# 3D Geometric Shape Assembly via Efficient Point Cloud Matching

arXiv: https://arxiv.org/abs/2407.10542 · HTML: https://mlsanity.com/paper/2407.10542/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 50 references that are in the map.
- First posted on arXiv 15 Jul 2024.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [SuperGlue: Learning Feature Matching with Graph Neural Networks](https://mlsanity.com/paper/1911.11763/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [Transporter Networks: Rearranging the Visual World for Robotic Manipulation](https://mlsanity.com/paper/2010.14406/) (2020)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [On the Relationship between Self-Attention and Convolutional Layers](https://mlsanity.com/paper/1911.03584/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Geometric Transformer for Fast and Robust Point Cloud Registration](https://mlsanity.com/paper/2202.06688/) (2022)
- [Hypercorrelation Squeeze for Few-Shot Segmentation](https://mlsanity.com/paper/2104.01538/) (2021)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [Neighbourhood Consensus Networks](https://mlsanity.com/paper/1810.10510/) (2018)
- [CoFiNet: Reliable Coarse-to-fine Correspondences for Robust Point Cloud Registration](https://mlsanity.com/paper/2110.14076/) (2021)
- [PQ-NET: A Generative Part Seq2Seq Network for 3D Shapes](https://mlsanity.com/paper/1911.10949/) (2019)
- [Efficient Neighbourhood Consensus Networks via Submanifold Sparse Convolutions](https://mlsanity.com/paper/2004.10566/) (2020)
- [CATs: Cost Aggregation Transformers for Visual Correspondence](https://mlsanity.com/paper/2106.02520/) (2021)
- [Generative 3D Part Assembly via Dynamic Graph Learning](https://mlsanity.com/paper/2006.07793/) (2020)
- [ClusterGNN: Cluster-based Coarse-to-Fine Graph Neural Network for Efficient Feature Matching](https://mlsanity.com/paper/2204.11700/) (2022)
- [Learning 3D Part Assembly from a Single Image](https://mlsanity.com/paper/2003.09754/) (2020)
- [Form2Fit: Learning Shape Priors for Generalizable Assembly from Disassembly](https://mlsanity.com/paper/1910.13675/) (2019)
- [Shonan Rotation Averaging: Global Optimality by Surfing SO(p)n](https://mlsanity.com/paper/2008.02737/) (2020)
- [Convolutional Hough Matching Networks](https://mlsanity.com/paper/2103.16831/) (2021)
- [Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priors](https://mlsanity.com/paper/2205.14886/) (2022)
- [Breaking Bad: A Dataset for Geometric Fracture and Reassembly](https://mlsanity.com/paper/2210.11463/) (2022)
- [Learning Part Generation and Assembly for Structure-aware Shape Synthesis](https://mlsanity.com/paper/1906.06693/) (2019)
- [RGL-NET: A Recurrent Graph Learning framework for Progressive Part Assembly](https://mlsanity.com/paper/2107.12859/) (2021)

## Built on by (most cited first, 9 of 9)

- [GARF: Learning Generalizable 3D Reassembly for Real-World Fractures](https://mlsanity.com/paper/2504.05400/) (2025)
- [A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts](https://mlsanity.com/paper/2410.14770/) (2024)
- [BiAssemble: Learning Collaborative Affordance for Bimanual Geometric Assembly](https://mlsanity.com/paper/2506.06221/) (2025)
- [TORA: Topological Representation Alignment for 3D Shape Assembly](https://mlsanity.com/paper/2604.04050/) (2026)
- [Geometric Point Attention Transformer for 3D Shape Reassembly](https://mlsanity.com/paper/2411.17788/) (2024)
- [Combinative Matching for Geometric Shape Assembly](https://mlsanity.com/paper/2508.09780/) (2025)
- [E-M3RF: An Equivariant Multimodal 3D Re-assembly Framework](https://mlsanity.com/paper/2511.21422/) (2025)
- [CRAG: Can 3D Generative Models Help 3D Assembly?](https://mlsanity.com/paper/2602.22629/) (2026)
- [LLM2R: From Large Language Models to 3D Reassemblers](https://mlsanity.com/paper/2610.18604/) (2026)

## Abstract (arXiv)

Learning to assemble geometric shapes into a larger target structure is a pivotal task in various practical applications. In this work, we tackle this problem by establishing local correspondences between point clouds of part shapes in both coarse- and fine-levels. To this end, we introduce Proxy Match Transform (PMT), an approximate high-order feature transform layer that enables reliable matching between mating surfaces of parts while incurring low costs in memory and computation. Building upon PMT, we introduce a new framework, dubbed Proxy Match TransformeR (PMTR), for the geometric assembly task. We evaluate the proposed PMTR on the large-scale 3D geometric shape assembly benchmark dataset of Breaking Bad and demonstrate its superior performance and efficiency compared to state-of-the-art methods. Project page: https://nahyuklee.github.io/pmtr.