  Firing a gun leaves marks on cartridge cases which purportedly uniquely
identify the gun. Firearms examiners typically use a visual examination to
evaluate if two cartridge cases were fired from the same gun, and this is a
subjective process that has come under scrutiny. Matching can be done in a more
reproducible manner using automated algorithms. In this paper, we develop
methodology to compare topographical measurements of cartridge cases. We
demonstrate the use of a record linkage framework in this context. We compare
performance using topographical measurements to older reflectance microscopy
images, investigating the extent to which the former produce more accurate
comparisons. Using a diverse collection of images of over 1,100 cartridge
cases, we find that overall performance is generally improved using
topographical data. Some subsets of the data achieve almost perfect predictive
performance in terms of precision and recall, while some produce extremely poor
performance. Further work needs to be done to assess if examiners face similar
difficulties on certain gun and ammunition combinations. For automatic methods,
a fuller investigation into their fairness and robustness is necessary before
they can be deployed in practice.
