CNNs on Surfaces using Rotation-Equivariant Features

• URL: http://arxiv.org/abs/2006.01570v1
• Date: Tue, 2 Jun 2020 12:46:00 GMT
• Title: CNNs on Surfaces using Rotation-Equivariant Features
• Authors: Ruben Wiersma, Elmar Eisemann, Klaus Hildebrandt
• Abstract summary: Transport of filter kernels on surfaces results in a rotational ambiguity, which prevents a uniform alignment of these kernels on the surface. We propose a network architecture for surfaces that consists of vector-valued, rotation-equivariant features. We evaluate the resulting networks on shape correspondence and shape classifications tasks and compare their performance to other approaches.
• Score: 10.259432250871997
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper is concerned with a fundamental problem in geometric deep learning that arises in the construction of convolutional neural networks on surfaces. Due to curvature, the transport of filter kernels on surfaces results in a rotational ambiguity, which prevents a uniform alignment of these kernels on the surface. We propose a network architecture for surfaces that consists of vector-valued, rotation-equivariant features. The equivariance property makes it possible to locally align features, which were computed in arbitrary coordinate systems, when aggregating features in a convolution layer. The resulting network is agnostic to the choices of coordinate systems for the tangent spaces on the surface. We implement our approach for triangle meshes. Based on circular harmonic functions, we introduce convolution filters for meshes that are rotation-equivariant at the discrete level. We evaluate the resulting networks on shape correspondence and shape classifications tasks and compare their performance to other approaches.

Related papers

• Differential Geometry in Neural Implicits [0.6198237241838558]
  We introduce a neural implicit framework that bridges discrete differential geometry of triangle meshes and continuous differential geometry of neural implicit surfaces. It exploits the differentiable properties of neural networks and the discrete geometry of triangle meshes to approximate them as the zero-level sets of neural implicit functions.
  arXiv  Detail & Related papers  (2022-01-23T13:40:45Z)
• Field Convolutions for Surface CNNs [19.897276088740995]
  We present a novel surface convolution operator acting on vector fields based on a simple observation. This formulation combines intrinsic spatial convolution with parallel transport in a scattering operation. We achieve state-of-the-art results on standard benchmarks in fundamental geometry processing tasks.
  arXiv  Detail & Related papers  (2021-04-08T17:11:14Z)
• Deep Positional and Relational Feature Learning for Rotation-Invariant Point Cloud Analysis [107.9979381402172]
  We propose a rotation-invariant deep network for point clouds analysis. The network is hierarchical and relies on two modules: a positional feature embedding block and a relational feature embedding block. Experiments show state-of-the-art classification and segmentation performances on benchmark datasets.
  arXiv  Detail & Related papers  (2020-11-18T04:16:51Z)
• Primal-Dual Mesh Convolutional Neural Networks [62.165239866312334]
  We propose a primal-dual framework drawn from the graph-neural-network literature to triangle meshes. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them. We provide theoretical insights of our approach using tools from the mesh-simplification literature.
  arXiv  Detail & Related papers  (2020-10-23T14:49:02Z)
• Neural Subdivision [58.97214948753937]
  This paper introduces Neural Subdivision, a novel framework for data-driven coarseto-fine geometry modeling. We optimize for the same set of network weights across all local mesh patches, thus providing an architecture that is not constrained to a specific input mesh, fixed genus, or category. We demonstrate that even when trained on a single high-resolution mesh our method generates reasonable subdivisions for novel shapes.
  arXiv  Detail & Related papers  (2020-05-04T20:03:21Z)
• A Rotation-Invariant Framework for Deep Point Cloud Analysis [132.91915346157018]
  We introduce a new low-level purely rotation-invariant representation to replace common 3D Cartesian coordinates as the network inputs. Also, we present a network architecture to embed these representations into features, encoding local relations between points and their neighbors, and the global shape structure. We evaluate our method on multiple point cloud analysis tasks, including shape classification, part segmentation, and shape retrieval.
  arXiv  Detail & Related papers  (2020-03-16T14:04:45Z)
• PUGeo-Net: A Geometry-centric Network for 3D Point Cloud Upsampling [103.09504572409449]
  We propose a novel deep neural network based method, called PUGeo-Net, to generate uniform dense point clouds. Thanks to its geometry-centric nature, PUGeo-Net works well for both CAD models with sharp features and scanned models with rich geometric details.
  arXiv  Detail & Related papers  (2020-02-24T14:13:29Z)
• Quaternion Equivariant Capsule Networks for 3D Point Clouds [58.566467950463306]
  We present a 3D capsule module for processing point clouds that is equivariant to 3D rotations and translations. We connect dynamic routing between capsules to the well-known Weiszfeld algorithm. Based on our operator, we build a capsule network that disentangles geometry from pose.
  arXiv  Detail & Related papers  (2019-12-27T13:51:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.