focus on 3D shape graphs like human bodies.”
Generating 3D faces using Convolutional Mesh Autoencoders (2018, methodology): “This method resembles the intrinsic mesh convolution of [31] and [5] for specific choices of the weight functions.”
Dynamic Graph CNN for Learning on Point Clouds (2018, methodology): “The Geodesic CNN (GCNN) is a deep CNN on meshes generalizing the notion of patches using local intrinsic parameterization [Masci et al. 2015].”
SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017, methodology): “[18, 2, 17, 16], we go without handcrafted feature descriptors as inputs, like the local histogram of normal vectors known as SHOT descriptors [24], and force the network to learn from the geometry (i.”
PCPNet Learning Local Shape Properties from Raw Point Clouds (2017, methodology): “However, several methods have also been proposed for shape segmentation [GZC15,MGA ∗ 17] and even shape correspondence [MBBV15,WHC ∗ 16,BMRB16], among many others.”
Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs (2017, neutral): “[24] define convolution over patch descriptors around every vertex of a 3D mesh using geodesic distances, formulated in a deep learning architecture.”