[Paper Review] Arc-support Line Segments Revisited: An Efficient and High-quality Ellipse Detection

Changsheng Lu, Siyu Xia+2 more|arXiv (Cornell University)|Oct 8, 2018

Image and Object Detection Techniques39 references4 citations

TL;DR

This paper proposes an efficient and accurate ellipse detection method using arc-support line segments (arc-support LSs) to improve detection robustness in real-world images. By leveraging geometric features like polarity and gradient direction, the method forms arc-support groups, generates initial ellipses via constrained fitting, and refines candidates through hierarchical clustering and verification, achieving state-of-the-art F-measure scores on three public datasets with competitive speed.

ABSTRACT

Over the years many ellipse detection algorithms spring up and are studied broadly, while the critical issue of detecting ellipses accurately and efficiently in real-world images remains a challenge. In this paper, we propose a valuable industry-oriented ellipse detector by arc-support line segments, which simultaneously reaches high detection accuracy and efficiency. To simplify the complicated curves in an image while retaining the general properties including convexity and polarity, the arc-support line segments are extracted, which grounds the successful detection of ellipses. The arc-support groups are formed by iteratively and robustly linking the arc-support line segments that latently belong to a common ellipse. Afterward, two complementary approaches, namely, locally selecting the arc-support group with higher saliency and globally searching all the valid paired groups, are adopted to fit the initial ellipses in a fast way. Then, the ellipse candidate set can be formulated by hierarchical clustering of 5D parameter space of initial ellipses. Finally, the salient ellipse candidates are selected and refined as detections subject to the stringent and effective verification. Extensive experiments on three public datasets are implemented and our method achieves the best F-measure scores compared to the state-of-the-art methods. The source code is available at https://github.com/AlanLuSun/High-quality-ellipse-detection.

Motivation & Objective

• To address the challenge of detecting ellipses accurately and efficiently in real-world images with noise, occlusion, blur, and cluttered edges.
• To develop a method that balances high detection accuracy with computational efficiency, suitable for industrial applications.
• To exploit geometric features such as polarity, gradient direction, and arc-support structure to improve ellipse detection robustness.
• To enable detection of incomplete ellipses (elliptic arcs) with variable angular coverage.
• To provide a self-calibrated, high-precision verification mechanism that reduces false positives while maintaining localization accuracy.

Proposed method

• The method extracts arc-support line segments to simplify complex curves while preserving convexity and polarity, filtering out non-elliptical structures.
• Arc-support groups are formed by iteratively linking line segments that likely belong to the same ellipse using geometric constraints and polarity consistency.
• Initial ellipses are generated via two complementary strategies: local saliency-based selection and global paired-group search, both guided by three novel geometric constraints.
• The initial ellipse set is clustered in a 5D parameter space using hierarchical clustering to group similar ellipses and reduce redundancy.
• A rigorous verification step uses geometric and intensity-based constraints to reject false positives and refine the final detections.
• A self-calibrated refinement process enhances localization accuracy by iteratively optimizing ellipse parameters based on edge support.

Experimental results

Research questions

• RQ1 Can arc-support line segments effectively represent elliptical structures while filtering out non-elliptical edges in complex images?
• RQ2 How can polarity and gradient direction information be leveraged to improve the robustness and efficiency of ellipse detection?
• RQ3 To what extent can the proposed method detect incomplete ellipses (elliptic arcs) with varying angular coverage?
• RQ4 Can the method achieve both high accuracy and high efficiency, outperforming state-of-the-art approaches in F-measure and processing time?
• RQ5 How does the combination of local and global initial ellipse generation strategies improve detection completeness and reduce false positives?

Key findings

• The proposed method achieves the highest F-measure scores on three public datasets, outperforming existing state-of-the-art ellipse detection methods.
• The method successfully detects small ellipses with semi-major axes as small as 20 pixels and low axes ratios (e.g., 0.25), though extremely small or oblate ellipses remain challenging.
• Detection performance is invariant to ellipse orientation, with consistent success across all 90° orientations tested.
• The method can detect elliptic arcs with angular coverage as low as 165°, thanks to the configurable parameter $ T_{ac} $, demonstrating robustness to incomplete ellipses.
• Image upscaling by a factor of two improves detection performance, reducing failure regions in the detection map, indicating scalability.
• Polarity-specific detection is achieved by filtering arc-support LSs based on polarity, enabling targeted detection of bright-or-dark-belt ellipses without reprocessing.