# Learning shape correspondence with anisotropic convolutional neural networks

arXiv: https://arxiv.org/abs/1605.06437 · HTML: https://mlsanity.com/paper/1605.06437/

## Key facts

- Cited by 95 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2016.

## Built on by (most cited first, 30 of 95)

- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [DPFM: Deep Partial Functional Maps](https://mlsanity.com/paper/2110.09994/) (2021)
- [Unsupervised Deep Multi-Shape Matching](https://mlsanity.com/paper/2207.09610/) (2022)
- [Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matching](https://mlsanity.com/paper/2204.13453/) (2022)
- [Learning Multi-resolution Functional Maps with Spectral Attention for Robust Shape Matching](https://mlsanity.com/paper/2210.06373/) (2022)
- [BuildingNet: Learning to Label 3D Buildings](https://mlsanity.com/paper/2110.04955/) (2021)
- [Zero-Shot 3D Shape Correspondence](https://mlsanity.com/paper/2306.03253/) (2023)
- [Generalized Simplicial Attention Neural Networks](https://mlsanity.com/paper/2309.02138/) (2023)
- [ACID: Action-Conditional Implicit Visual Dynamics for Deformable Object Manipulation](https://mlsanity.com/paper/2203.06856/) (2022)
- [Flattening-Net: Deep Regular 2D Representation for 3D Point Cloud Analysis](https://mlsanity.com/paper/2212.08892/) (2022)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [pathGCN: Learning General Graph Spatial Operators from Paths](https://mlsanity.com/paper/2207.07408/) (2022)
- [Surrogate Modeling of Car Drag Coefficient with Depth and Normal Renderings](https://mlsanity.com/paper/2306.06110/) (2023)
- [Field Convolutions for Surface CNNs](https://mlsanity.com/paper/2104.03916/) (2021)
- [DEBOSH: Deep Bayesian Shape Optimization](https://mlsanity.com/paper/2109.13337/) (2021)
- [Learning Feature Aggregation for Deep 3D Morphable Models](https://mlsanity.com/paper/2105.02173/) (2021)
- [Implicit field supervision for robust non-rigid shape matching](https://mlsanity.com/paper/2203.07694/) (2022)
- [SRFeat: Learning Locally Accurate and Globally Consistent Non-Rigid Shape Correspondence](https://mlsanity.com/paper/2209.07806/) (2022)
- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations](https://mlsanity.com/paper/2201.09656/) (2021)
- [Deep Structural Causal Shape Models](https://mlsanity.com/paper/2208.10950/) (2022)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [Finsler-Laplace-Beltrami Operators with Application to Shape Analysis](https://mlsanity.com/paper/2404.03999/) (2024)
- [The Manifold Scattering Transform for High-Dimensional Point Cloud Data](https://mlsanity.com/paper/2206.10078/) (2022)

## Abstract (arXiv)

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.