Fast algorithms for matching CCD images to a stellar catalogue

TL;DR

This paper introduces two novel, highly efficient algorithms for matching star coordinate lists to catalogues, significantly reducing computation time and enabling rapid, robust identification in wide-field astronomical images.

Contribution

The paper presents two new algorithms that match star lists to catalogues faster by using triangle shapes and probabilistic search ordering, outperforming previous methods.

Findings

Successfully matched 100% of 10,063 images in 6 ms on average

Search time varies less than 1 ms for list sizes 10-200

Algorithms are nearly independent of list size, enabling constant-time performance

Abstract

Two new algorithms are described for matching two dimensional coordinate lists of point sources that are signifcantly faster than previous methods. By matching rarely occurring triangles (or more complex shapes) in the two lists, and by ordering searches by decreasing probability of success, it is demonstrated that very few candidates need be considered to find a successful match. Moreover, by immediately testing the suitability of a potential match using an efficient mechanism, the need to process the entire candidate set is avoided, yielding considerable performance improvements. Triangles are described by a cosine metric that reduces the density of triangle space, permitting efficient searches. An alternative shape characterization method that reduces computational overhead in the construction phase is discussed. The algorithms are tested on a set of 10 063 wide-field survey images, with fields-of-view up to 4.8 x 3.6 deg, successfully matching 100% of the images in a mean elapsed time of 6 ms (2.4 GHz Athlon CPU). The elapsed time of the searching phase is shown to vary by less than 1 ms for list sizes between 10 and 200 points, demonstrating that fast, robust searches may be completed in nearly constant time, independent of list size.