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

The congruent matching cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) for firearm evidence identification and error rate estimation. The CMC method divides the correlated image pairs into cells and uses four parameters to quantify topography similarity and pattern congruency of the correlated cell pairs in firearm breech face impressions on fired cartridge cases. A preliminary conservative numerical identification criterion of C = 6 CMCs was suggested for identifying images of cartridge cases fired from the same firearm. The CMC method was validated by correlations using both three-dimensional (3D) topography images and two-dimensional (2D) optical images from a set of 40 cartridge cases fired from a firearm set composed of 10 consecutively manufactured pistol slides. However, in the original CMC method, due to the difference in the effective data area of the correlated cells, final CMCs obtained from an image pair presented different data quantity (or validity level), and thus the empirical criterion C = 6 CMCs did not remain optimal for identification when the correlated cell size changed. In this study, a normalized congruent matching area (NCMA) method that considers the difference in the data area in each correlated cell pair was developed. Based on the NCMA method, an optimal range of cell sizes for breech face identification with granular characteristics was determined. A binomial model was used to fit the known nonmatching NCMA probability distribution Ψ _NCMA, and a beta-binomial model was used to fit the known matching NCMA probability distribution Φ _NCMA. An experimental improvement in the normalized identification criterion C of around 6 % was observed in the validation tests when the cell sizes were in the optimal range.