# Parametric Point Cloud Completion for Polygonal Surface Reconstruction

arXiv: https://arxiv.org/abs/2503.08363 · HTML: https://mlsanity.com/paper/2503.08363/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 11 Mar 2025.

## Builds on (most cited first, 30 of 31)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [PoinTr: Diverse Point Cloud Completion with Geometry-Aware Transformers](https://mlsanity.com/paper/2108.08839/) (2021)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [GRNet: Gridding Residual Network for Dense Point Cloud Completion](https://mlsanity.com/paper/2006.03761/) (2020)
- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [SeedFormer: Patch Seeds based Point Cloud Completion with Upsample Transformer](https://mlsanity.com/paper/2207.10315/) (2022)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations](https://mlsanity.com/paper/2303.10613/) (2023)
- [ProxyFormer: Proxy Alignment Assisted Point Cloud Completion with Missing Part Sensitive Transformer](https://mlsanity.com/paper/2302.14435/) (2023)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [Point2CAD: Reverse Engineering CAD Models from 3D Point Clouds](https://mlsanity.com/paper/2312.04962/) (2023)
- [LAKe-Net: Topology-Aware Point Cloud Completion by Localizing Aligned Keypoints](https://mlsanity.com/paper/2203.16771/) (2022)
- [City3D: Large-Scale Building Reconstruction from Airborne LiDAR Point Clouds](https://mlsanity.com/paper/2201.10276/) (2022)
- [CSDN: Cross-modal Shape-transfer Dual-refinement Network for Point Cloud Completion](https://mlsanity.com/paper/2208.00751/) (2022)
- [Reconstructing Compact Building Models from Point Clouds Using Deep Implicit Fields](https://mlsanity.com/paper/2112.13142/) (2021)
- [FBNet: Feedback Network for Point Cloud Completion](https://mlsanity.com/paper/2210.03974/) (2022)
- [PolyGNN: Polyhedron-based Graph Neural Network for 3D Building Reconstruction from Point Clouds](https://mlsanity.com/paper/2307.08636/) (2023)

## Built on by (most cited first, 6 of 6)

- [Learning Generalizable Shape Completion with SIM(3) Equivariance](https://mlsanity.com/paper/2509.26631/) (2025)
- [MGPC: Multimodal Network for Generalizable Point Cloud Completion With Modality Dropout and Progressive Decoding](https://mlsanity.com/paper/2601.03660/) (2026)
- [HeartFormer: Semantic-Aware Dual-Structure Transformers for 3D Four-Chamber Cardiac Point Cloud Reconstruction](https://mlsanity.com/paper/2512.00264/) (2025)
- [BuildAnyPoint: 3D Building Structured Abstraction from Diverse Point Clouds](https://mlsanity.com/paper/2602.23645/) (2026)
- [Unified Primitive Proxies for Structured Shape Completion](https://mlsanity.com/paper/2601.00759/) (2026)
- [Confidence-Driven Facade Refinement of 3D Building Models Using MLS Point Clouds](https://mlsanity.com/paper/2604.03797/) (2026)

## Abstract (arXiv)

Existing polygonal surface reconstruction methods heavily depend on input completeness and struggle with incomplete point clouds. We argue that while current point cloud completion techniques may recover missing points, they are not optimized for polygonal surface reconstruction, where the parametric representation of underlying surfaces remains overlooked. To address this gap, we introduce parametric completion, a novel paradigm for point cloud completion, which recovers parametric primitives instead of individual points to convey high-level geometric structures. Our presented approach, PaCo, enables high-quality polygonal surface reconstruction by leveraging plane proxies that encapsulate both plane parameters and inlier points, proving particularly effective in challenging scenarios with highly incomplete data. Comprehensive evaluations of our approach on the ABC dataset establish its effectiveness with superior performance and set a new standard for polygonal surface reconstruction from incomplete data. Project page: https://parametric-completion.github.io.