DiffusionNet: Discretization Agnostic Learning on Surfaces

  title={DiffusionNet: Discretization Agnostic Learning on Surfaces},
  author={Nicholas Sharp and Souhaib Attaiki and Keenan Crane and Maks Ovsjanikov},
  journal={ACM Transactions on Graphics (TOG)},
  pages={1 - 16}
We introduce a new general-purpose approach to deep learning on three-dimensional surfaces based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in resolution and sampling of a surface—a basic property that is crucial for practical applications. Our networks can be discretized on various geometric representations, such as triangle meshes or point clouds, and can even be trained on one… 

Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching

This work presents a novel non-rigid shape matching framework based on multi-resolution functional maps with spectral attention that is applicable in both supervised and unsupervised settings, and shows that it is possible to train the network so that it can adapt the spectral resolution, depending on the given shape input.

SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence

A novel learning-based framework that combines the local accuracy of contrastive learning with the global consistency of geometric approaches, for robust non-rigid matching, applicable to local feature learning in both the 3D and 2D domains is presented.

Unsupervised Deep Multi-Shape Matching

A novel approach for deep multi-shape matching that ensures cycle-consistent multi-matchings while not depending on an explicit template shape is presented, and it is demonstrated that the unsupervised method even outperforms recent supervised methods.

DeltaConv: Anisotropic Geometric Deep Learning with Exterior Calculus

A new convolution operator is introduced called DeltaConv, which combines geometric operators from exterior calculus to enable the construction of anisotropic filters on point clouds and shows improved accuracy compared to state-of-the-art approaches on several benchmarks, while also speeding up training and inference.

DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds

DeltaConv,aconvolutionlayer is introduced that combinesgeometricoperators fromvectorcalculustoenable theconstruction of anisotropicfiltersonpointclouds and co-ordinatesystemfortangentialdirectionsonsurfaces.

An introduction to deep learning on meshes

This course aims to take a deep dive into the discrete mesh representation, the most popular representation for shapes in computer graphics and provides different ways of covering aspects of deep learning on meshes for the virtual audience.

Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks

OAVNN is a rotation equivariant network that is robust to planar symmetric inputs that includes a symmetry-sensitive orientation aware linear layer and an attention mechanism that relates directional information across points.

Discretization-Agnostic Deep Self-Supervised 3D Surface Parameterization

A novel self-supervised framework that enables learning a discretization-agnostic parameterization at a lower resolution and then directly inferring the parameterization for a higher-resolution mesh without retraining is presented.

Anisotropic Multi-Scale Graph Convolutional Network for Dense Shape Correspondence

A novel hybrid geometric deep learning-based model that learns geometrically meaningful and discretization-independent features with a U-Net model as the primary node feature extraction module, followed by a successive spectral-based graph convolutional network is introduced.


This work presents a new GNN architecture called Graph Anisotropic Diffusion, which alters-nates between linear diffusion, for which a closed-form solution is available, and local anisotropic filters to obtain efficient multi-hop an isotropic kernels.



A Concise and Provably Informative Multi‐Scale Signature Based on Heat Diffusion

The Heat Kernel Signature, called the HKS, is obtained by restricting the well‐known heat kernel to the temporal domain and shows that under certain mild assumptions, HKS captures all of the information contained in the heat kernel, and characterizes the shape up to isometry.

Shape correspondence using anisotropic Chebyshev spectral CNNs

A novel architecture for shape correspondence, termed Anisotropic Chebyshev spectral CNNs (ACSCNNs), based on a new extension of the manifold convolution operator, that is able to provide better than the state-of-the-art results in several datasets even if using constant functions as inputs.

MeshCNN: a network with an edge

This paper utilizes the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes, and demonstrates the effectiveness of MeshCNN on various learning tasks applied to 3D meshes.

Dynamic Graph CNN for Learning on Point Clouds

This work proposes a new neural network module suitable for CNN-based high-level tasks on point clouds, including classification and segmentation called EdgeConv, which acts on graphs dynamically computed in each layer of the network.

PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation

This paper designs a novel type of neural network that directly consumes point clouds, which well respects the permutation invariance of points in the input and provides a unified architecture for applications ranging from object classification, part segmentation, to scene semantic parsing.

Geodesic Convolutional Neural Networks on Riemannian Manifolds

Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional neural networks (CNN) paradigm to non-Euclidean manifolds is introduced, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.

FAUST: Dataset and Evaluation for 3D Mesh Registration

A novel mesh registration technique that combines 3D shape and appearance information to produce high-quality alignments is addressed with a new dataset called FAUST that contains 300 scans of 10 people in a wide range of poses together with an evaluation methodology.

ARPACK users' guide - solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods

The Arnoldi factorization, the implicitly restarted Arnoldi method: structure of the Eigenvalue problem Krylov subspaces and projection methods, and more.

Field Convolutions for Surface CNNs

This formulation combines intrinsic spatial convolution with parallel transport in a scattering operation while placing no constraints on the filters themselves, providing a definition of convolution that commutes with the action of isometries, has increased descriptive potential, and is robust to noise and other nuisance factors.

Primal-Dual Mesh Convolutional Neural Networks

This work extends a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and defines convolutions on two types of graphs constructed from an input mesh, and introduces a pooling operation that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion.