# Deep Algebraic Fitting for Multiple Circle Primitives Extraction from Raw Point Clouds

arXiv: https://arxiv.org/abs/2204.00920 · HTML: https://mlsanity.com/paper/2204.00920/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 92 references that are in the map.
- First posted on arXiv 2 Apr 2022.

## Builds on (most cited first, 23 of 23)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [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)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [NetVLAD: CNN architecture for weakly supervised place recognition](https://mlsanity.com/paper/1511.07247/) (2015)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [Modeling Point Clouds with Self-Attention and Gumbel Subset Sampling](https://mlsanity.com/paper/1904.03375/) (2019)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [3D Point Capsule Networks](https://mlsanity.com/paper/1812.10775/) (2018)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [PIE-NET: Parametric Inference of Point Cloud Edges](https://mlsanity.com/paper/2007.04883/) (2020)
- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)
- [PointSIFT: A SIFT-like Network Module for 3D Point Cloud Semantic Segmentation](https://mlsanity.com/paper/1807.00652/) (2018)
- [Know What Your Neighbors Do: 3D Semantic Segmentation of Point Clouds](https://mlsanity.com/paper/1810.01151/) (2018)
- [Learning Part Boundaries from 3D Point Clouds](https://mlsanity.com/paper/2007.07563/) (2020)
- [LSANet: Feature Learning on Point Sets by Local Spatial Aware Layer](https://mlsanity.com/paper/1905.05442/) (2019)
- [Fast and numerically stable circle fit](https://mlsanity.com/paper/1505.03795/) (2015)

## Abstract (arXiv)

The shape of circle is one of fundamental geometric primitives of man-made engineering objects. Thus, extraction of circles from scanned point clouds is a quite important task in 3D geometry data processing. However, existing circle extraction methods either are sensitive to the quality of raw point clouds when classifying circle-boundary points, or require well-designed fitting functions when regressing circle parameters. To relieve the challenges, we propose an end-to-end Point Cloud Circle Algebraic Fitting Network (Circle-Net) based on a synergy of deep circle-boundary point feature learning and weighted algebraic fitting. First, we design a circle-boundary learning module, which considers local and global neighboring contexts of each point, to detect all potential circle-boundary points. Second, we develop a deep feature based circle parameter learning module for weighted algebraic fitting, without designing any weight metric, to avoid the influence of outliers during fitting. Unlike most of the cutting-edge circle extraction wisdoms, the proposed classification-and-fitting modules are originally co-trained with a comprehensive loss to enhance the quality of extracted circles.Comparisons on the established dataset and real-scanned point clouds exhibit clear improvements of Circle-Net over SOTAs in terms of both noise-robustness and extraction accuracy. We will release our code, model, and data for both training and evaluation on GitHub upon publication.