Forensic Science International 207 (2011) 101–105

Quantitative assessment of evidential weight for a fingerprint comparison I.Generalisation to the comparison of a mark with set of ten prints from a suspect

Cedric Neumann a,b,*, Ian W. Evett a, James E. Skerrett a, Ismael Mateos-Garcia a

a Forensic Science Service, 2920 Solihull Parkway, Birmingham Business Park, Birmingham B37 7YN, United Kingdomb Forensic Science Program, Eberly College of Science, The Pennsylvania State University, University Park, PA 16802, USA

A R T I C L E I N F O

Article history:

Received 17 March 2010

Received in revised form 2 September 2010

Accepted 13 September 2010

Available online 20 October 2010

Keywords:

Fingerprints

Likelihood ratio

Weight of evidence

A B S T R A C T

The authors have published elsewhere a quantitative method for assessing weight of evidence in the case

where a finger mark from a crime scene is compared with a control print taken from a single finger of a

suspect. The approach is based on the notion of calculating a likelihood ratio (LR) that addresses a pair of

propositions relating to the single finger that was the origin of the crime mark. In practice, things are

rather different because the crime mark will not just be compared with a single finger from a suspect but

with a set of prints from all of his/her fingers; likewise, when the mark is compared with a database, this

will consist of ten print records from random individuals. It is clear that ‘‘finger propositions’’ are not

realistic in this situation and we show how our approach may be generalised to address a pair of

propositions that relate to the person that made the crime mark. It often is the case that information is

present at the crime scene that enables some inference to be drawn relating to which of the offender’s ten

fingers left a particular mark of interest. This kind of inference may profitably be drawn into the formal

analysis. We illustrate our approach with an example.

� 2010 Elsevier Ireland Ltd. All rights reserved.

Contents lists available at ScienceDirect

Forensic Science International

journal homepage: www.elsev ier .com/ locate / forsc i in t

1. Introduction

Following the early work from other [1–5], Neumann et al. [6]have described a quantitative method for assigning a value to theweight of evidence associated with a comparison between a latentfingermark from a crime scene and a control fingerprint from aknown individual (referred to as a mark and a print, respectively,from here on). The method is based on mathematical comparisonof configurations of minutiae and addresses ‘‘finger’’ propositionsof the kind:

Hp: the mark was made by the finger that made the print.Hd: the mark was made by some unknown finger.

These are evaluated by the calculation of a likelihood ratio (LR) andGood [7] has shown that weight of evidence is meaningfully assessedby the logarithm of the LR. However, in practice the mark will not justbe compared with a single finger but with a set of prints thatrepresent all of the suspect’s fingers. Also, the defence propositionmay be addressed by reference to a database consisting of sets of ten-print records from a representative set of individuals. Given theavailability of such samples and such a database, we show in this

* Corresponding author.

E-mail address: Cedric.Neumann@me.com (C. Neumann).

0379-0738/$ – see front matter � 2010 Elsevier Ireland Ltd. All rights reserved.

doi:10.1016/j.forsciint.2010.09.006

paper how the analysis may be generalised to address ‘‘person’’propositions of the kind:

Hp: the mark was made by the person who provided the set ofcontrol prints.Hd: the mark was made by some unknown person.

Cook et al. [8] have explained the concept of a hierarchy of propositionsthat contained three levels: source, activity and offence. They explainedhow, the higher up the hierarchy are the propositions that the scientistcan address, the greater the assistance he/she provides to a court of law.In our example, both pairs of propositions are at source level;nevertheless, it is clear that the second pair are of greater value to acourt. Throughout the paper, we will refer to the first and second pair asfinger propositions and person propositions respectively.

To address person propositions, we take into account an aspectof fingerprint examination that was not considered in the originalanalysis: we recognise that it will sometimes be reasonable for thescene examiner to make a judgement about which of the offender’sfingers left the crime mark.

In the next section, we give a brief summary of the quantitativemodel for comparison of minutiae. We next consider how the modelcan be extended to address propositions relating to persons, ratherthan individual fingers. The analysis is then applied to an examplemark/print comparison to illustrate how the method mightbe applied in casework. We show and explain the change in thelikelihood ratio (LR) that results from the change in propositions

Table 1Variables extracted from minutiae configurations.

Notation Description Units

d Radius—the distance between a minutia and the centre of the polygon Pixels

s Side length—the distance between a minutia and the next contiguous minutia in a clockwise direction Pixels

u Angle—the direction of a minutia relative to the line from the centre of the polygon to the minutia Radians

t Type–type of the minutia {ridge ending, bifurcation, unknown} [1–3]

Table 2Structure of the reference collection used in this study.

General pattern Finger Number of images

Arch Thumb 830

Fore finger 660

Middle finger 659

Ring finger 660

Ulnar loop Thumb 1998

Fore finger 1996

Middle finger 660

Ring finger 659

Whorl Thumb 1996

Fore finger 660

Middle finger 659

Ring finger 659

C. Neumann et al. / Forensic Science International 207 (2011) 101–105102

2. The quantitative model for comparing minutiaeconfigurations

The Neumann et al. [6] method for addressing propositions likethe first pair in the introduction is based on abstracting numericalfeature arrays from corresponding minutiae configurations inmark and print by a method of triangulation. In summary, thisconsists of organising a given configuration of minutiae around itscentre, which is defined as that point whose coordinates are themeans of the cartesian coordinates of the individual minutiae. Thusa polygon is defined, which consists of a series of adjacent triangleswith a common vertex at the centre of the configuration.

The variables detailed in Table 1 are measured for each minutiaon the mark and the print and organised in a feature array for eachconfiguration, defined as:

wðkÞ ¼ ðfdi;si; ui; tig; i ¼ 1;2; . . . ; kÞ;

where k is the number of minutiae in the configuration. We use w

in this context because we may be considering a mark y(k), printx(k), database member z(k) or a simulated mark. Notice that w(k) isan ordered set, and rotation independent, provided that all featurearrays are always recorded in the same manner by the software(i.e. anti-clockwise around the centre).

The form of LR derived to address ‘‘finger’’ propositions in [6] is:

LRfinger ¼pðyðkÞjxðkÞminÞ

ð1=NÞPN

i¼1 pðyðkÞjzðkÞi;minÞ(1)

where the meaning of the various symbols is as follows:

LRfinger the likelihood ratio calculated for ‘‘fingerpropositions’’ – as in the first pair of propositionsin the introduction

k the number of minutiae in each of the twoconfigurations that are being compared. This is anumber between 3 and 12

yðkÞ the set of observations made on the mark. Theobservations are organised in a feature array asdescribed in Section 2

xðkÞi;min the set of observations on the k configuration inthe print that is closest to yðkÞ. The observationsare organised in a feature array as describedin Section 2

N the number of prints in the reference database

zðkÞi;min the set of k observations in the i’th member of thereference database that is closest to yðkÞ. Theobservations are organised in a feature array asdescribed in Section 2

pðyðkÞj . . .Þ the probability density of yðkÞ given that the markcame from the same finger as the k configurationspecified after the conditioning bar.

The probability densities p(y(k)| . . . ) are computed by means ofsimulation that takes into account: (a) variation that is known to

occur between examiners in the marking up of the position andorientation of minutiae; and (b) the distortion processes that occurwhen a mark is laid down on a surface by a finger.

Our research has been carried out for values of k from 3 to 12.Extensive studies have been carried out to optimise the computa-tion process according to a range of desiderata that includerobustness to these sources of variation.

3. Data

Several sources of data were used in the Neumann et al. [6]study and are described in full in that paper. Each database had itsown limitations. The data used for calculating probability densitiesfor the denominator of the LR, while suitable for the research thatwas carried out, would not necessarily be suitable for anoperational system. The size and representativeness of that datawere not tested; and issues such as relatedness between differentfingers from the same person, or between different people werenot studied.

More specifically, it consisted of a reference collection of 12,096fingers that had been taken under control conditions fromapproximately 12,000 individuals. This collection has not beenvalidated to serve as a reference database for casework purposes;rather, its purpose was to study the distribution of fingerprintpatterns (e.g., whorl, loop, arch) across the different fingers of thehand (e.g., thumb, forefinger etc.). The data from right and lefthands were pooled together. The breakdown of the database isshown in Table 2. For calculating LR’s for finger propositions, thedistinctions between finger types were ignored: so this was treatedsimply as a database of 12,096 fingers.

For the purpose of addressing person propositions, we createdan artificial database of 10-print records as follows. Six of therecords, selected at random, were discarded, leaving 12,090 printsthat were assigned randomly into 1209 groups of 10. Each group of10 was randomly ordered from one to ten, where the ten integerswere taken to correspond to the fingers of the hand according tothe convention shown in Table 3. Because of our selection process,the resulting finger number of any fingerprint in our new databasewas likely to be different from the real finger number of thatfingerprint.

Table 3Correspondence between fingers and finger numbers; indication of probabilities

assigned in Example 3 to use with Eq. (4).

Finger number (g) Finger Probability

Pr(G = gjIcs)

1 Right thumb 0.02

2 Right forefinger 0.08

3 Right middle finger 0.3

4 Right ring finger 0.2

5 Right little finger 0.1

6 Left thumb 0.025

7 Left forefinger 0.1

8 Left middle finger 0.1

9 Left ring finger 0.05

10 Left little finger 0.025

[()TD$FIG]

Fig. 1. (a) Example mark. (b) Example print from a right ring finger. Corresponding

minutiae are indicated by white dots.

C. Neumann et al. / Forensic Science International 207 (2011) 101–105 103

Again, we haven’t considered the suitability of this database foroperational use. We realise that it incorporates unsubstantiatedassumptions about the uniformity of minutiae configurations andpatterns across the ten fingers of the hand. However, it servesadequately to illustrate the principles of our approach.

4. Example

Fig. 1 presents an example of the comparison between a crimescene mark and the ring finger of the right hand of a givenindividual. An examiner has performed the comparison and hasfound 8 corresponding minutiae. The examiner was also able toexplain all the slight differences between the mark and the print byeffects of distortion, matrix and development technique.

4.1. Example 1

Using the reference database of 12,096 fingers, the LR that wascalculated for finger propositions, as given by Eq. (1) was2.97 � 109. The probability density assigned to the numeratorwas 0.0080; that assigned to the denominator was 2.72 � 10�12.The results are summarised in Table 4.

With a validated model, a LR of approximately 3 billion wouldrepresent extremely powerful evidence in support of theprosecution proposition: indeed, it is of the same order ofmagnitude that would be reported for a full 10-locus matchbetween two unmixed DNA profiles in the UK. However, we mustrecognise that finger propositions are not the most appropriatepropositions from the viewpoint of a court.

5. Extension to person propositions

We now extend the analysis to take into consideration that aperson, whether it be a suspect or a contributor to a referencedatabase, has up to ten fingers. It is widespread practice to takecontrol prints from all of a person’s fingers and so a crime scenemark may be compared with prints from up to ten fingers from anygiven individual.

We assume that the suspect has provided a control sample thatconsists of prints from all ten fingers, taken under carefully

Table 4Summary of the results obtained for examples 1, 2 and 3.

Numerator Denominator LR

Example 1 (Finger proposition) 8.0�10�3 2.72�10�12 2.97�109

Example 2 (Person proposition)

Pr(G = g|Ics) = 0.1

8.39�10�4 2.72�10�12 3.08�108

Example 3 (Person proposition)

Pr(G = g|Ics) as in Table 3

1.68�10�3 2.11�10�12 7.92�108

controlled conditions. We also assume that, to evaluate thedenominator of the LR, there is a reference database that consists ofcontrol prints, taken under controlled conditions, from M

individuals, who are representative, in some sense, of thepopulation of alternative sources for the crime mark.

In many countries, it is standard practice to number the fingersfrom an individual using the integers one to ten (Table 3). Weassume that the scene examiner carries out the examinationwithout being aware of any particular suspect and, using only thecircumstances relating to the way that the mark was laid down,

[()TD$FIG]

Fig. 2. Schema of the sash window in Example 3. The right handle is magnified and

the positions of the mark (A) and the smudge (B) are represented. The dotted line

indicates that these friction ridges are under the handle.

C. Neumann et al. / Forensic Science International 207 (2011) 101–105104

infers a probability distribution for G, the finger number of thefinger that made it, that we denote as follows:

PrðG ¼ gjIcsÞ; g ¼ 1;2; . . . ;10 (2)

where Ics denotes the observations at the crime scene relating tothe way that the mark was laid down.

We emphasise that our assumption incorporates the notionthat the probability distribution depends only on information fromthe scene and is independent of the individual who made the mark.Such inferences can be particularly informative when multiplemarks have been deposited as a single act of touch (referred to assimultaneous impression) [9]. For example, the observation of fourmarks on the side of a glass and of one opposing mark on the otherside, may allow the inference that all five marks were produced atthe same time by a single person, and so the single mark wasprobably left by a thumb, while the four opposing marks wereprobably left by the remaining fingers.

By combining (1) and (2), the LR for person propositions is givenby:

LRpers ¼P10

g¼1 pðyðkÞjxðkÞmin:gÞPrðG ¼ gjIcsÞ

ð1=MÞPM

i¼1

P10g¼1 pðyðkÞjzðkÞi;min:gÞPrðG ¼ gjIcsÞ

(3)

where xðkÞmin:g is the configuration in the print from the gth finger ofthe suspect that is closest to the crime mark; and zðkÞi;min:g is theconfiguration from the gth finger of the ith member of the databasethat is closest to the crime mark.

It will usually be the case that only one of the ten termspðyðkÞjxðkÞmin:gÞ in the numerator will be non-negligible – let this befor finger g0. Then it is a conservative approximation to write

LR pers �pðyðkÞjxðkÞmin:g0

ÞPrðG ¼ g0jIcsÞ

ð1=MÞPM

i¼1

P10g¼1 pðyðkÞjzðkÞi;min:gÞPrðG ¼ gjIcsÞ

(4)

6. Example continued

The two following examples are variations of the examplepresented in Fig. 1.

6.1. Example 2

The crime scene examiner has recovered the mark in Fig. 1 froma plane surface, such as a wall. There were no other relevant marks.In this case, the examiner has no reason for assigning anythingother than a uniform distribution: in other words, Pr(G = g j Ics) isassigned the value 0.1 for all values of g.

To compute LRpers using Eq. (4), we refer to the artificialdatabase of 1209 individuals for the denominator. The outcome isshown in Table 4. Note that the denominator is unchanged fromexample 1: this is because every finger in the person database isassigned the same weight and so, in this case, the database differsfrom that in example one by the omission of the 6 records thatwere randomly discarded in creating the artificial database. Thenumerator, however, is reduced by a factor of 10, purely because ofthe uncertainty in relation to which of the ten fingers of theoffender was the origin of the mark at the scene.

In this example, then, the LR for person propositions is one-tenth what it would have been for finger propositions. Clearly, it isof value to the court to be aware of this.

6.1.1. Example 3

In this example, we imagine that the mark in Fig. 1 wasrecovered from under the right handle of a sash window (whenlooking through the window from inside the room) that was usedas the exit point during a burglary (Trace A in Fig. 2). The crime

scene examiner has also observed a smudged mark on the right ofthe recovered mark (Trace B in Fig. 2). No ridge detail informationis present on that smudge; however, it led the examiner to considerthat the mark and the smudge were left simultaneously bysomebody who was opening the window. Given this view, itfollows that the finger that left the mark of interest (Fig. 1) had atleast one finger on its right side, considering the hand from thepalm-up view.

The crime scene examiner has passed this information, Ics, tothe fingerprint examiner. Based on this, and before comparing themark with any control prints, the fingerprint examiner considersthe following combinations of fingers to be more probable thanothers: right fore and middle fingers; right middle and ring fingers;left middle and fore fingers; left ring and middle fingers.Furthermore, since the mark has been recovered on the righthand handle of the sash window, the examiner assigns a higherprobability of the mark being left by a finger on a right hand.

In summary, prior to his examination, the examiner assigns theprobabilities presented in Table 3 to each finger number, given thecase information, Ics. Note that these probabilities need to add to one.

For the numerator recall that the examiner found theconfiguration closest to the mark in the print from the right ringfinger of the suspect, so g0 = 4; and from Table 3, we see thatPr(G = 4|Ics) = 0.2. For the denominator, the values in Table 3 areused to weight the contributions for each finger, from eachdatabase member, to the overall sum. The outcome of thecalculations is shown in Table 4. The numerator is twice what itwas in Example 2, because of our changed probability distributionfor finger number, G. The denominator is changed, but not greatly,as a result of the weighting applied to the different finger numbers.

7. Discussion

The assumptions that underlie our adoption of the notion of theprobability distribution Pr(G = g|Ics) are fundamental to the analysisthat we present. What we are assuming here is that the issue ofwhich of the ten fingers made the mark is not disputed betweenprosecution and defence. This is reasonable because the condition-ing includes only Ics: no consideration is taken with regard towhether prosecution or defence proposition were true. We couldconsider the event that G = g as a proposition and proceed as we dowith most of forensic science evidence: the scientist would be asked

C. Neumann et al. / Forensic Science International 207 (2011) 101–105 105

to consider likelihoods of the form Pr(Ics|G = g). These could beincorporated into our calculation, by means of the adoption of somekind of prior distribution Pr(G = g), based on knowledge of thedistribution of finger numbers that leave marks at crime scenes. Inprinciple, there is no particular difficulty with that approach but wehave not followed it for reasons of simplicity. We are aware thatfingerprint experts are, in general, comfortable with the notion ofconsidering such probabilities, but note that we are not aware of anystudies of competence in this regard.

In the example that we have considered, we have seen that therelative impact on the LR when changing from finger to personpropositions is not of great importance when they are both in thebillions. It might be of more impact when the LR’s are in thehundreds. However, this is not certain. We have seen that the effectof Pr(G = g|Ics) is more important on the numerator. Assuming that,in practice, the model would not be used when it is clear that themark and the print originate from different sources, pðyðkÞjxðkÞmin:g0

Þwill always be reasonably large and it is unlikely that variations ofthe Pr(G = g|Ics) term in the numerator will have a drastic impact.

8. Conclusion

It is quite common that configurations of minutiae in two (ormore) marks at a scene are found to be similar to configurations inprints from two different fingers from a suspect. No formalmechanism has ever existed for assessing the evidential value ofsuch an occurrence. However, we can see how the method that wehave described here may be applied to the problem. Certainly, it isa matter of considering person, rather than finger, propositions andthe extension of Eq. (4) to deal with multiple pairs of similarconfigurations is straightforward in principle.

We believe that the approach we have described in this paperhas not been attempted in the literature before. The currentparadigm in the fingerprint community is to recognise onlycategorical opinions of source. If we accept that the opinion that aparticular finger proposition is true with absolute certainty, then itis not necessary to move to person propositions: if the fingerbelongs to the suspect, then it is certain that he left the mark,notwithstanding any other considerations. However, we want tomove to a paradigm that recognises the validity of numericalmeasures of weight of evidence. Therefore, we need to develop aframework that addresses the propositions that are the most usefulto the justice system, such as person propositions.

Developing this reasoning further, we see that addressing thecorrect source level propositions enables to add relevanceinformation, and start addressing what Cook et al. [8] calledactivity level propositions. For example, if a set of marks arerecovered from a knife, and if it can be inferred that they have beenleft by the person who used it to stab a victim (e.g., if left in thevictim’s blood), the fingerprint examiner might consider itreasonable to address propositions relating to whether or notthe suspect is the person who carried out the stabbing.

Thus far, our quantitative approach has been based solely on theconfiguration of a set of minutiae. There is also a need to takeaccount of overall pattern of ridge flow, which might haveimportant impact on evidential value in some cases. We aredeveloping an approach to this aspect of the problem that we hopeto submit in a future paper.

We also recognise that there are many issues relating to thepresentation of numerical weights of evidence to a court. DNAprofiling is, of course, the forensic field that has led to much debateand there is much to be resolved. The logical framework ofinterpretation that we have invoked in our research is, we believe,the only tenable one in existence but we do not deny the existenceof contrary views. The issues require the attention of all of thevarious participants in the criminal legal process-scientific, police,legal and judicial. We hope to prepare a paper to initiate relevantdebate with particular regard to the field of fingerprints.

References

[1] C. Champod, Reconnaissance Automatique et Analyse Statistique des Minuties surles Empreintes Digitales, Ph.D. Thesis, University of Lausanne, 1995.

[2] D. Stoney, Measurement of fingerprint individuality, in: H. Lee, R. Gaensslen (Eds.),Advances in Fingerprint Technology, 2nd ed., CRC Press, Boca Raton, 2001, pp. 327–388.

[3] C. Champod, I.W. Evett, A probabilistic approach to fingerprint evidence, J. ForensicIdent. 51 (2001) 101–122.

[4] N. Egli, C. Champod, P. Margot, Evidence evaluation in fingerprint comparison andautomated fingerprint identification systems—modeling within finger variability,For. Sci. Int. 176 (2006) 189–195.

[5] C. Neumann, C. Champod, R. Puch-Solis, N. Egli, A. Anthonioz, A. Bromage-Griffiths,Computation of likelihood ratios in fingerprint identification for configurations ofany number of minutiae, J. For. Sci. 52 (2007) 54–64.

[6] C. Neumann, I.W. Evett, J.E. Skerrett, Assigning a numerical weight of evidence to afingerprint comparison, J. Roy. Stat. Soc. A, (2010) submitted for publication.

[7] I.J. Good, Probability and the Weighing of Evidence, Griffin, London, 1950.[8] R. Cook, I.W. Evett, G. Jackson, P.J. Jones, J.A. Lambert, A hierarchy of propositions:

deciding which level to address in casework, Sci. Justice 38 (1998) 231–240.[9] SWGFAST, Standard for Simultaneous Impression Examination, version 1, May

12th 2008, pp. 20.