# PCAM: Product of Cross-Attention Matrices for Rigid Registration of Point Clouds

arXiv: https://arxiv.org/abs/2110.01269 · HTML: https://mlsanity.com/paper/2110.01269/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 55 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 19 of 19)

- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [3DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructions](https://mlsanity.com/paper/1603.08182/) (2016)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [RPM-Net: Robust Point Matching using Learned Features](https://mlsanity.com/paper/2003.13479/) (2020)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registration](https://mlsanity.com/paper/1605.03344/) (2016)
- [PRNet: Self-Supervised Learning for Partial-to-Partial Registration](https://mlsanity.com/paper/1910.12240/) (2019)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [DeepGMR: Learning Latent Gaussian Mixture Models for Registration](https://mlsanity.com/paper/2008.09088/) (2020)
- [SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group](https://mlsanity.com/paper/1612.07386/) (2016)
- [Learning multiview 3D point cloud registration](https://mlsanity.com/paper/2001.05119/) (2020)
- [Learning Compact Geometric Features](https://mlsanity.com/paper/1709.05056/) (2017)
- [Learning 3D-3D Correspondences for One-shot Partial-to-partial Registration](https://mlsanity.com/paper/2006.04523/) (2020)
- [Correspondence Matrices are Underrated](https://mlsanity.com/paper/2010.16085/) (2020)
- [Registration Loss Learning for Deep Probabilistic Point Set Registration](https://mlsanity.com/paper/2011.02229/) (2020)

## Built on by (most cited first, 20 of 20)

- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [REGTR: End-to-end Point Cloud Correspondences with Transformers](https://mlsanity.com/paper/2203.14517/) (2022)
- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [RING++: Roto-translation Invariant Gram for Global Localization on a Sparse Scan Map](https://mlsanity.com/paper/2210.05984/) (2022)
- [MatchNorm: Learning-based Point Cloud Registration for 6D Object Pose Estimation in the Real World](https://mlsanity.com/paper/2203.15309/) (2022)
- [SPEAL: Skeletal Prior Embedded Attention Learning for Cross-Source Point Cloud Registration](https://mlsanity.com/paper/2312.08664/) (2023)
- [Full Transformer Framework for Robust Point Cloud Registration with Deep Information Interaction](https://mlsanity.com/paper/2112.09385/) (2021)
- [SEM-GAT: Explainable Semantic Pose Estimation using Learned Graph Attention](https://mlsanity.com/paper/2308.03718/) (2023)
- [Point Tree Transformer for Point Cloud Registration](https://mlsanity.com/paper/2406.17530/) (2024)
- [Unlocking Generalization Power in LiDAR Point Cloud Registration](https://mlsanity.com/paper/2503.10149/) (2025)
- [Q-REG: End-to-End Trainable Point Cloud Registration with Surface Curvature](https://mlsanity.com/paper/2309.16023/) (2023)
- [DeepPointMap: Advancing LiDAR SLAM with Unified Neural Descriptors](https://mlsanity.com/paper/2312.02684/) (2023)
- [3D Registration in 30 Years: A Survey](https://mlsanity.com/paper/2412.13735/) (2024)
- [A Strong Baseline for Point Cloud Registration via Direct Superpoints Matching](https://mlsanity.com/paper/2307.01362/) (2023)
- [Mining and Transferring Feature-Geometry Coherence for Unsupervised Point Cloud Registration](https://mlsanity.com/paper/2411.01870/) (2024)
- [Challenging the Universal Representation of Deep Models for 3D Point Cloud Registration](https://mlsanity.com/paper/2211.16301/) (2022)
- [Global Point Cloud Registration Network for Large Transformations](https://mlsanity.com/paper/2403.18040/) (2024)
- [Capsule-ConvKAN: A Hybrid Neural Approach to Medical Image Classification](https://mlsanity.com/paper/2507.06417/) (2025)
- [From Single Scan to Sequential Consistency: A New Paradigm for LIDAR Relocalization](https://mlsanity.com/paper/2602.03198/) (2026)
- [Temporal-Aware Fusion for Robust Outdoor LiDAR Localization](https://mlsanity.com/paper/2609.36432/) (2026)

## Abstract (arXiv)

Rigid registration of point clouds with partial overlaps is a longstanding problem usually solved in two steps: (a) finding correspondences between the point clouds; (b) filtering these correspondences to keep only the most reliable ones to estimate the transformation. Recently, several deep nets have been proposed to solve these steps jointly. We built upon these works and propose PCAM: a neural network whose key element is a pointwise product of cross-attention matrices that permits to mix both low-level geometric and high-level contextual information to find point correspondences. These cross-attention matrices also permits the exchange of context information between the point clouds, at each layer, allowing the network construct better matching features within the overlapping regions. The experiments show that PCAM achieves state-of-the-art results among methods which, like us, solve steps (a) and (b) jointly via deepnets. Our code and trained models are available at https://github.com/valeoai/PCAM.