# Persistence-based Hough Transform for Line Detection

arXiv: https://arxiv.org/abs/2504.16114 · HTML: https://mlsanity.com/paper/2504.16114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 18 references that are in the map.
- First posted on arXiv 18 Apr 2025.

## Builds on (most cited first, 1 of 1)

- [A Survey on Hough Transform, Theory, Techniques and Applications](https://mlsanity.com/paper/1502.02160/) (2015)

## Built on by (most cited first, 1 of 1)

- [Topologically Stable Hough Transform](https://mlsanity.com/paper/2603.08245/) (2026)

## Abstract (arXiv)

The Hough transform is a popular and classical technique in computer vision for the detection of lines (or more general objects). It maps a pixel into a dual space -- the Hough space: each pixel is mapped to the set of lines through this pixel, which forms a curve in Hough space. The detection of lines then becomes a voting process to find those lines that received many votes by pixels. However, this voting is done by thresholding, which is susceptible to noise and other artifacts. In this work, we present an alternative voting technique to detect peaks in the Hough space based on persistent homology, which very naturally addresses limitations of simple thresholding. Experiments on synthetic data show that our method significantly outperforms the original method, while also demonstrating enhanced robustness. This work seeks to inspire future research in two key directions. First, we highlight the untapped potential of Topological Data Analysis techniques and advocate for their broader integration into existing methods, including well-established ones. Secondly, we initiate a discussion on the mathematical stability of the Hough transform, encouraging exploration of mathematically grounded improvements to enhance its robustness.