# DualConvMesh-Net: Joint Geodesic and Euclidean Convolutions on 3D Meshes

arXiv: https://arxiv.org/abs/2004.01002 · HTML: https://mlsanity.com/paper/2004.01002/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Apr 2020.

## Built on by (most cited first, 30 of 42)

- [OpenScene: 3D Scene Understanding with Open Vocabularies](https://mlsanity.com/paper/2211.15654/) (2022)
- [Mix3D: Out-of-Context Data Augmentation for 3D Scenes](https://mlsanity.com/paper/2110.02210/) (2021)
- [Bidirectional Projection Network for Cross Dimension Scene Understanding](https://mlsanity.com/paper/2103.14326/) (2021)
- [One Thing One Click: A Self-Training Approach for Weakly Supervised 3D Semantic Segmentation](https://mlsanity.com/paper/2104.02246/) (2021)
- [Segment3D: Learning Fine-Grained Class-Agnostic 3D Segmentation without Manual Labels](https://mlsanity.com/paper/2312.17232/) (2023)
- [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)
- [Contrastive Boundary Learning for Point Cloud Segmentation](https://mlsanity.com/paper/2203.05272/) (2022)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [4DContrast: Contrastive Learning with Dynamic Correspondences for 3D Scene Understanding](https://mlsanity.com/paper/2112.02990/) (2021)
- [BuildingNet: Learning to Label 3D Buildings](https://mlsanity.com/paper/2110.04955/) (2021)
- [ODIN: A Single Model for 2D and 3D Segmentation](https://mlsanity.com/paper/2401.02416/) (2024)
- [Multimodal Semi-Supervised Learning for 3D Objects](https://mlsanity.com/paper/2110.11601/) (2021)
- [Omni-supervised Point Cloud Segmentation via Gradual Receptive Field Component Reasoning](https://mlsanity.com/paper/2105.10203/) (2021)
- [Multiplayer Interactive World Models with Representation Autoencoders](https://mlsanity.com/paper/2607.05352/) (2026)
- [Open Vocabulary 3D Scene Understanding via Geometry Guided Self-Distillation](https://mlsanity.com/paper/2407.13362/) (2024)
- [Dense Multimodal Alignment for Open-Vocabulary 3D Scene Understanding](https://mlsanity.com/paper/2407.09781/) (2024)
- [Learning Feature Aggregation for Deep 3D Morphable Models](https://mlsanity.com/paper/2105.02173/) (2021)
- [Cross-Modal and Uncertainty-Aware Agglomeration for Open-Vocabulary 3D Scene Understanding](https://mlsanity.com/paper/2503.16707/) (2025)
- [Laplacian2Mesh: Laplacian-Based Mesh Understanding](https://mlsanity.com/paper/2202.00307/) (2022)
- [3DeformRS: Certifying Spatial Deformations on Point Clouds](https://mlsanity.com/paper/2204.05687/) (2022)
- [Exploiting Local Geometry for Feature and Graph Construction for Better 3D Point Cloud Processing with Graph Neural Networks](https://mlsanity.com/paper/2103.15226/) (2021)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [PointMatch: A Consistency Training Framework for Weakly Supervised Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/2202.10705/) (2022)
- [ALSTER: A Local Spatio-Temporal Expert for Online 3D Semantic Reconstruction](https://mlsanity.com/paper/2311.18068/) (2023)
- [AttWalk: Attentive Cross-Walks for Deep Mesh Analysis](https://mlsanity.com/paper/2104.11571/) (2021)
- [PSSNet: Planarity-sensible Semantic Segmentation of Large-scale Urban Meshes](https://mlsanity.com/paper/2202.03209/) (2022)
- [Picasso: A CUDA-based Library for Deep Learning over 3D Meshes](https://mlsanity.com/paper/2103.15076/) (2021)
- [Mesh Convolution with Continuous Filters for 3D Surface Parsing](https://mlsanity.com/paper/2112.01801/) (2021)

## Abstract (arXiv)

We propose DualConvMesh-Nets (DCM-Net) a family of deep hierarchical convolutional networks over 3D geometric data that combines two types of convolutions. The first type, geodesic convolutions, defines the kernel weights over mesh surfaces or graphs. That is, the convolutional kernel weights are mapped to the local surface of a given mesh. The second type, Euclidean convolutions, is independent of any underlying mesh structure. The convolutional kernel is applied on a neighborhood obtained from a local affinity representation based on the Euclidean distance between 3D points. Intuitively, geodesic convolutions can easily separate objects that are spatially close but have disconnected surfaces, while Euclidean convolutions can represent interactions between nearby objects better, as they are oblivious to object surfaces. To realize a multi-resolution architecture, we borrow well-established mesh simplification methods from the geometry processing domain and adapt them to define mesh-preserving pooling and unpooling operations. We experimentally show that combining both types of convolutions in our architecture leads to significant performance gains for 3D semantic segmentation, and we report competitive results on three scene segmentation benchmarks. Our models and code are publicly available.