DiffusionNet: Discretization Agnostic Learning on Surfaces

@article{Sharp2022DiffusionNetDA,
  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)},
  year={2022},
  volume={41},
  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… 

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References

SHOWING 1-10 OF 128 REFERENCES

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.
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