# Picasso: A CUDA-based Library for Deep Learning over 3D Meshes

arXiv: https://arxiv.org/abs/2103.15076 · HTML: https://mlsanity.com/paper/2103.15076/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 72 references that are in the map.
- First posted on arXiv 28 Mar 2021.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [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)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [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)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Matterport3D: Learning from RGB-D Data in Indoor Environments](https://mlsanity.com/paper/1709.06158/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [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)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Large-scale Point Cloud Semantic Segmentation with Superpoint Graphs](https://mlsanity.com/paper/1711.09869/) (2017)

## Built on by (most cited first, 4 of 4)

- [3DeformRS: Certifying Spatial Deformations on Point Clouds](https://mlsanity.com/paper/2204.05687/) (2022)
- [PSSNet: Planarity-sensible Semantic Segmentation of Large-scale Urban Meshes](https://mlsanity.com/paper/2202.03209/) (2022)
- [Mesh Convolution with Continuous Filters for 3D Surface Parsing](https://mlsanity.com/paper/2112.01801/) (2021)
- [Learning Self-Prior for Mesh Inpainting Using Self-Supervised Graph Convolutional Networks](https://mlsanity.com/paper/2305.00635/) (2023)

## Abstract (arXiv)

We present Picasso, a CUDA-based library comprising novel modules for deep learning over complex real-world 3D meshes. Hierarchical neural architectures have proved effective in multi-scale feature extraction which signifies the need for fast mesh decimation. However, existing methods rely on CPU-based implementations to obtain multi-resolution meshes. We design GPU-accelerated mesh decimation to facilitate network resolution reduction efficiently on-the-fly. Pooling and unpooling modules are defined on the vertex clusters gathered during decimation. For feature learning over meshes, Picasso contains three types of novel convolutions namely, facet2vertex, vertex2facet, and facet2facet convolution. Hence, it treats a mesh as a geometric structure comprising vertices and facets, rather than a spatial graph with edges as previous methods do. Picasso also incorporates a fuzzy mechanism in its filters for robustness to mesh sampling (vertex density). It exploits Gaussian mixtures to define fuzzy coefficients for the facet2vertex convolution, and barycentric interpolation to define the coefficients for the remaining two convolutions. In this release, we demonstrate the effectiveness of the proposed modules with competitive segmentation results on S3DIS. The library will be made public through https://github.com/hlei-ziyan/Picasso.