# Supervised Fitting of Geometric Primitives to 3D Point Clouds

arXiv: https://arxiv.org/abs/1811.08988 · HTML: https://mlsanity.com/paper/1811.08988/

## Key facts

- Cited by 91 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2018.

## Built on by (most cited first, 30 of 91)

- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM](https://mlsanity.com/paper/2411.04954/) (2024)
- [SketchGen: Generating Constrained CAD Sketches](https://mlsanity.com/paper/2106.02711/) (2021)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [CAD-Recode: Reverse Engineering CAD Code from Point Clouds](https://mlsanity.com/paper/2412.14042/) (2024)
- [CAD-SIGNet: CAD Language Inference from Point Clouds using Layer-wise Sketch Instance Guided Attention](https://mlsanity.com/paper/2402.17678/) (2024)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Point2Cyl: Reverse Engineering 3D Objects from Point Clouds to Extrusion Cylinders](https://mlsanity.com/paper/2112.09329/) (2021)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [Engineering Sketch Generation for Computer-Aided Design](https://mlsanity.com/paper/2104.09621/) (2021)
- [SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations](https://mlsanity.com/paper/2303.10613/) (2023)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [Reconstructing editable prismatic CAD from rounded voxel models](https://mlsanity.com/paper/2209.01161/) (2022)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023)
- [HPNet: Deep Primitive Segmentation Using Hybrid Representations](https://mlsanity.com/paper/2105.10620/) (2021)
- [PartNeRF: Generating Part-Aware Editable 3D Shapes without 3D Supervision](https://mlsanity.com/paper/2303.09554/) (2023)
- [Point2CAD: Reverse Engineering CAD Models from 3D Point Clouds](https://mlsanity.com/paper/2312.04962/) (2023)
- [Point Primitive Transformer for Long-Term 4D Point Cloud Video Understanding](https://mlsanity.com/paper/2208.00281/) (2022)
- [Img2CAD: Reverse Engineering 3D CAD Models from Images through VLM-Assisted Conditional Factorization](https://mlsanity.com/paper/2408.01437/) (2024)
- [PC2WF: 3D Wireframe Reconstruction from Raw Point Clouds](https://mlsanity.com/paper/2103.02766/) (2021)
- [CADOps-Net: Jointly Learning CAD Operation Types and Steps from Boundary-Representations](https://mlsanity.com/paper/2208.10555/) (2022)
- [TransCAD: A Hierarchical Transformer for CAD Sequence Inference from Point Clouds](https://mlsanity.com/paper/2407.12702/) (2024)
- [CPFN: Cascaded Primitive Fitting Networks for High-Resolution Point Clouds](https://mlsanity.com/paper/2109.00113/) (2021)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)
- [SHARP Challenge 2023: Solving CAD History and pArameters Recovery from Point clouds and 3D scans. Overview, Datasets, Metrics, and Baselines](https://mlsanity.com/paper/2308.15966/) (2023)
- [PartSTAD: 2D-to-3D Part Segmentation Task Adaptation](https://mlsanity.com/paper/2401.05906/) (2024)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)
- [ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation](https://mlsanity.com/paper/2205.14573/) (2022)

## Abstract (arXiv)

Fitting geometric primitives to 3D point cloud data bridges a gap between low-level digitized 3D data and high-level structural information on the underlying 3D shapes. As such, it enables many downstream applications in 3D data processing. For a long time, RANSAC-based methods have been the gold standard for such primitive fitting problems, but they require careful per-input parameter tuning and thus do not scale well for large datasets with diverse shapes. In this work, we introduce Supervised Primitive Fitting Network (SPFN), an end-to-end neural network that can robustly detect a varying number of primitives at different scales without any user control. The network is supervised using ground truth primitive surfaces and primitive membership for the input points. Instead of directly predicting the primitives, our architecture first predicts per-point properties and then uses a differential model estimation module to compute the primitive type and parameters. We evaluate our approach on a novel benchmark of ANSI 3D mechanical component models and demonstrate a significant improvement over both the state-of-the-art RANSAC-based methods and the direct neural prediction.