ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

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

61 citations recorded by the source corpus.

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we propose ShapeNet, a generalization of the popular convolutional neural networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use ShapeNet to learn invariant shape feature descriptors that significantly outperform recent state-of-the-art methods, and show that previous approaches such as heat and wave kernel signatures, optimal spectral descriptors, and intrinsic shape contexts can be obtained as particular configurations of ShapeNet.

Subfields: Model Architectures, Graph Learning

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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.”
Deep Convolutional Networks on Graph-Structured Data (2015, background): “More recently, [12] introduced Shapenet, another generalization of convolutions on non-Euclidean domains based on geodesic polar coordinates, which was successfully applied to shape analysis, and allows comparison across different manifolds.”
Molecular graph convolutions: moving beyond fingerprints (2016, methodology): “Convolutional networks on non-Euclidean mani-2 folds were described by Masci et al. (2015).”
Parallel Transport Convolution: A New Tool for Convolutional Neural Networks on Manifolds (2018, methodology): “In addition, there is another recent method discussed in [24], in which convolution is directly considered on the spatial domain using local integral on geodesic disc although it does not involve manifold structure as transportation on manifold is not considered.”
Deep Learning 3D Shape Surfaces Using Geometry Images (2016, methodology): “Hence, CNN-based deformable shape analysis methods propose the use of geodesic convolutional filters as patches or model spectral-CNN’s using the eigen decomposition of the Laplace-Beltrami operator to derive robust shape descriptors [1,6,19].”