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DiffusionNet: Discretization Agnostic Learning on Surfaces
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In this paper, a simple diffusion layer is proposed for spatial communication on 3D mesh surfaces, and the spatial support of diffusion is optimized as a continuous network parameter ranging from purely local to totally global, removing the burden of manually choosing neighborhood sizes.Abstract:
We introduce a new approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks automatically generalize across different samplings and resolutions of a surface -- a basic property which 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 representation then applied to another. We optimize the spatial support of diffusion as a continuous network parameter ranging from purely local to totally global, removing the burden of manually choosing neighborhood sizes. The only other ingredients in the method are a multi-layer perceptron applied independently at each point, and spatial gradient features to support directional filters. The resulting networks are simple, robust, and efficient. Here, we focus primarily on triangle mesh surfaces, and demonstrate state-of-the-art results for a variety of tasks including surface classification, segmentation, and non-rigid correspondence.read more
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Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization
TL;DR: SyNoRiM as mentioned in this paper is a method to jointly register multiple non-rigid shapes by synchronizing the maps relating learned functions defined on the point clouds, which achieves state-of-the-art performance in registration accuracy.
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Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes
Sara Hahner,Jochen Garcke +1 more
TL;DR: In this article, the authors transform the discretization of the surfaces to semi-regular meshes that have a locally regular connectivity and whose meshing is hierarchical, and they apply the same spatial convolutional filters to the local neighborhoods and define a pooling operator that can be applied to every semiregular mesh and visualize the underlying dynamics of unseen mesh sequences with an autoencoder trained on different classes of meshes.
Journal ArticleDOI
Self-Supervised Learning for Non-Rigid Registration Between Near-Isometric 3D Surfaces in Medical Imaging
TL;DR: Li et al. as discussed by the authors proposed a self-supervised method to learn shape correspondences directly from a group of bone surfaces segmented from CT scans, without any supervision from time-consuming and error-prone manual annotations.
Journal ArticleDOI
Multi Point-Voxel Convolution (MPVConv) for deep learning on point clouds
TL;DR: Wu et al. as mentioned in this paper proposed a new convolutional neural network, called Multi Point-Voxel Convolution (MPVConv), for deep learning on point clouds.
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DPFM: Deep Partial Functional Maps.
TL;DR: DPFM as discussed by the authors uses the functional map framework, which can be trained in a supervised or unsupervised manner, and learns descriptors directly from the data, thus both improving robustness and accuracy in challenging cases.
References
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Book ChapterDOI
A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes
TL;DR: In this paper, the authors investigate whether such resampling operations can be avoided, and propose a simple and direct encoding approach, which does not only increase processing efficiency due to its simplicity but also avoids any loss in data fidelity.
Proceedings Article
Primal-Dual Mesh Convolutional Neural Networks
TL;DR: In this article, a primal-dual framework is proposed to aggregate features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism, which can handle variations in the mesh connectivity by clustering mesh faces in a task-driven fashion.
Journal ArticleDOI
CNNs on surfaces using rotation-equivariant features
TL;DR: In this article, the authors propose a network architecture for surfaces that consists of vector-valued, rotation-equivariant features, which makes it possible to locally align features which were computed in arbitrary coordinate systems, when aggregating features in a convolution layer.
Journal ArticleDOI
MeshWalker: deep mesh understanding by random walks
Alon Lahav,Ayellet Tal +1 more
TL;DR: MeshWalker as discussed by the authors proposes to represent the mesh by random walks along the surface, which "explore" the mesh's geometry and topology, and feed the walk into a Recurrent Neural Network (RNN) that "remembers" the history of the walk.