# Analyzing Deviations of Dyadic Lines in Fast Hough Transform

arXiv: https://arxiv.org/abs/2311.10064 · HTML: https://mlsanity.com/paper/2311.10064/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 12 references that are in the map.
- First posted on arXiv 16 Nov 2023.

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

- [A High-Accuracy Fast Hough Transform with Linear-Log-Cubed Computational Complexity for Arbitrary-Shaped Images](https://mlsanity.com/paper/2509.00231/) (2025)

## Abstract (arXiv)

Fast Hough transform is a widely used algorithm in pattern recognition. The algorithm relies on approximating lines using a specific discrete line model called dyadic lines. The worst-case deviation of a dyadic line from the ideal line it used to construct grows as O(log(n)), where n is the linear size of the image. But few lines actually reach the worst-case bound. The present paper addresses a statistical analysis of the deviation of a dyadic line from its ideal counterpart. Specifically, our findings show that the mean deviation is zero, and the variance grows as O(log(n)). As n increases, the distribution of these (suitably normalized) deviations converges towards a normal distribution with zero mean and a small variance. This limiting result makes an essential use of ergodic theory.