# Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds

arXiv: https://arxiv.org/abs/1806.01759 · HTML: https://mlsanity.com/paper/1806.01759/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2018.

## Built on by (most cited first, 30 of 62)

- [An End-to-End Transformer Model for 3D Object Detection](https://mlsanity.com/paper/2109.08141/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Self-Supervised Pretraining of 3D Features on any Point-Cloud](https://mlsanity.com/paper/2101.02691/) (2021)
- [Bidirectional Projection Network for Cross Dimension Scene Understanding](https://mlsanity.com/paper/2103.14326/) (2021)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [Point Density-Aware Voxels for LiDAR 3D Object Detection](https://mlsanity.com/paper/2203.05662/) (2022)
- [Contrastive Boundary Learning for Point Cloud Segmentation](https://mlsanity.com/paper/2203.05272/) (2022)
- [STPLS3D: A Large-Scale Synthetic and Real Aerial Photogrammetry 3D Point Cloud Dataset](https://mlsanity.com/paper/2203.09065/) (2022)
- [Learning Semantic Segmentation of Large-Scale Point Clouds with Random Sampling](https://mlsanity.com/paper/2107.02389/) (2021)
- [Density-preserving Deep Point Cloud Compression](https://mlsanity.com/paper/2204.12684/) (2022)
- [Parameter is Not All You Need: Starting from Non-Parametric Networks for 3D Point Cloud Analysis](https://mlsanity.com/paper/2303.08134/) (2023)
- [Deep Learning Based 3D Segmentation: A Survey](https://mlsanity.com/paper/2103.05423/) (2021)
- [Learning Inner-Group Relations on Point Clouds](https://mlsanity.com/paper/2108.12468/) (2021)
- [Efficient 3D Deep LiDAR Odometry](https://mlsanity.com/paper/2111.02135/) (2021)
- [Deep Learning-based 3D Point Cloud Classification: A Systematic Survey and Outlook](https://mlsanity.com/paper/2311.02608/) (2023)
- [PCSCNet: Fast 3D Semantic Segmentation of LiDAR Point Cloud for Autonomous Car using Point Convolution and Sparse Convolution Network](https://mlsanity.com/paper/2202.10047/) (2022)
- [A comprehensive overview of deep learning techniques for 3D point cloud classification and semantic segmentation](https://mlsanity.com/paper/2405.11903/) (2024)
- [Point2Pix: Photo-Realistic Point Cloud Rendering via Neural Radiance Fields](https://mlsanity.com/paper/2303.16482/) (2023)
- [Lie Group Decompositions for Equivariant Neural Networks](https://mlsanity.com/paper/2310.11366/) (2023)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [Neural Field Convolutions by Repeated Differentiation](https://mlsanity.com/paper/2304.01834/) (2023)
- [CUF: Continuous Upsampling Filters](https://mlsanity.com/paper/2210.06965/) (2022)
- [Foveation in the Era of Deep Learning](https://mlsanity.com/paper/2312.01450/) (2023)
- [Continuous Conditional Random Field Convolution for Point Cloud Segmentation](https://mlsanity.com/paper/2110.06085/) (2021)
- [MKConv: Multidimensional Feature Representation for Point Cloud Analysis](https://mlsanity.com/paper/2107.12655/) (2021)
- [Neural Gaussian Scale-Space Fields](https://mlsanity.com/paper/2405.20980/) (2024)
- [RADU: Ray-Aligned Depth Update Convolutions for ToF Data Denoising](https://mlsanity.com/paper/2111.15513/) (2021)
- [Full Point Encoding for Local Feature Aggregation in 3D Point Clouds](https://mlsanity.com/paper/2303.04458/) (2023)
- [CKGConv: General Graph Convolution with Continuous Kernels](https://mlsanity.com/paper/2404.13604/) (2024)
- [Gaussian Mixture Convolution Networks](https://mlsanity.com/paper/2202.09153/) (2022)

## Abstract (arXiv)

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point clouds. Previous techniques have developed approximations to convolutions for restricted conditions. Unfortunately, their applicability is limited and cannot be used for general point clouds. We propose an efficient and effective method to learn convolutions for non-uniformly sampled point clouds, as they are obtained with modern acquisition techniques. Learning is enabled by four key novelties: first, representing the convolution kernel itself as a multilayer perceptron; second, phrasing convolution as a Monte Carlo integration problem, third, using this notion to combine information from multiple samplings at different levels; and fourth using Poisson disk sampling as a scalable means of hierarchical point cloud learning. The key idea across all these contributions is to guarantee adequate consideration of the underlying non-uniform sample distribution function from a Monte Carlo perspective. To make the proposed concepts applicable to real-world tasks, we furthermore propose an efficient implementation which significantly reduces the GPU memory required during the training process. By employing our method in hierarchical network architectures we can outperform most of the state-of-the-art networks on established point cloud segmentation, classification and normal estimation benchmarks. Furthermore, in contrast to most existing approaches, we also demonstrate the robustness of our method with respect to sampling variations, even when training with uniformly sampled data only. To support the direct application of these concepts, we provide a ready-to-use TensorFlow implementation of these layers at https://github.com/viscom-ulm/MCCNN