Topological Hough Transform Project

This project implements a Topological Hough Transform for detecting lines in images, alongside a baseline Hough Transform for comparison. It includes tools for generating synthetic data, visualizing results, and evaluating performance using confusion matrices.

Features

• Topological Hough Transform: A novel approach to line detection with persistence diagrams.
• Baseline Hough Transform: Standard OpenCV-based line detection for comparison.
• Synthetic Data Generation: Create noisy lines for testing and evaluation.
• Visualization: Plot persistence diagrams, Hough spaces, and detected lines.
• Evaluation: Generate confusion matrices to compare detection methods.

Installation

Clone the repository and install dependencies:

git clone https://github.com/martinuray/TopologicalHoughTransform.git

Using the repository

The experiments for the iDSC'25 paper "Persistence-Based Hough Transform for Line Detection" can be found in the experiments_idsc25 folder. Each experiment is organized in a separate python script.

The code and experiments for the EuroCG'26 paper "Topologically Stable Hough Transform" can be found in the experiments_eurocg26 folder. The one experiment is located in visualization.py and can be run to visualize the results of the topological Hough transform. The data to replicate the experiments is available by setting the DEBUG flag.

Contributing

Contributions are welcome! Please follow these steps:

1. Fork the repository.
2. Create a new branch for your feature or bugfix.
3. Submit a pull request with a clear description of your changes.

License

This project is licensed under the MIT License. See the LICENSE file for details.

Cite

In case you think this project is useful for your work, please cite it as follows:

@online{ferner2025,
  title = {Persistence-Based {{Hough Transform}} for {{Line Detection}}},
  author = {Ferner, Johannes and Huber, Stefan and Messineo, Saverio and Pop, Angel and Uray, Martin},
  booktitle = {Proc.\ of the 7th Int.\ Data Science Conference (iDSC 2025)},
  date = {2025-05-22},
  year = 2025,
  month = may,
  doi = {10.48550/arXiv.2504.16114},
  url = {http://arxiv.org/abs/2504.16114},
}

@inproceedings{huber2026,
  title = {Topologically Stable Hough Transform},
  author = {Stefan Huber and Krist{\'o}f Husz{\'a}r and Michael Kerber and Martin Uray},
  booktitle = {Proc.\ of the 42nd European Workshop on Computational Geometry (EuroCG 2026)},
  year = {2026},
  month = mar,
  url = {https://arxiv.org/abs/2603.08245},
}

Acknowledgments

he financial support by the Austrian Federal Ministry of Economy, Energy and Tourism, the National Foundation for Research, Technology and Development and the Christian Doppler Research Association is gratefully acknowledged.

We thank Lukas Lürzer for the help on preparing the code for publication.

Contact

For questions or feedback, please contact Martin Uray.