Probabilistic Cross-Identification in Crowded Fields as an Assignment Problem

TL;DR

This paper presents a novel method for probabilistic cross-identification in crowded astronomical fields by formulating it as an assignment problem and solving it efficiently with the Hungarian algorithm, improving catalog matching accuracy.

Contribution

It introduces a new approach that maps the cross-identification challenge to a discrete optimization problem and demonstrates its effectiveness in simulated data.

Findings

Efficiently solves catalog matching in crowded fields.

Achieves accurate associations in mock universe tests.

Applicable to large astronomical surveys.

Abstract

One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood partitioning to the fundamental assignment problem of discrete mathematics and efficiently solve the two-way catalog-level matching in the realm of combinatorial optimization using the so-called Hungarian algorithm. We introduce the method, demonstrate its performance in a mock universe where the true associations are known, and discuss the applicability of the new procedure to large surveys.