Some approaches for analysis of ballistics 

signatures using cross-correlation functions

James Yen

Statistical Engineering Division, ITL, NIST

In collaboration with: T.V. Vorburger, J. Song, 

A. Zheng, T.B. Renegar, H. Soons, W. Chu, R. Silver of 

PML and R.M. Thompson of OLES

Thanks, re: NBIDE project: S. Ballou, OLES; 

J. Filliben, SED/ITL; B. Bachrach, IAI

Forensics @ NIST 2012 Symposium 

Gaithersburg, MD, November 28 – 30, 2012

1
Introduction

• Goal: Demonstrating approaches to analyzing and 

modeling similarity scores for forensic identifications

• The approaches are demonstrated on the NBIDE (NIST 

Ballistic Identification Designed Experiment) breech 

face impression set analyzed by maximum areal crosscorrelation function

• Tools include graphical representations of the data, and 

estimating contributions to correlation from various 

effects

2
A firing pin topographical image 

(vertical proportions not drawn to scale)

3
A breech face topographical image 

(vertical proportions not drawn to scale)

4
Areal Cross-Correlation Function

5
CCF properties

• CCF is brute force in being global and un-weighted 

(and computationally intensive)

• CCF is especially appropriate for NIST SRM bullets 

and cartridge cases (each surface was 

manufactured to be virtually identical)

• There are more “clever” strategies for 

identification: Consecutive matching striae for 

bullets, Congruent matching cells (NIST), 

application of multivariate pattern and 

discrimination methods by Petraco, et al.

6
NBIDE (NIST Ballistic Identification 

Designed Experiment) 

• 12 new guns: 4 Ruger, 4 Smith-Wesson, 4 Sig Sauer

• Each gun fired 9 times: 3 times each of ammunition 

brands: Winchester, Remington, PMC

• 3 x 4 x 3 x 3 = 108 cartridge cases

• CCF of each casing to every other casing measured

• Experiment Design by J.Filliben; casings were fired 

at OLES facility, and were given random ID before 

measurements and correlations

• Note: Certain commercial equipment may be identified in this 

presentation in order to specify certain experimental procedures. This 

does not imply recommendation or endorsement by NIST, nor does it 

imply that the equipment are the best available for the purpose.

7
The NBIDE Guns

8
Mechanical firing of NBIDE guns

9
CCF values for correlations of breech faces 

of match and non-match cartridge cases

10
• Exploratory data analysis: always graph the data!

• The figure on the next slide partitions the match 

and non-match CCFs by Reference Casing 

(Matches, lower triangles ; Non-matches, upper 

triangles). 

• The plot following that is a color/intensity 

depiction of a CCF matrix

• (These may not be so easy for much larger 

sample size, or if you don’t have round-robin 

comparisons.)

11

Graphical depictions of CCF data
Non-match and Match CCFs by Casing

12
• CCF color matrix for topographic images of 108 breech face impressions for 12 BIDE guns. 

The data are ordered by gun(large groupings) then by ammo within each grouping. 13
Empirical Modeling of CCF scores

• Average CCF between two casings can possibly be 

modeled as combination of several terms:

– Average Non-match CCF

– Increase in average CCF due to casings being from 

same gun (we hope this increase is large)

– Increase in average CCF due to same ammunition 

brand/type?

– Increase in average CCF due to guns being of same 

brand/type (for non-matches)?

All the above terms come with their own ‘errors’ and 

variabilities.

14
Estimated empirical effects for NBIDE 

BF CCFs (only)

• Average Non-match CCF: 0.21 (std.dev. 0.04, 

std.err. 0.0004)

• Average CCF for Matches: 0.61 (std.dev. 0.14, 

std.err. 0.005)

15
Non-match CCFs for NBIDE BF

• Average effect of same gunbrand in non-matches 

is 0.01 (std.err. 0.001)

• All estimated brand effects and/or interactions < 

0.04 in non-match CCFs

• Of the ammunitions, PMC gave lowest CCFs on 

the average: the lowest effect was PMC-PMC pair 

– So having same ammunition brand may not 

necessarily increase the CCF for non-match casings

• Tendency: Ruger high, Smith-Wesson low

16
NBIDE Match BF CCF effects

• Average Match CCF: 

– Ruger 0.70 (std.dev. 0.11, std.err. 0.01) 

– Sig-Sauer 0.62 (std.dev=0.14, std.err. 0.01) 

– Smith-Wesson 0.52 (std.dev. 0.09, std.err. 0.01)

• Random effect standard deviation of individual guns 

(measures variability between guns of each brand):

– Ruger 0.07

– Sig-Sauer 0.12 (due to one gun with low match CCFs)

– Smith-Wesson 0.05

17
Estimated Ammunition Brand effects 

in Matches

• Average effect of having Same ammunition in 

Matches = 0.03 [std. err. (<.01)]

• Highest average ammunition effect for 

matches is PMC-PMC with .04 (std. err. 0.02)

• Ammunition combination as a random effect 

has .02 standard deviation

18
NBIDE BF Points about CCF

• Manufacturer effects much more evident in 

matches than non-matches

• On the average, Ruger yields higher CCF, Sm-W 

lower CCF, for both matches and non-matches 

• PMC-PMC combination yields (slightly) higher 

CCF for matches , lower CCF for non-matches

• Estimated gun brand effects are smaller, and 

ammunition effects are much smaller, than the 

(Match vs. Non-Match) effect on the CCF score

19
Final Points

• These patterns may NOT be true for human 

examiners or other automatic systems 

• Specific conclusions do not necessarily hold 

in other ballistics scenarios (different guns, 

different ammunition, etc.)

• However, these or similar methods of 

analyses can be useful for a variety of 

ballistics and other forensics applications

20