用拓扑方法改进霍夫变换，让直线检测更抗噪。
Persistence-based Hough Transform for Line Detection
- 用持久同调代替传统阈值投票，自动识别显著峰值。
- 合成数据上准确率显著提升，对噪声更鲁棒。
- 适合关注数学稳定性与拓扑分析的视觉研究者。
霍夫变换是计算机视觉中检测直线（或更一般目标）的经典方法。它将像素映射到对偶空间——霍夫空间：每个像素对应通过该点的所有直线，这些直线在霍夫空间中形成一条曲线。直线检测转化为寻找接收大量投票的峰值。然而，传统方法依赖阈值化进行投票，易受噪声和伪影影响。本文提出一种基于持久同调的替代投票机制，可自然克服简单阈值化的局限。在合成数据上的实验表明，新方法显著优于原方法，同时具备更强的鲁棒性。本工作旨在激发未来两个方向的研究：其一，强调拓扑数据分析技术的潜力，倡导将其融入现有方法（包括经典方法）；其二，引发对霍夫变换数学稳定性的讨论，鼓励探索基于数学原理的改进以增强其鲁棒性。
原文摘要 · Abstract (English)
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.
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