Correlation of firing pin impressions based on congruent matching cross-sections (CMX) method

• A new method named congruent matching cross-sections (CMX) is proposed.
• Each firing pin impression is sliced into layers alongside circular cross-sections.
• A differential profile method is applied to convert the cross-sections to profiles.
• Correlation function is used for quantifying similarity of the pair-wise profiles.
• Three parameters are used to determine the congruency of the correlated impressions.

Comparison of firing pin impressions of cartridge cases is an important part of firearms evidence identification. However, compared with breach face impressions, there is only a limited surface area over which firing pin impressions can be compared. Furthermore, the curvature of firing pin impressions makes it difficult to perform automatic correlations of the surfaces. In this study, a new method and related algorithm named congruent matching cross-sections (CMX) are proposed. Each firing pin impression is sliced into layers and the resulting circular cross-sections are converted to two dimensional linear profiles by a polar coordinate transformation. The differential profile extraction method is used for extracting the high frequency micro-features, or the individual characteristics, for accurate correlation. Three parameters are proposed for determining whether these pairwise firing pin impressions are fired from the same firearm. The cross-correlation function (CCF) is used for quantifying similarity of the pairwise profiles which represent the two correlated firing pin images. If the correlated cartridge pair is fired from the same firearm, the maximum CCF value between each of the profile pairs from the reference and the correlated firing pin impressions will be high. The other two parameters relate to the horizontal (or angular) and vertical range of relative shifts that the profiles undergo to obtain the maximum CCF. These shifts are the phase angle θ which corresponds to a horizontal shift of the 2D profiles and the vertical shift distance of slice section, i.e. where the profiles match in the depth of the impression. These shift parameters are used to determine the congruency of the pairwise profile patterns. When these parameter values and their statistical distributions are collected for analysis, the CMX number is derived as a key parameter for a conclusive identification or exclusion. Validation tests using 40 cartridge cases of three different brands fired from 10 firearms produced by three different manufacturers yielded clear separation between known matching (KM) and known non-matching (KNM) image pairs, which strongly supports the effectiveness and feasibility of the proposed CMX method.