Convolutional neural networks on surfaces via seamless toric covers

By Haggai Maron, Meirav Galun, Noam Aigerman, M. Trope, Nadav Dym, Ersin Yumer, Vladimir G. Kim, Yaron Lipman. 2017

246 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Geology, Model Architectures, 3D Vision & Pose

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Citations in the corpus

Generating 3D faces using Convolutional Mesh Autoencoders (2018, background): “[30] embed mesh surfaces into planar images to apply conventional CNNs.”
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.”
DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation (2019, methodology): “Other mesh-based methods use existing [48, 36] or learned [22, 23] parameterization techniques to describe 3D surfaces by morphing 2D planes.”
A Papier-Mache Approach to Learning 3D Surface Generation (2018, neutral): “Various other parameterization techniques, such as local polar coordinates [22, 4] and global seamless maps [21] have been used for deep learning on 2-manifolds.”
3D shape segmentation via shape fully convolutional networks (2017, neutral): “[32] using a global seam-less parameterization for which the convolution operator is well deﬁned but can only be used on sphere-like meshes.”
Spherical CNNs on Unstructured Grids (2019, methodology): “Masci et al. (2015) perform convolutions directly on manifolds using cross-correlation based on geodesic distances and Maron et al. (2017) use an optimal surface parameterization method (seamless toric covers) to parameterize genus-zero shapes into 2D signals for analysis using conventional planar…”
PointCNN: Convolution On X-Transformed Points (2018, background): “Besides point cloud, sparse data in irregular domains can be represented as graphs, or meshes, and a line of work have been proposed for feature learning from such representations [31, 55, 30].”
DiffusionNet: Discretization Agnostic Learning on Surfaces (2020, methodology): “We train a 128-width DiffusionNet with dropout to segment the human body parts on the composite dataset of [Maron et al. 2017], containing models from several other human shape datasets [Adobe 2016; Anguelov et al.”
MeshCNN: a network with an edge (2019, methodology): “The final segmentation predictions from MeshCNN semantic segmentation network with pooling and unrolling layers on a (held out) test set is shown in Figure 9.”
BSP-Net: Generating Compact Meshes via Binary Space Partitioning (2019, methodology): “Few deep networks can generate polygonal meshes directly, and such methods are limited to genus-zero meshes [17, 27, 44], piece-wise genus-zero [12] meshes, meshes sharing the same connectivity [11, 41], or meshes with very low number of vertices [7].”
Surface Networks (2017, background): “More recently, [24] proposes to learn surface convolutional network from a canonical representation of planar flat-torus, with excellent performance on shape segmentation and classification, although such canonical representations may introduce exponential scale changes that can introduce instabilit”
SAL: Sign Agnostic Learning of Shapes From Raw Data (2019, methodology): “[32, 33] use geometry images as global parameterizations, while [27] use conformal global parameterizations to reduce the number of degrees of freedom of the map.”
Tangent Convolutions for Dense Prediction in 3D (2018, background): “[32] design ConvNets on surfaces for sphere-type shapes.”
ABC: A Big CAD Model Dataset for Geometric Deep Learning (2018, background): “More recently, [39] presented a surface CNN based on the canonical representation of planar ﬂat-torus.”
Graph Element Networks: adaptive, structured computation and memory (2019, background): “The ﬁeld of geometric deep-learning (Bronstein et al., 2017) aims to build deep networks for graphs (Bruna et al., 2013; Defferrard et al., 2016; Kipf & Welling, 2016) and non-Euclidean manifolds (Maron et al., 2017).”
Deep Learning 3D Shapes Using Alt-az Anisotropic 2-Sphere Convolution (2018, background): “Toric covers (Maron et al. (2017)) is a seamless representation which stitches four copies of a genus-0 surface and globally maps them onto a planar flat torus.”
3D-CODED: 3D Correspondences by Deep Deformation (2018, background): “…on various shape representations, such as volumetric grids [17,47], point clouds [34,35,16], geometry images [39,38], seamlessly parameterized surfaces [26], by aligning a shape to a grid via distance-preserving maps [15], by folding a surface [48] or by predicting chart representations [18].”