# High-dimensional Convolutional Networks for Geometric Pattern Recognition

arXiv: https://arxiv.org/abs/2005.08144 · HTML: https://mlsanity.com/paper/2005.08144/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2020.

## Built on by (most cited first, 24 of 24)

- [Deep Hough Voting for Robust Global Registration](https://mlsanity.com/paper/2109.04310/) (2021)
- [P2-Net: Joint Description and Detection of Local Features for Pixel and Point Matching](https://mlsanity.com/paper/2103.01055/) (2021)
- [PeRFception: Perception using Radiance Fields](https://mlsanity.com/paper/2208.11537/) (2022)
- [Neural Reprojection Error: Merging Feature Learning and Camera Pose Estimation](https://mlsanity.com/paper/2103.07153/) (2021)
- [DQS3D: Densely-matched Quantization-aware Semi-supervised 3D Detection](https://mlsanity.com/paper/2304.13031/) (2023)
- [DiffSSC: Semantic LiDAR Scan Completion using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2409.18092/) (2024)
- [RPSRNet: End-to-End Trainable Rigid Point Set Registration Network using Barnes-Hut 2D-Tree Representation](https://mlsanity.com/paper/2104.05328/) (2021)
- [Leveraging Image Matching Toward End-to-End Relative Camera Pose Regression](https://mlsanity.com/paper/2211.14950/) (2022)
- [Deep Learning-based Point Cloud Registration for Augmented Reality-guided Surgery](https://mlsanity.com/paper/2405.03314/) (2024)
- [Visual Correspondence Hallucination](https://mlsanity.com/paper/2106.09711/) (2021)
- [Learning to Register Unbalanced Point Pairs](https://mlsanity.com/paper/2207.04221/) (2022)
- [Phase2vec: Dynamical systems embedding with a physics-informed convolutional network](https://mlsanity.com/paper/2212.03857/) (2022)
- [Points2Sound: From mono to binaural audio using 3D point cloud scenes](https://mlsanity.com/paper/2104.12462/) (2021)
- [Dynamic Convolution for 3D Point Cloud Instance Segmentation](https://mlsanity.com/paper/2107.08392/) (2021)
- [Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning](https://mlsanity.com/paper/2306.11406/) (2023)
- [OE3DIS: Open-Ended 3D Point Cloud Instance Segmentation](https://mlsanity.com/paper/2408.11747/) (2024)
- [(Just) A Spoonful of Refinements Helps the Registration Error Go Down](https://mlsanity.com/paper/2108.03257/) (2021)
- [Putting 3D Spatially Sparse Networks on a Diet](https://mlsanity.com/paper/2112.01316/) (2021)
- [Revisiting LiDAR Registration and Reconstruction: A Range Image Perspective](https://mlsanity.com/paper/2112.02779/) (2021)
- [Interpolation-Aware Padding for 3D Sparse Convolutional Neural Networks](https://mlsanity.com/paper/2108.06925/) (2021)
- [Leveraging Inlier Correspondences Proportion for Point Cloud Registration](https://mlsanity.com/paper/2201.12094/) (2022)
- [LEADER: Learning Reliable Local-to-Global Correspondences for LiDAR Relocalization](https://mlsanity.com/paper/2604.11355/) (2026)
- [3D Motion Perception of Binocular Vision Target with PID-CNN](https://mlsanity.com/paper/2511.20332/) (2025)
- [PointCNN++: Performant Convolution on Native Points](https://mlsanity.com/paper/2511.23227/) (2025)

## Abstract (arXiv)

Many problems in science and engineering can be formulated in terms of geometric patterns in high-dimensional spaces. We present high-dimensional convolutional networks (ConvNets) for pattern recognition problems that arise in the context of geometric registration. We first study the effectiveness of convolutional networks in detecting linear subspaces in high-dimensional spaces with up to 32 dimensions: much higher dimensionality than prior applications of ConvNets. We then apply high-dimensional ConvNets to 3D registration under rigid motions and image correspondence estimation. Experiments indicate that our high-dimensional ConvNets outperform prior approaches that relied on deep networks based on global pooling operators.