Anchor Relative Topology for Sparse Point Correspondence in Sensor-Derived Observations

Area of Science:

• Computer Vision
• Signal Processing
• Geometric Deep Learning

Background:

• Sparse point correspondence is crucial for sensing systems, but traditional methods struggle with sparse, overlapping, or noisy data.
• Existing pipelines often prioritize global transforms over accurate point identity inference, leading to fragility.

Purpose of the Study:

• To introduce Anchor Relative Topology (ART), a correspondence-first approach for robust sparse point matching.
• To evaluate ART's effectiveness against classical methods on synthetic and real-world datasets.

Main Methods:

• ART treats anchor-centered relative point layouts as the primary geometric signal.
• It involves local centering, bounded rotation search, kernelized topology-consistency scoring, and partial one-to-one assignment with unmatched point handling.
• Two variants, ART-RH and ART-AD, are proposed to enhance anchor recall and adapt to local structure, respectively.

Main Results:

• ART-RH achieved a mean F1 score of 0.7907 on a synthetic benchmark, outperforming rigid CPD correspondence (0.6965).
• ART demonstrated effectiveness on real-world data, including retinal image control points and star-point identification under partial overlap.
• ART variants consistently yielded higher correspondence F1 scores than coordinate-only baselines.

Conclusions:

• Anchor-relative topology is a valuable signal for sparse point correspondence problems where identity is critical.
• ART offers a robust alternative to global transform-first methods, providing an explicit runtime-accuracy trade-off.
• The proposed method enhances accuracy and reliability in challenging sparse sensing applications.