Learning shape correspondence with anisotropic convolutional neural networks

Abstract

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks.

Cited by in corpus (44)

• Geometric deep learning: going beyond Euclidean data
• MeshCNN: A Network with an Edge
• Deep Continuous Fusion for Multi-Sensor 3D Object Detection
• Residual Gated Graph ConvNets
• DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications
• Graph-based Spatial-temporal Feature Learning for Neuromorphic Vision Sensing
• SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters
• 3D Point Cloud Classification and Segmentation using 3D Modified Fisher Vector Representation for Convolutional Neural Networks
• SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation
• Tangent Convolutions for Dense Prediction in 3D
• Triplet-Center Loss for Multi-View 3D Object Retrieval
• Geometric deep learning on graphs and manifolds using mixture model CNNs
• Dual-Primal Graph Convolutional Networks
• Generating 3D faces using Convolutional Mesh Autoencoders
• Efficient Deformable Shape Correspondence via Kernel Matching
• ZerNet: Convolutional Neural Networks on Arbitrary Surfaces via Zernike Local Tangent Space Estimation
• PFCNN: Convolutional Neural Networks on 3D Surfaces Using Parallel Frames
• PointGrow: Autoregressively Learned Point Cloud Generation with Self-Attention
• PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations
• Single Image 3D Hand Reconstruction with Mesh Convolutions
• Graph Neural Networks for IceCube Signal Classification
• DAR-Net: Dynamic Aggregation Network for Semantic Scene Segmentation
• FeaStNet: Feature-Steered Graph Convolutions for 3D Shape Analysis
• HeterSkinNet: A Heterogeneous Network for Skin Weights Prediction
• Graph-Based Object Classification for Neuromorphic Vision Sensing
• SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator
• A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes
• Graph Signal Processing: Overview, Challenges and Applications
• FrameNet: Learning Local Canonical Frames of 3D Surfaces from a Single RGB Image
• Mesh-based Autoencoders for Localized Deformation Component Analysis
• Graph Convolutions on Spectral Embeddings: Learning of Cortical Surface Data
• Angular Triplet-Center Loss for Multi-view 3D Shape Retrieval
• SurfConv: Bridging 3D and 2D Convolution for RGBD Images
• Recovering Geometric Information with Learned Texture Perturbations
• Learning Local Shape Descriptors from Part Correspondences With Multi-view Convolutional Networks
• Latent Space Representation for Shape Analysis and Learning
• 3D Shape Segmentation with Geometric Deep Learning
• Deep Learning Parametrization for B-Spline Curve Approximation
• MeshCNN Fundamentals: Geometric Learning through a Reconstructable Representation
• Revisiting convolutional neural network on graphs with polynomial approximations of Laplace-Beltrami spectral filtering
• Multi-Kernel Diffusion CNNs for Graph-Based Learning on Point Clouds
• Wall Stress Estimation of Cerebral Aneurysm based on Zernike Convolutional Neural Networks
• 3D-MOV: Audio-Visual LSTM Autoencoder for 3D Reconstruction of Multiple Objects from Video
• Learning Spectral Transform Network on 3D Surface for Non-rigid Shape Analysis