# MT-PCR: Hybrid Mamba-Transformer Network with Spatial Serialization for Point Cloud Registration

arXiv: https://arxiv.org/abs/2506.13183 · HTML: https://mlsanity.com/paper/2506.13183/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Point clouds, detection and remote sensing, one of 10 directions in State-space sequence models (S4, Mamba).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Placed in

- State-space sequence models (S4, Mamba) / [Point clouds, detection and remote sensing](https://mlsanity.com/ssm/point-clouds-detection-and-remote-sensing/)

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age](https://mlsanity.com/paper/1606.05830/) (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)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Simple linear attention language models balance the recall-throughput tradeoff](https://mlsanity.com/paper/2402.18668/) (2024)
- [PPFNet: Global Context Aware Local Features for Robust 3D Point Matching](https://mlsanity.com/paper/1802.02669/) (2018)
- [D3Feat: Joint Learning of Dense Detection and Description of 3D Local Features](https://mlsanity.com/paper/2003.03164/) (2020)
- [Samba: Simple Hybrid State Space Models for Efficient Unlimited Context Language Modeling](https://mlsanity.com/paper/2406.07522/) (2024)
- [The Perfect Match: 3D Point Cloud Matching with Smoothed Densities](https://mlsanity.com/paper/1811.06879/) (2018)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [3DFeat-Net: Weakly Supervised Local 3D Features for Point Cloud Registration](https://mlsanity.com/paper/1807.09413/) (2018)
- [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)
- [3D Registration with Maximal Cliques](https://mlsanity.com/paper/2305.10854/) (2023)
- [Point Mamba: A Novel Point Cloud Backbone Based on State Space Model with Octree-Based Ordering Strategy](https://mlsanity.com/paper/2403.06467/) (2024)
- [USIP: Unsupervised Stable Interest Point Detection from 3D Point Clouds](https://mlsanity.com/paper/1904.00229/) (2019)
- [Rotation-Invariant Transformer for Point Cloud Matching](https://mlsanity.com/paper/2303.08231/) (2023)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [Mamba3D: Enhancing Local Features for 3D Point Cloud Analysis via State Space Model](https://mlsanity.com/paper/2404.14966/) (2024)
- [MetaLA: Unified Optimal Linear Approximation to Softmax Attention Map](https://mlsanity.com/paper/2411.10741/) (2024)
- [A Consistency-Aware Spot-Guided Transformer for Versatile and Hierarchical Point Cloud Registration](https://mlsanity.com/paper/2410.10295/) (2024)

## Abstract (arXiv)

Point cloud registration (PCR) is a fundamental task in 3D computer vision and robotics. Most learning-based PCR methods rely on Transformer architectures, which suffer from quadratic computational complexity. This limitation restricts the resolution of point clouds that can be processed, inevitably leading to information loss. In contrast, Mamba, a recently proposed model based on state-space models, achieves linear computational complexity while maintaining strong long-range contextual modeling capabilities. However, directly applying Mamba to PCR tasks yields suboptimal performance due to the unordered and irregular nature of point cloud data. To address these challenges, we propose MT-PCR, the first point cloud registration framework that integrates Mamba and Transformer modules. Specifically, we serialize point cloud features using Z-order space-filling curves to enforce spatial locality, enabling Mamba to better model the geometric structure of the inputs. Additionally, we remove the order-indicator module commonly used in Mamba-based sequence modeling, leading to improved performance in our setting. The serialized features are then processed by an optimized Mamba encoder, followed by a Transformer-based feature refinement stage. Extensive experiments on multiple benchmarks demonstrate that MT-PCR outperforms Transformer-based and other state-of-the-art methods in both accuracy and efficiency, significantly reducing GPU memory usage and FLOPs.