# Plane Geometry Diagram Parsing

arXiv: https://arxiv.org/abs/2205.09363 · HTML: https://mlsanity.com/paper/2205.09363/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 16 of 16)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Scene Graph Generation by Iterative Message Passing](https://mlsanity.com/paper/1701.02426/) (2017)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [FCOS: A simple and strong anchor-free object detector](https://mlsanity.com/paper/2006.09214/) (2020)
- [Towards End-to-End Lane Detection: an Instance Segmentation Approach](https://mlsanity.com/paper/1802.05591/) (2018)
- [Semantic Instance Segmentation with a Discriminative Loss Function](https://mlsanity.com/paper/1708.02551/) (2017)
- [Instance Segmentation by Jointly Optimizing Spatial Embeddings and Clustering Bandwidth](https://mlsanity.com/paper/1906.11109/) (2019)
- [End-to-End Wireframe Parsing](https://mlsanity.com/paper/1905.03246/) (2019)
- [Learning to Parse Wireframes in Images of Man-Made Environments](https://mlsanity.com/paper/2007.07527/) (2020)
- [Fully Convolutional Scene Graph Generation](https://mlsanity.com/paper/2103.16083/) (2021)
- [EmbedMask: Embedding Coupling for One-stage Instance Segmentation](https://mlsanity.com/paper/1912.01954/) (2019)

## Built on by (most cited first, 20 of 20)

- [UniGeo: Unifying Geometry Logical Reasoning via Reformulating Mathematical Expression](https://mlsanity.com/paper/2212.02746/) (2022)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understanding](https://mlsanity.com/paper/2409.09039/) (2024)
- [FormalGeo: An Extensible Formalized Framework for Olympiad Geometric Problem Solving](https://mlsanity.com/paper/2310.18021/) (2023)
- [LANS: A Layout-Aware Neural Solver for Plane Geometry Problem](https://mlsanity.com/paper/2311.16476/) (2023)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [A Symbolic Character-Aware Model for Solving Geometry Problems](https://mlsanity.com/paper/2308.02823/) (2023)
- [Enhancing the Geometric Problem-Solving Ability of Multimodal LLMs via Symbolic-Neural Integration](https://mlsanity.com/paper/2504.12773/) (2025)
- [AutoGPS: Automated Geometry Problem Solving via Multimodal Formalization and Deductive Reasoning](https://mlsanity.com/paper/2505.23381/) (2025)
- [Fuse, Reason and Verify: Geometry Problem Solving with Parsed Clauses from Diagram](https://mlsanity.com/paper/2407.07327/) (2024)
- [Learning to Solve Geometry Problems via Simulating Human Dual-Reasoning Process](https://mlsanity.com/paper/2405.06232/) (2024)
- [Pi-GPS: Enhancing Geometry Problem Solving by Unleashing the Power of Diagrammatic Information](https://mlsanity.com/paper/2503.05543/) (2025)
- [NeSyGeo: A Neuro-Symbolic Framework for Multimodal Geometric Reasoning Data Generation](https://mlsanity.com/paper/2505.17121/) (2025)
- [Towards Geometry Problem Solving in the Large Model Era: A Survey](https://mlsanity.com/paper/2506.02690/) (2025)
- [Geoclidean: Few-Shot Generalization in Euclidean Geometry](https://mlsanity.com/paper/2211.16663/) (2022)
- [GAPS: Geometry-Aware Problem Solver](https://mlsanity.com/paper/2401.16287/) (2024)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [PPTBench: Can Coding Agents Reconstruct the Visual World through Structured, Editable Slides](https://mlsanity.com/paper/2609.29718/) (2026)
- [Multi-Agent Debate and Visual Information Extraction for SeePhys Pro: A 1st-Place Technical Report from ICML 2026 AI4Math Track 3 Challenge](https://mlsanity.com/paper/2607.21946/) (2026)
- [From Symbolic Perception to Logical Deduction: A Framework for Guiding Language Models in Geometric Reasoning](https://mlsanity.com/paper/2609.10335/) (2026)

## Abstract (arXiv)

Geometry diagram parsing plays a key role in geometry problem solving, wherein the primitive extraction and relation parsing remain challenging due to the complex layout and between-primitive relationship. In this paper, we propose a powerful diagram parser based on deep learning and graph reasoning. Specifically, a modified instance segmentation method is proposed to extract geometric primitives, and the graph neural network (GNN) is leveraged to realize relation parsing and primitive classification incorporating geometric features and prior knowledge. All the modules are integrated into an end-to-end model called PGDPNet to perform all the sub-tasks simultaneously. In addition, we build a new large-scale geometry diagram dataset named PGDP5K with primitive level annotations. Experiments on PGDP5K and an existing dataset IMP-Geometry3K show that our model outperforms state-of-the-art methods in four sub-tasks remarkably. Our code, dataset and appendix material are available at https://github.com/mingliangzhang2018/PGDP.