Measurement Science & Standards in 

Forensic Firearms Analysis

NIST, July 10-11, 2012

Comparison and Interpretation of 

Impressed Marks Left by a Firearm 

on Cartridge Cases 

Fabiano Riva1, Christophe Champod1, 

Rob Hermsen2, Erwin Mattijssen2, Pascal Pieper2

1 Forensic Science Institute, UNIL

2 The Netherlands Forensic Science Institute (NFI)
Objective

• To bring an objective measure of the weight associated with 

comparison results between impressed marks (breech face 

and firing pin) on cartridge cases.

3D 

acquisition

FP and BF 

comparison

Interpretative

model

Similarity

scores

Likelihood Ratio (LR)
3D measurement

Confocal detection 

profiler

μscan of Nanofocus®

Resolution: 2 μm

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Primer Cup Cutting

Automatic segmentation of the primer cup taking advantage of 

normal vectors

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Marks separation

Automatic separation of the marks taking advantage of normal 

vectors

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Firing pin alignment using ICP

Firing pin

N°1

Firing pin

N°2

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Firing pin alignment using ICP

Ceska Zebrojovka

Sample A

Ceska Zebrojovka

Sample B

Alignment

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Breech face alignment

SIG Sauer

Sample A

SIG Sauer

Alignment Sample B

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Similarity metrics (scores)

Similarities

quantification

3 Scores

Correlation index

Euclidean distance

Normal vectors difference

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A B

3x Scores 

BFM

3x Scores

FPM

A

A B

B

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Towards a likelihood ratio (LR)

The LR represents the ratio between the probability to observe the 

comparison results (E) under two different hypothesis: H1 : The 

cartridge cases are fired by the same firearm versus H2: The 

cartridge cases are fired by different* firearms

* With the same class 

characteristics

LR =

Pr E H1,I

( )

Pr E H2,I

( )

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Within distribution: Results of 

comparisons between cartridge 

cases fired by the same firearms

Between distribution: Results of 

comparisons between cartridge 

cases fired by different* firearms

Evaluate the results (E) of a comparison as a ratio of the 

likelihoods under both propositions invoking the within and 

the between distributions.
Reduction to two dimensions by PCA

A B

A B

A B

A B

within + between

using 3 scores

within + between

using 3 scores

within + between

using 6 scores (3xFPM + 3xBFM)

PCAPCAPCA

PC 1

PC 2

PC 1

PC 2

PC 1

PC 2

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Bi-dimensional case

Within (H1)

Between (H2)

LR =

p

(PC1,PC2 H1)

p

(PC1,PC2 H2 )

p (PC1,PC2H2) p (PC1,PC2H1)

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Samples used initially
Overall performances (P228)
Overall performances (P226)
Methodology for an operational application

Questioned 

cartridge case

Suspected 

firearms

Within Between

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Towards an operational application

 Ammunition influence: Is it possible to make abstraction of 

the type of ammunition?

 Faster establishment of the within distribution: Can we 

use a limited number of samples to establish the within

distribution?

 Generalization of the between distribution: Has the 

between distribution to be re-established for each case?

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Additional data to test the different options 

 Within distribution

 Firearm W1 (SIG Sauer P228)

 60 Geco, 60 Geco SX, 60 Winchester, 60 Fiocchi

 Firearm W2 (SIG Sauer P226)

 60 Geco, 60 Geco SX, 60 Winchester, 60 Fiocchi

 Between distribution

 79 firearms (SIG Sauer P226,P228,Pro)

 79 Geco, 79 Geco SX, 79 Winchester, 79 Fiocchi

8x Within of

1770 comparisons

4x Between of

3081 comparisons

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Effect of Ammunition

Examples: Geco vs Geco SX and Winchester vs Geco SX

Geco 

Within

Between

Within

Between

Winchester Geco SX 

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Generalization of the between distribution

 Comparison between the LRs calculated using the between

distribution established with one ammunition (A) and with four 

ammunition types (A+B+C+D) . 

(A) (A+B+C+D)

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Generalization of the between distribution

High correlation supports the use of a ”general between distribution”

LRs calculated using only the Between established with Geco SX

LRs calculated using

the Between 

established

with 4 ammo types

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Generalization of the between distribution

Low correlation leads to an under- or – overestimation of the LRs

>1010

~100

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Conclusions

 This system offers an objective measure of the weight 

of evidence (LR). It is characterized by low rates of 

misleading evidence (RMED and RMEP).

 The LRs that it provides are very indicative of the true 

state.

 From an operational perspective:

 The within distribution can be established using a limited 

number of samples (7 cases) without adverse 

consequences (stable RMEP and RMED).

 If available, the between distribution has to be 

established using the same type of ammunition. 

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