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

Sparse point correspondence is a recurring signal-processing problem in sensing systems that reduce measurements to compact point observations, including image-control points, detected landmarks, star centroids, and target candidates. Many pipelines first estimate a global transform and only then infer point identities, an order that can be fragile when observations are sparse, partially overlapping, and contaminated by false or missing detections. This paper proposes Anchor Relative Topology (ART), a correspondence-first method that treats anchor-centered relative point layouts as the primary geometric signal. For each candidate anchor pair, ART removes translation by local centering, searches over a bounded rotation variable, evaluates a kernelized topology-consistency score, and recovers a partial one-to-one assignment with explicit unmatched-point handling. Two practical variants are reported: ART-RH increases the anchor-hypothesis budget to improve anchor recall, whereas ART-AD adapts the kernel width and angular grid from local structure. On a 1944-case synthetic benchmark, ART-RH achieves a mean F1 score of 0.7907, compared with 0.6965 for rigid CPD correspondence. Real sensor-derived protocols further show that ART remains effective on retinal image control points and provides useful identity recovery on telemetry-derived star-point cases under strong partial overlap. In the reported synthetic and real sparse-coordinate protocols, the ART variants achieve higher correspondence F1 than the evaluated classical coordinate-only baselines, while retaining an explicit runtime-accuracy trade-off. These results indicate that anchor-relative topology is useful when exact sparse correspondence identities are more important than a single global transform.