Congruent Matching Cells Research Articles

A preliminary study of the manufacturing of breech faces.

Firearm examiners may face challenges with subclass characteristics. Subclass characteristics have the potential to be confused with individual characteristics if a careful analysis for the presence of subclass characteristics is not performed. Several case studies are reported in the literature that discuss the presence of subclass characteristics and advise firearm examiners to disregard these characteristics for identification purposes. As far as can be determined, no fundamental study has been performed that explores the various methods used in firearm manufacturing and assess the potential of subclass characteristics being produced. In this study broaching, plunge milling, and lathe turning were used to produce consecutively manufactured breech faces for a Thompson/Center® (T/C®) Contender® G2 pistol. The breech faces were finished by tumbling or glass bead blasting. The 3D topographical scans of the breech faces were collected using a confocal microscope and then compared using the National Institute of Standards and Technology (NIST) congruent matching cells (CMC) algorithm. The results of this study demonstrated the presence of subclass characteristics after manufacturing by broaching and plunge milling. Lathe turning did not produce any subclass characteristics. ANOVA and Kruskal-Wallis H tests were used to determine significant differences between finishing methods within each manufacturing method. Significant differences were found in glass bead blasting versus tumbling and glass bead blasting versus no finish. No significant differences were found in no finish versus tumbling.

Automated interpretation of comparison scores for firearm toolmarks on cartridge case primers

An automated approach for evaluating the strength of the evidence of firearm toolmark comparison results is presented for a common source scenario. First, comparison scores are derived describing the similarity of marks typically encountered on the primer of fired cartridge cases: aperture shear striations as well as breechface and firing pin impressions. Subsequently, these scores are interpreted using reference distributions of comparison scores obtained for representative known matching (KM) and known non-matching (KNM) ballistic samples in a common source, score-based likelihood ratio (LR) system. We study various alternatives to set up such an LR system and compare them using qualitative and quantitative criteria known from the literature. As an example, results are applied to establish a system suitable for a firearm-ammunition combination often encountered in casework: Glock firearms with Fiocchi nickel primer ammunition. The system outputs an LR and a measure of LR uncertainty. The range of possible LR-values is limited to a minimum and maximum value in areas of the score domain with little reference data. Finally, the feasibility of combining LRs of different mark types into one LR for the entire primer is assessed. For the distribution models considered in this paper, different modeling approaches are optimal for different types of similarity scores. For the chosen firearm-ammunition combination, non-parametric Kernel Density Estimation (KDE) models perform best for similarity scores based on the correlation coefficient, whereas parametric models perform best for the Congruent Matching Cells (CMC) scores, assuming binomial and beta-binomial models for KM and KNM score distributions respectively. Finally, it is demonstrated that individual LRs of different mark types can be combined into one LR, to interpret a set of different marks on the primer as a whole.

A Study in Reproducibility: The Congruent Matching Cells Algorithm and cmcR Package

Scientific research is driven by our ability to use methods, procedures, and materials from previous studies and further research by adding to it. As the need for computationally-intensive methods to analyze large amounts of data grows, the criteria needed to achieve reproducibility, specifically computational reproducibility, have become more sophisticated. In general, prosaic descriptions of algorithms are not detailed or precise enough to ensure complete reproducibility of a method. Results may be sensitive to conditions not commonly specified in written-word descriptions such as implicit parameter settings or the programming language used. To achieve true computational reproducibility, it is necessary to provide all intermediate data and code used to produce published results. In this paper, we consider a class of algorithms developed to perform firearm evidence identification on cartridge case evidence known as the *Congruent Matching Cells* (CMC) methods. To date, these algorithms have been published as textual descriptions only. We introduce the first open-source implementation of the Congruent Matching Cells methods in the R package cmcR. We have structured the cmcR package as a set of sequential, modularized functions intended to ease the process of parameter experimentation. We use cmcR and a novel variance ratio statistic to explore the CMC methodology and demonstrate how to fill in the gaps when provided with computationally ambiguous descriptions of algorithms.

Reporting likelihood ratio for casework in firearm evidence identification

Likelihood ratio (LR) plays an important role in estimating the weight of evidence in firearm evidence identifications. LR is computed from a statistical model including the distribution of the known-matching (KM or within) and known-nonmatching (KNM or between) comparison scores. Current LR procedures rely on KM/KNM scores from existing reference firearm toolmark data sets or alternatively from generating a set of test fires using multiple firearms. Both procedures may contain theoretical or practical issues which may hinder the LR procedures from reporting an unbiased LR estimation in casework. In this paper, a reference data set was established from a set of firearms, each test-fired two cartridge cases, resulting in a basic data set and a control data set. The congruent matching cells (CMC) method was used to generate CMC scores that are used to fit in the KM/KNM statistical distributions for LR estimation. In the initial test, 130 firearms from eight manufacturers were used for generating a reference data set consisting of 260 cartridge cases representing 130 KM and 8385 KNM pairwise breech face images. Test results showed that the KM and KNM distribution intersect at CMC=2, which is equivalent to LR=1 (equally to support both the prosecutor and the defense propositions). When the CMC threshold is increased to 6 or more, the LR values are higher than a million, which can provide extremely strong support to the conclusion of the same firearm (or the prosecutor's proposition) in the casework of firearm evidence identification.

Virtual image standard (VIS) for performance evaluation of the congruent matching cells (CMC) algorithms in firearm evidence identifications

The congruent matching cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) in 2012 for automatic and objective firearm evidence identifications and estimation of the weight of evidence in firearm evidence identifications. Since 2013, five CMC algorithms have been developed at NIST. In this paper, the virtual image standard (VIS) is proposed through trimming and stitching KNM images for quantitative performance evaluations of different CMC algorithms. The evaluation criteria include the correlation accuracy (both the CMC numbers and distribution pattern), correlation efficiency, false positive (FP) error rate, and the maximum separation of known matching (KM) and known non-matching (KNM) image pairs. The VIS composes correlation cells from different KNM images, which can provide a ground truth for verifying the CMC numbers, distribution patterns, and FP errors. By identifying three groups of VIS, the Convergence CMC algorithm showed superior performances for the future casework in firearm evidence identifications. Lastly, the success of this study suggests that the VIS could also be used to optimize the correlation parameters, to develop and test new CMC algorithms, and evaluate the performance before it is put into use for firearm examiner's casework.

Statistical models for firearm and tool mark image comparisons based on the congruent matching cells (CMC) method

In the branch of forensic science known as firearm evidence identification, various similarity scores have been proposed to compare firearm marks. Some similarity score comparisons, for example, congruent matching cells (CMC) method, are based on pass-or-fail tests. The CMC method compares the pairwise topography images of breech face impressions, from which the similarity score is derived for quantifying their topography similarity. For an image pair, the CMC method determines a certain number of correlated cell pairs. Next, each correlated pair is determined to be a congruent match cell (CMC) pair, or not based on several identification parameters. The number of CMC pairs as a threshold is required so that the two images of surface topographies can be either identified as matching or determined to be non-matching. To reliably estimate error rates or evaluate likelihood ratio (LR), the key is to find an appropriate probability distribution for the frequency distribution of the observed CMC results. This paper discusses four statistical models for CMC measurements, which are binomial and three binomial-related probability distributions. In previous studies, for a sequence of binomial distributed or other binomial-related distributed random variables (r.v.), the number of Bernoulli trials N for each r.v. is assumed to be the same. However, in practice, N(the number of cell pairs in an image pair) varies from one r.v. (or one image pair) to another. In that case, the term, frequency function, of the CMC results is not appropriate. In this paper, the generalized frequency function is introduced to depict the behavior of the CMC values and its limiting distribution is provided. Based on that, nonlinear regression models are used to estimate the model parameters. The methodology is applied to a set of actual CMC values of fired cartridge cases.

Convergence-improved congruent matching cells (CMC) method for firing pin impression comparison.

A firing pin impression is usually concave in shape with a small textured area, which makes it difficult to perform automated algorithm-based comparison. The congruent matching cells (CMC) method was invented for accurate breech face impression comparison, in which a reference impression is divided into correlation cells. Each cell is registered to a cell-sized area of the comparison impression that has maximum similarity in surface topography. Four parameters are used to quantify the congruent matching pattern of the registration position and orientation. This paper aims to further develop the cell-division-matching method based on a convergence feature and to develop practical convergence-improved algorithms for firing pin impression comparison. The convergence feature refers to the tendency of the x-y registration positions of correlated cell pairs to converge at the correct registration angle when comparing same-source samples at different orientations. The areal Gaussian filter is employed to extract high-frequency micro-features; the least-squares matching method is used to improve each cross-correlation precision and reach convergence in the registration positions of correlated cell pairs; and a density-based clustering algorithm is introduced to collect the registration positions of dense cell pairs relative to a virtual common center and to remove outliers. Improvements are achieved in the reliability and accuracy of the number of congruent matching cell pairs (CMCs) collected, which represents the quantification of the degree of pairwise impression similarity. Experiments in this report used 40 firing pin impression samples on cartridge cases fired from 10 pistols. The results included no false identifications or false exclusions.

Evaluating Likelihood Ratio (LR) for firearm evidence identifications in forensic science based on the Congruent Matching Cells (CMC) method

Firearm evidence identification has been challenged by the 2008 and 2009 National Research Council (NRC) reports and by legal proceedings on its fundamental assumptions, its procedure involving subjective interpretations, and the lack of a statistical foundation for evaluation of error rates or other measures for the weight of evidence. To address these challenges, researchers of the National Institute of Standards and Technology (NIST) recently developed a Congruent Matching Cells (CMC) method for automatic and objective firearm evidence identification and quantitative error rate evaluation. Based on the CMC method, a likelihood ratio (LR) procedure is proposed in this paper aiming to provide a scientific basis for firearm evidence identification and a method for evaluation of the weight of evidence. The initial LR evaluations using two sets of 9mm cartridge cases’ breech face impression images with different sample sizes, imaging methods and ammunition showed that for all the declared identifications of the tested 2D and 3D image pairs, the evaluated LRs for the least favorable scenario were well above an order of 106, which provides Extremely Strong Support for a prosecution proposition (e.g. a same-source proposition) in a Bayesian frame. The LR evaluations also showed that for all the declared exclusions of the tested 3D image pairs, the evaluated LRs for the least favorable scenario were above an order of 102, which provides Moderately Strong Support for a defense proposition (e.g. a different-source proposition) in a Bayesian frame.

Three-Dimensional Analysis of Cartridge Case Double-Casts.

Due to the shot-to-shot variability in tool mark reproduction on fired cartridge cases, a method of replication is needed for the creation of training and testing sets. Double-casting is one method that has been used for this application, but the accuracy and variability of this method needs to be characterized. Three firearms were used to fire 25 cartridges each to create the master cartridge cases. The double-casting method consists of creating a silicone mold of the master cartridge case. A plastic resin mix is then poured into the mold to create the double-cast reproduction. Fifteen double-casts of each of the 75 fired cartridge cases were created across different silicone molds to analyze within- and between-mold variability. The master cartridge cases and double-casts were scanned with a confocal microscope (Sensofar® S neox) to create three-dimensional representations of the surfaces. Two similarity metrics were used for the objective comparison of the double-casts to their master cartridge cases: the areal correlation coefficient (ACCFMAX ) and the number of congruent matching cells (CMC). The ACCFMAX and CMC data, along with visual examinations, showed that the double-casting method produces accurate reproductions. Within-mold variability was found to be minimal, and between-mold variability was low. These results illustrate that double-casting can be applied for training and testing purposes.

The Use of Correlated Binomial Distribution in Estimating Error Rates for Firearm Evidence Identification

In the branch of forensic science known as firearm evidence identification, estimating error rates is a fundamental challenge. Recently, a new quantitative approach known as the congruent matching cells (CMC) method was developed to improve the accuracy of ballistic identifications and provide a basis for estimating error rates. To estimate error rates, the key is to find an appropriate probability distribution for the relative frequency distribution of observed CMCs overlaid on a relevant measured firearm surface such as the breech face of a cartridge case. Several probability models based on the assumption of independence between cell pair comparisons have been proposed, but the assumption of independence among the cell pair comparisons from the CMC method may not be valid. This article proposes statistical models based on dependent Bernoulli trials, along with corresponding methodology for parameter estimation. To demonstrate the potential improvement from the use of the dependent Bernoulli trial model, the methodology is applied to an actual data set of fired cartridge cases.

Automatic identification of firing pin impressions based on the Congruent Matching Cell (CMC) method

Firing pin impression is a kind of important physical evidence for forensic investigations. However, due to the small effective area and complex topography, the identifications are still rest on manual evaluations, and the studies on automatic recognition and identification are rare. In this paper, an automatic identification solution for three-dimensional (3D) firing pin impressions is proposed using a newly developed isotropic areal spline filter to extract the individual characteristics from the high order form of firing pin impressions, and an improved algorithm of the Congruent Matching Cells (CMC) method based on the valid data based normalized cross-correlation (VDNCC) to perform the identifications. This method is tested using 4,005 correlations from 90 cartridge cases. The results indicate that the proposed method is effective for identifications of firing pin impressions. The validation tests also show that the characteristics of the ammunitions may seriously affect the identifications and should be tested before performing test fires.

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.

Using statistical models in estimating error rates for forensic firearm identification

Estimating error rates for firearm evidence identification is a fundamental challenge in forensic science. The recently developed Congruent Matching Cells (CMC) method provides applications to firearm evidence identification. To estimate error rates, appropriate statistical models are needed for the CMC values. In this paper, in addition to the binomial probability distribution the correlated binomial distribution is proposed. For an image comparison, the correlated binomial distribution can be applied to the cell pairs from CMC method. An application to an actual data set demonstrates that the correlated binomial distribution fits the relative frequency distribution of CMC values much better than the binomial distribution.

Estimating error rates for firearm evidence identifications in forensic science

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 convergence algorithm for correlation of breech face images based on the congruent matching cells (CMC) method

The Congruent Matching Cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) for accurate firearm evidence identification and error rate estimation. The CMC method is based on the principle of discretization. The toolmark 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. An identification (declared match) requires a significant number of CMCs, that is, cell pairs that meet both similarity and pattern congruency requirements. The use of cell correlations reduces the effects of “invalid regions” in the compared image pairs and increases the correlation accuracy. The identification accuracy of the CMC method can be further improved by considering 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 same-source samples at different relative orientations. In this paper, the difference of the convergence feature between known matching (KM) and known non-matching (KNM) image pairs is characterized, based on which an improved algorithm is developed for breech face image correlations using the CMC method. Its advantage is demonstrated by comparison with three existing CMC algorithms using four datasets. The datasets address three different brands of consecutively manufactured pistol slides, with significant differences in the distribution overlap of cell pair topography similarity for KM and KNM image pairs. For the same CMC threshold values, the convergence algorithm demonstrates noticeably improved results by reducing the number of false-positive or false-negative CMCs in a comparison.

A Review of NIST Projects in Surface and Topography Metrology for Firearm Evidence Identification in Forensic Science

This is a review of the National Institute of Standards and Technology’s (NIST) efforts in surface metrology and topography measurements for firearm evidence identifications in forensic science. Based on the research projects in surface metrology and standardization, NIST researchers have developed Standard Reference Material (SRM) Bullets and Cartridge Cases (Certain commercial equipment, instruments, or materials are identified in this paper to specify adequately the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose) and established a 2D/3D Ballistics Topography Measurement System. They formulated a Traceability and Quality System to support nationwide ballistics identifications within the National Integrated Ballistics Information Network (NIBIN) in the United States. They have recently proposed a Congruent Matching Cells (CMC) method for accurate ballistic identification and error rate estimation, which provides a statistical foundation and a practical method to promote firearm evidence identifications from qualitative image comparisons to quantitative topography measurements.

An Improved Algorithm of Congruent Matching Cells (CMC) Method for Firearm Evidence Identifications

The Congruent Matching Cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) for firearm evidence identifications. The CMC method divides the measured image of a surface area, such as a breech face impression from a fired cartridge case, into small correlation cells and uses four identification parameters to identify correlated cell pairs originating from the same firearm. The CMC method was validated by identification tests using both 3D topography images and optical images captured from breech face impressions of 40 cartridge cases fired from a pistol with 10 consecutively manufactured slides. In this paper, we discuss the processing of the cell correlations and propose an improved algorithm of the CMC method which takes advantage of the cell correlations at a common initial phase angle and combines the forward and backward correlations to improve the identification capability. The improved algorithm is tested by 780 pairwise correlations using the same optical images and 3D topography images as the initial validation.

Fired Cartridge Case Identification Using Optical Images and the Congruent Matching Cells (CMC) Method.

The Congruent Matching Cells (CMC) method for ballistics identification was invented at the National Institute of Standards and Technology (NIST). The CMC method is based on the correlation of pairs of small correlation cells instead of the correlation of entire images. Four identification parameters – TCCF, Tθ, Tx and Ty are proposed for identifying correlated cell pairs originating from the same firearm. The correlation conclusion (matching or non-matching) is determined by whether the number of CMC is ≥ 6. This method has been previously validated using a set of 780 pair-wise 3D topography images. However, most ballistic images stored in current local and national databases are in an optical intensity (grayscale) format. As a result, the reliability of applying the CMC method on optical intensity images is an important issue. In this paper, optical intensity images of breech face impressions captured on the same set of 40 cartridge cases are correlated and analyzed for the validation test of CMC method using optical images. This includes correlations of 63 pairs of matching images and 717 pairs of non-matching images under top ring lighting. Tests of the method do not produce any false identification (false positive) or false exclusion (false negative) results, which support the CMC method and the proposed identification criterion, C = 6, for firearm breech face identifications using optical intensity images.

3D topography measurements on correlation cells—a new approach to forensic ballistics identifications

Based on three-dimensional (3D) topography measurements on correlation cells, the National Institute of Standards and Technology (NIST) has developed the ‘NIST Ballistics Identification System (NBIS)’ aimed at accurate ballistics identifications and fast ballistics evidence searches. The 3D topographies are divided into arrays of correlation cells to identify ‘valid correlation areas’ and eliminate ‘invalid correlation areas’ from the matching and identification procedure. A ‘congruent matching cells’ (CMC)’ method using three types of identification parameters of the paired correlation cells (cross correlation function maximum CCFmax, spatial registration position in x–y and registration angle θ) is used for high accuracy ballistics identifications. ‘Synchronous processing’ is proposed for correlating multiple cell pairs at the same time to increase the correlation speed. The proposed NBIS can be used for correlations of both geometrical topographies and optical intensity images. All the correlation parameters and algorithms are in the public domain and subject to open tests. An error rate reporting procedure has been developed that can greatly add to the scientific support for the firearm and toolmark identification specialty, and give confidence to the trier of fact in court proceedings. The NBIS is engineered to employ transparent identification parameters and criteria, statistical models and correlation algorithms. In this way, interoperability between different ballistics identification systems can be more easily achieved. This interoperability will make the NBIS suitable for ballistics identifications and evidence searches with large national databases, such as the National Integrated Ballistic Information Network in the United States.