# Self-Parameterization Based Multi-Resolution Mesh Convolution Networks

arXiv: https://arxiv.org/abs/2408.13762 · HTML: https://mlsanity.com/paper/2408.13762/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 25 Aug 2024.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [Indices Matter: Learning to Index for Deep Image Matting](https://mlsanity.com/paper/1908.00672/) (2019)
- [Subdivision-Based Mesh Convolution Networks](https://mlsanity.com/paper/2106.02285/) (2021)
- [Deep Geometric Texture Synthesis](https://mlsanity.com/paper/2007.00074/) (2020)
- [Neural Subdivision](https://mlsanity.com/paper/2005.01819/) (2020)
- [Primal-Dual Mesh Convolutional Neural Networks](https://mlsanity.com/paper/2010.12455/) (2020)
- [MeshWalker: Deep Mesh Understanding by Random Walks](https://mlsanity.com/paper/2006.05353/) (2020)
- [Surface Multigrid via Intrinsic Prolongation](https://mlsanity.com/paper/2104.13755/) (2021)

## Abstract (arXiv)

This paper addresses the challenges of designing mesh convolution neural networks for 3D mesh dense prediction. While deep learning has achieved remarkable success in image dense prediction tasks, directly applying or extending these methods to irregular graph data, such as 3D surface meshes, is nontrivial due to the non-uniform element distribution and irregular connectivity in surface meshes which make it difficult to adapt downsampling, upsampling, and convolution operations. In addition, commonly used multiresolution networks require repeated high-to-low and then low-to-high processes to boost the performance of recovering rich, high-resolution representations. To address these challenges, this paper proposes a self-parameterization-based multi-resolution convolution network that extends existing image dense prediction architectures to 3D meshes. The novelty of our approach lies in two key aspects. First, we construct a multi-resolution mesh pyramid directly from the high-resolution input data and propose area-aware mesh downsampling/upsampling operations that use sequential bijective inter-surface mappings between different mesh resolutions. The inter-surface mapping redefines the mesh, rather than reshaping it, which thus avoids introducing unnecessary errors. Second, we maintain the high-resolution representation in the multi-resolution convolution network, enabling multi-scale fusions to exchange information across parallel multi-resolution subnetworks, rather than through connections of high-to-low resolution subnetworks in series. These features differentiate our approach from most existing mesh convolution networks and enable more accurate mesh dense predictions, which is confirmed in experiments.