A convergence algorithm for correlation of breech face images based on the congruent matching cells (CMC) method
Introduction
The parts of a firearm that make forcible contact with a cartridge case, such as firing pin, breech face and ejector, create toolmarks on the surface of the cartridge case [1], in firearm identification, these toolmarks are compared to assess whether two cartridge cases were fired from the same firearm. One challenge for the identification of breech face impressions is that, depending on the contact situation during firing, not all the regions of the samples may have been well impressed by the firearm breech face. The overall similarity of the compared surface images, and the accuracy of their registration, may be reduced by these “invalid” correlation regions [2].
In 2012, a new method for ballistics identifications, named Congruent Matching Cells (CMC), was invented at the National Institute of Standards and Technology (NIST) [3]. The CMC method is based on the principle of discretization. The surface image of the reference sample is divided into correlation cells. Each cell is registered to the cell-sized area of the compared image that has maximum surface topography similarity. For each resulting cell pair, one parameter quantifies the similarity of the cell surface topography and three parameters quantify the pattern congruency of the registration position and orientation. The similarity metric of the CMC method is the number of congruent matching cell pairs, i.e., the number of cell pairs that have both a sufficiently similar topography and a congruent registration pattern. Similar to the manual comparison process by a trained examiner, this approach reduces the confounding of “valid” and “invalid” regions, providing opportunities for improved discrimination of comparison results for same-source and different-source samples. Initial tests were performed using both 3D topography images [4] and 2D reflectance microscopy images [5] of breech face impressions from a set of 40 cartridge cases ejected from pistols with 10 consecutively manufactured slides. The tests showed no overlap between the CMC distributions for known matching (KM) and known non-matching (KNM) comparisons [4], [5].
The accuracy of the CMC method can be further improved by considering a feature named “convergence”, which means the tendency of the x–y registration positions of the correlated cell pairs to converge at the correct registration angle when comparing same-source samples at different relative orientations. In this paper, the concept and algorithms of the CMC method are reviewed in Section 2. In Section 3, we analyze the difference of the convergence feature between KM and KNM image correlations and develop the convergence algorithm. Validation tests using four datasets are conducted in Section 4, followed by conclusions in Section 5.
Section snippets
Basic concept of the CMC method
The impression of a firearm’s breech face on the primer of a cartridge case is affected by the firing conditions, primer material, pre-fire primer marks, contaminants, corrosion, and wear of the gun slide. As a result, both “valid” and “invalid” correlation regions may exist on the breech face impressions [3], [6]. The “valid correlation region” represents complete contact between the cartridge case and the firearm parts in the firing process, and a transfer of “individual characteristics” [1]
Methods
Ideally, we would like to identify as many CMCs for KM image correlations as the total CMC algorithm, while avoiding the additional false positive CMCs identified by this algorithm for KNM image correlations. To meet this goal, we use an additional criterion for the preliminary identification of possible matching or non-matching image pairs. With such a procedure, the initial and total CMC algorithms can be combined, with the advantages of both for identifying KM and KNM image pairs.
After
Validation test and results
Validation tests were conducted on four sets of cartridge case’s breech face impressions, namely the Fadul [9], Weller [11], Hamby [12] and Lightstone [13] datasets. The breech face impression topographies were measured by a disk scanning confocal microscope [14]. The original images have a nominal image area of about 3.8 mm × 3.8 mm, or approximately 1200 × 1200 pixels, with a nominal pixel spacing of 3.125 μm. The images were first trimmed to remove impression edge areas with strong roll-off, firing
Discussion and conclusion
We developed a convergence algorithm that combines the advantage of the initial CMC algorithm for KNM comparisons with the advantage of the total CMC algorithm for KM comparisons. The new algorithm exploits a feature named “convergence”, that is, the tendency of the x–y registration positions of the correlated cell pairs to converge at the correct registration angle when comparing KM samples at different relative orientations. For each discretized rotation angle of the compared image, the
Acknowledgements
The funding for this work is provided by the Special Programs Office (SPO) of NIST. The authors are grateful to D. Ott of NIST for assistance with the algorithm and test design; to X. A. Zheng of NIST for providing the topography images; to T. V. Vorburger and J. Libert of NIST for their review and helpful comments on the manuscript; and to R. M. Thompson of NIST for his insights on ballistics identification.
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