# Laplacian2Mesh: Laplacian-Based Mesh Understanding

arXiv: https://arxiv.org/abs/2202.00307 · HTML: https://mlsanity.com/paper/2202.00307/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 106 references that are in the map.
- First posted on arXiv 1 Feb 2022.

## Builds on (most cited first, 30 of 46)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Bag of Tricks for Image Classification with Convolutional Neural Networks](https://mlsanity.com/paper/1812.01187/) (2018)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [SEGCloud: Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/1710.07563/) (2017)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)

## Built on by (most cited first, 11 of 11)

- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [E(3)-Equivariant Mesh Neural Networks](https://mlsanity.com/paper/2402.04821/) (2024)
- [Open-Vocabulary Semantic Part Segmentation of 3D Human](https://mlsanity.com/paper/2502.19782/) (2025)
- [HodgeFormer: Transformers for Learnable Operators on Triangular Meshes through Data-Driven Hodge Matrices](https://mlsanity.com/paper/2509.01839/) (2025)
- [Leveraging Point Transformers for Detecting Anatomical Landmarks in Digital Dentistry](https://mlsanity.com/paper/2504.11418/) (2025)
- [A Recipe for Geometry-Aware 3D Mesh Transformers](https://mlsanity.com/paper/2411.00164/) (2024)
- [A Task-driven Network for Mesh Classification and Semantic Part Segmentation](https://mlsanity.com/paper/2306.05246/) (2023)
- [Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph Neural Networks](https://mlsanity.com/paper/2402.10365/) (2024)
- [Relaxed Total Generalized Variation Regularized Piecewise Smooth Mumford-Shah Model for Triangulated Surface Segmentation](https://mlsanity.com/paper/2507.19284/) (2025)
- [GFT-GCN: Privacy-Preserving 3D Face Mesh Recognition with Spectral Diffusion](https://mlsanity.com/paper/2511.19958/) (2025)
- [Semantic Segmentation of Textured Non-manifold 3D Meshes using Transformers](https://mlsanity.com/paper/2604.01836/) (2026)

## Abstract (arXiv)

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.