mlsanityData to 7 Oct 2026

PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representation

arXiv 2110.07882 ↗First posted 15 Oct 2021cs.CVcited by 9

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Abstract (arXiv)

3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some challenges for the existing deep neural network (DNN)-based methods on polygon mesh representation, such as handling the variations in the degree and permutations of the vertices and their pairwise distances. To overcome these challenges, we propose a DNN-based method (PolyNet) and a specific polygon mesh representation (PolyShape) with a multi-resolution structure. PolyNet contains two operations; (1) a polynomial convolution (PolyConv) operation with learnable coefficients, which learns continuous distributions as the convolutional filters to share the weights across different vertices, and (2) a polygonal pooling (PolyPool) procedure by utilizing the multi-resolution structure of PolyShape to aggregate the features in a much lower dimension. Our experiments demonstrate the strength and the advantages of PolyNet on both 3D shape classification and retrieval tasks compared to existing polygon mesh-based methods and its superiority in classifying graph representations of images. The code is publicly available from https://myavartanoo.github.io/polynet/.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 38 of its 62 references that are in the map. First posted on arXiv 15 Oct 2021.

Builds on

38 of 62 references.

References · 38

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,223
  3. 2017PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Spacecited by 4,384
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  5. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
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  10. 2016Geometric deep learning on graphs and manifolds using mixture model CNNscited by 468
  11. 2018Spherical CNNscited by 452
  12. 2019Relation-Shape Convolutional Neural Network for Point Cloud Analysiscited by 346
26 more
  1. 2016OctNet: Learning Deep 3D Representations at High Resolutionscited by 340
  2. 2016Learning Convolutional Neural Networks for Graphscited by 314
  3. 2015Diffusion-Convolutional Neural Networkscited by 268
  4. 2018SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filterscited by 261
  5. 2015Deep Convolutional Networks on Graph-Structured Datacited by 246
  6. 2018SO-Net: Self-Organizing Network for Point Cloud Analysiscited by 210
  7. 2017CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filterscited by 203
  8. 2017SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernelscited by 160
  9. 2018Point Convolutional Neural Networks by Extension Operatorscited by 154
  10. 2016Generative and Discriminative Voxel Modeling with Convolutional Neural Networkscited by 128
  11. 2018MeshNet: Mesh Neural Network for 3D Shape Representationcited by 95
  12. 2019Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generationcited by 89
  13. 2018Local Spectral Graph Convolution for Point Set Feature Learningcited by 84
  14. 2019GNN-FiLM: Graph Neural Networks with Feature-wise Linear Modulationcited by 75
  15. 2018RGCNN: Regularized Graph CNN for Point Cloud Segmentationcited by 70
  16. 2017O-CNN: Octree-based Convolutional Neural Networks for 3D Shape Analysiscited by 47
  17. 2018TextureNet: Consistent Local Parametrizations for Learning from High-Resolution Signals on Meshescited by 45
  18. 2018Learning 3D Shape Completion under Weak Supervisioncited by 40
  19. 2020MeshWalker: Deep Mesh Understanding by Random Walkscited by 32
  20. 2018Surface Networks via General Coverscited by 22
  21. 2019Graph Convolutional Gaussian Processescited by 20
  22. 2020Superpixel Image Classification with Graph Attention Networkscited by 20
  23. 2019LP-3DCNN: Unveiling Local Phase in 3D Convolutional Neural Networkscited by 14
  24. 2016FusionNet: 3D Object Classification Using Multiple Data Representationscited by 12
  25. 2020Probabilistic Numeric Convolutional Neural Networkscited by 10
  26. 2018SPNet: Deep 3D Object Classification and Retrieval using Stereographic Projectioncited by 8

Built on by

Cited by year

Citing papers per year: 2022: 2; 2023: 2; 2024: 2; 2025: 3.

9 papers.

  1. 2022A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspectivecited by 56
  2. 2024Geometry of Polynomial Neural Networkscited by 21
  3. 2022Equivariant Hypergraph Neural Networkscited by 14
  4. 2024Activation degree thresholds and expressiveness of polynomial neural networkscited by 14
  5. 2025Identifiability of Deep Polynomial Neural Networkscited by 12
  6. 2023ACL-SPC: Adaptive Closed-Loop system for Self-Supervised Point Cloud Completioncited by 9
  7. 2025The Alexander-Hirschowitz theorem for neurovarietiescited by 6
  8. 2023Self-supervised Learning for Enhancing Geometrical Modeling in 3D-Aware Generative Adversarial Networkcited by 1
  9. 2025Transferable and Undefendable Point Cloud Attacks via Medial Axis Transformcited by 1