k-d Match: A Fast Matching Algorithm for Sheared Stellar Samples

TL;DR

This paper introduces a fast, efficient algorithm for matching stellar catalogues with unknown affine transformations, significantly improving speed and enabling new applications in astronomy and imaging.

Contribution

The paper presents a novel logarithmic-time matching algorithm capable of handling arbitrary affine transformations, including shearing, for stellar catalogue registration.

Findings

Matching time is logarithmic in the number of objects.

Algorithm handles arbitrary affine transformations including shear.

Enables registration of previously unusable stellar data.

Abstract

This paper presents new and efficient algorithms for matching stellar catalogues where the transformation between the coordinate systems of the two catalagoues is unknown and may include shearing. Finding a given object whether a star or asterism from the first catalogue in the second is logarithmic in time rather than polynomial, yielding a dramatic speed up relative to a naive implementation. Both acceleration of the matching algorithm and the ability to solve for arbitrary affine transformations not only will allow the registration of stellar catalogues and images that are now impossible to use but also will find applications in machine vision and other imaging applications.