# Geodesic convolutional neural networks on Riemannian manifolds

arXiv: https://arxiv.org/abs/1501.06297 · HTML: https://mlsanity.com/paper/1501.06297/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2015.

## Built on by (most cited first, 6 of 6)

- [MeT: A Graph Transformer for Semantic Segmentation of 3D Meshes](https://mlsanity.com/paper/2307.01115/) (2023)
- [Multi-Task Learning based Convolutional Models with Curriculum Learning for the Anisotropic Reynolds Stress Tensor in Turbulent Duct Flow](https://mlsanity.com/paper/2111.00328/) (2021)
- [Identification of vortex in unstructured mesh with graph neural networks](https://mlsanity.com/paper/2311.06557/) (2023)
- [LBONet: Supervised Spectral Descriptors for Shape Analysis](https://mlsanity.com/paper/2411.08272/) (2024)
- [Iso-CapsNet: Isomorphic Capsule Network for Brain Graph Representation Learning](https://mlsanity.com/paper/2206.13465/) (2022)
- [Surface-biased Multi-Level Context 3D Object Detection](https://mlsanity.com/paper/2302.06291/) (2023)

## Abstract (arXiv)

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.