# Continuous Geodesic Convolutions for Learning on 3D Shapes

arXiv: https://arxiv.org/abs/2002.02506 · HTML: https://mlsanity.com/paper/2002.02506/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2020.

## Built on by (most cited first, 14 of 14)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapes](https://mlsanity.com/paper/2201.07788/) (2022)
- [ACID: Action-Conditional Implicit Visual Dynamics for Deformable Object Manipulation](https://mlsanity.com/paper/2203.06856/) (2022)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [Advancing 3D Point Cloud Understanding through Deep Transfer Learning: A Comprehensive Survey](https://mlsanity.com/paper/2407.17877/) (2024)
- [NeuralODF: Learning Omnidirectional Distance Fields for 3D Shape Representation](https://mlsanity.com/paper/2206.05837/) (2022)
- [Generalizable Local Feature Pre-training for Deformable Shape Analysis](https://mlsanity.com/paper/2303.15104/) (2023)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Anisotropic Multi-Scale Graph Convolutional Network for Dense Shape Correspondence](https://mlsanity.com/paper/2210.09466/) (2022)
- [SieveNet: Selecting Point-Based Features for Mesh Networks](https://mlsanity.com/paper/2308.12530/) (2023)
- [SelfGeo: Self-supervised and Geodesic-consistent Estimation of Keypoints on Deformable Shapes](https://mlsanity.com/paper/2408.02291/) (2024)
- [A Recipe for Geometry-Aware 3D Mesh Transformers](https://mlsanity.com/paper/2411.00164/) (2024)
- [CageNet: A Meta-Framework for Learning on Wild Meshes](https://mlsanity.com/paper/2505.18772/) (2025)
- [Intrinsic and Triangulation-Agnostic Attention: A Simple and Powerful Approach for Learning on Meshes](https://mlsanity.com/paper/2607.24954/) (2026)

## Abstract (arXiv)

The majority of descriptor-based methods for geometric processing of non-rigid shape rely on hand-crafted descriptors. Recently, learning-based techniques have been shown effective, achieving state-of-the-art results in a variety of tasks. Yet, even though these methods can in principle work directly on raw data, most methods still rely on hand-crafted descriptors at the input layer. In this work, we wish to challenge this practice and use a neural network to learn descriptors directly from the raw mesh. To this end, we introduce two modules into our neural architecture. The first is a local reference frame (LRF) used to explicitly make the features invariant to rigid transformations. The second is continuous convolution kernels that provide robustness to sampling. We show the efficacy of our proposed network in learning on raw meshes using two cornerstone tasks: shape matching, and human body parts segmentation. Our results show superior results over baseline methods that use hand-crafted descriptors.