Topologically Stable Hough Transform

TL;DR

This paper introduces a topologically stable version of the Hough transform for line detection in point clouds, utilizing persistent homology to identify candidate lines through a continuous score function.

Contribution

It presents a novel formulation replacing the classical voting scheme with a continuous score function and an efficient algorithm for candidate line detection.

Findings

Effective detection of lines in point clouds

Stable candidate lines identified via persistent homology

Improved robustness over traditional Hough transform

Abstract

We propose an alternative formulation of the well-known Hough transform to detect lines in point clouds. Replacing the discretized voting scheme of the classical Hough transform by a continuous score function, its persistent features in the sense of persistent homology give a set of candidate lines. We also devise and implement an algorithm to efficiently compute these candidate lines.