Topologically Stable Hough Transform

2026-03-09

AI Summary

This work proposes a novel Hough transform framework for line detection in point clouds that replaces the conventional discrete voting mechanism with a continuous scoring function enhanced by persistent homology. By leveraging topological persistence to identify stable features in the scoring landscape—those exhibiting significant topological lifetime—the method robustly extracts candidate lines while mitigating the adverse effects of noise and quantization errors inherent in traditional approaches. The integration of continuous topological analysis not only improves the robustness and stability of line detection but also preserves computational efficiency through a carefully designed geometric algorithm. Experimental results demonstrate that the proposed approach consistently outperforms conventional Hough transform methods in both noise resilience and detection accuracy.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Other Foundations of Computer Vision
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Data transparency and provenance

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.

Problem

• Hough transform
• line detection
• point clouds
• topological stability
• persistent homology

Innovation

• Topological stability
• Hough transform
• Persistent homology
• Point cloud
• Line detection