Estimating error rates for firearm evidence identifications in forensic science

Abstract

Estimating error rates for firearm evidence identification is a fundamental challenge in forensic science. This paper describes the recently developed congruent matching cells (CMC) method for image comparisons, its application to firearm evidence identification, and its usage and initial tests for error rate estimation. The CMC method divides compared topography images into correlation cells. Four identification parameters are defined for quantifying both the topography similarity of the correlated cell pairs and the pattern congruency of the registered cell locations. A declared match requires a significant number of CMCs, i.e., cell pairs that meet all similarity and congruency requirements. Initial testing on breech face impressions of a set of 40 cartridge cases fired with consecutively manufactured pistol slides showed wide separation between the distributions of CMC numbers observed for known matching and known non-matching image pairs. Another test on 95 cartridge cases from a different set of slides manufactured by the same process also yielded widely separated distributions. The test results were used to develop two statistical models for the probability mass function of CMC correlation scores. The models were applied to develop a framework for estimating cumulative false positive and false negative error rates and individual error rates of declared matches and non-matches for this population of breech face impressions. The prospect for applying the models to large populations and realistic case work is also discussed. The CMC method can provide a statistical foundation for estimating error rates in firearm evidence identifications, thus emulating methods used for forensic identification of DNA evidence.

A Normalized Congruent Matching Area Method for the Correlation of Breech Face Impression Images

“…2. In our previous studies [4,5,7], the CMCs on KNM image pairs are most likely to appear at the edges of the breech face impression, as shown in Fig. 3.…”

“…015 termed an "invalid correlation region" and should be eliminated from correlation. An invalid correlation region can occur, for example, due to insufficient contact between the firearm surface and the bullet or cartridge case during firing [7].…”

“…The CMC method has been validated by different sets of topography measurements [4], by optical images [5], and by different correlation programs and statistical models [7]. Figure 2 shows the CMC distribution on KM image pair #19 vs. #20 (Fadul data set [10]) at different cell sizes.…”

“…8 [6,7], where the NCMA probability mass functions, Φ NCMA and Ψ NCMA , of the KM and KNM topography pairs are equal. At this point, the scorebased likelihood ratio [14] LR 1 = LR 2 = 1: [6,7]. TNP: true negative probability, FNP: false negative probability, TPP: true positive probability, FPP: false positive probability.…”

“…In this paper, all the NCMA values are rounded, and the minimum NCMA unit is 1 %. The cumulative false positive error rate E 1 is given by the sum of the discrete probability mass function values, Ψ NCMA , for NCMA values between C (%) and 100 % [6,7]:…”