Forensic Science International 214 (2012) 195–199

Quantitative assessment of evidential weight for a fingerprint comparison. Part II:A generalisation to take account of the general pattern

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

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

A R T I C L E I N F O

Article history:

Received 11 March 2011

Received in revised form 9 August 2011

Accepted 11 August 2011

Available online 1 September 2011

Keywords:

Fingerprints

Likelihood ratio

Weight of evidence

A B S T R A C T

The authors have proposed a quantitative method for assessing weight of evidence in the case where a

fingermark from a crime scene is compared with a set of control prints from the ten fingers 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 individual who left the crime mark. The current method considers only

information extracted from minutiae, such as location, direction and type. It does not consider other

information usually taken into account by fingerprint examiners, such as the general pattern of the ridge

flow on the mark and the control prints. In this paper, we propose an improvement to our model that

allows a fingerprint examiner to take advantage of pattern information when assessing the evidential

weight to be assigned to a fingerprint comparison. We present an extension of the formal analysis

proposed earlier and we illustrate our approach with an example.

� 2011 Elsevier Ireland Ltd. All rights reserved.

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jou r nal h o mep age: w ww.els evier . co m/lo c ate / fo r sc i in t

1. Introduction

In [1], we have described a quantitative method for assigning avalue to the weight of evidence associated with a comparisonbetween a latent fingermark from a crime scene and a controlfingerprint from a known individual (referred to as a mark and aprint, respectively, from here on). The method was then general-ised [2] to better reflect actual practice. Indeed, the mark is usuallynot just compared with a single finger, but with a set of controlprints that represent all of the suspect’s fingers. The methodproposed in [2] is based on the mathematical comparison ofconfigurations of minutiae and addresses ‘‘person’’ propositions ofthe kind:

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

The model presented in [1,2] focuses on minutiae and does nottake into account other features of the ridge flow in fingerprints. Inthis paper, we introduce the possibility for fingerprint examinersto assign probabilities associated with the general pattern of theridge flow.

In the next section, we start from the model developed in [2]and we consider how it can be extended to include probabilitiesrelated to general pattern of ridge flows.

* Corresponding author. Tel.: +1 415 272 6752.

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

0379-0738/$ – see front matter � 2011 Elsevier Ireland Ltd. All rights reserved.

doi:10.1016/j.forsciint.2011.08.008

We then proceed to an example of a mark/print comparison toillustrate how the method might be applied in casework. We willshow how the Likelihood Ratio (LR) is affected by general patterninformation.

2. The quantitative model for assessing the weight offingerprint evidence

The method for assessing the weight of fingerprint evidence hasbeen developed in [1] and extended [2] to account for ‘‘person’’propositions.

In these papers, we defined the multi-dimensional variablesy(k), x(k), and z(k) to represent configurations of k minutiae on themark, the defendant’s print, and reference prints from a databaserespectively. These variables have been detailed in [1]. Eachvariable includes a set of 5k measurements describing the shape ofthe configuration (e.g. distance between minutiae, area of theconfiguration), and the types and directions of the minutiae.

The form of LR derived to assign weight to fingerprint evidenceis [2]:

LRpers ¼P10

g¼1 pðyðkÞjxðkÞmin:gÞPrðG ¼ gjIcsÞ

ð1=NÞPN

i¼1

P10g¼1 pðyðkÞjzðkÞi;min:gÞPrðG ¼ gjIcsÞ

(1)

where the meaning of the various symbols is as follows:

LRpers: The likelihood ratio calculated for ‘‘person’’ propositions– as in [2].

Table 2Correspondence 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

C. Neumann et al. / Forensic Science International 214 (2012) 195–199196

Ics: Observations at the crime scene relating to the circum-stances under which the mark was laid down.k: The number of minutiae in each of the two configurationsthat are being compared. In our current model, this is a numberbetween 3 and 12.G: Number of the considered finger (g = 1, 2, . . ., 10).y(k): The set of observations made for the k minutiae in themark.x kð Þ

min:g: The set of observations made for the k minutiae of theconfiguration in the print – from the g’th finger of the defendant– that is closest to y kð Þ.N: The number of sets of 10 prints in the reference database, i.e.the number of people.z kð Þ

i;min:g: The set of observations made for the k minutiae of theconfiguration of the print – of the g’th finger of the i’thindividual in the reference database – that is closest to y kð Þ.p(y(k)j. . .): The probability density of y kð Þ given that the markcame from the same finger as the k-minutiae configurationspecified after the conditioning bar.

The probability densities pðy kð Þj:::Þ are computed by means ofsimulation that takes into account: (a) variation that is known tooccur 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 [1].

3. Data

The model has been optimised using the National Institute ofStandards and Technology (NIST) SD27 dataset. Its performancehas been measured for values of k from 3 to 12, using a validationdataset constituted of data obtained from casework and from theU.S. National Fingerprint database [1].

The model uses a reference database for calculating probabilitydensities for the denominator of the LR. The collection isconstituted of 12,096 fingers from approximately 12,000 individ-uals. The specific breakdown of our dataset can be found in Table 1.The data from right and left hands were pooled together.

For the purpose of addressing the propositions discussed in thispaper, we created an artificial database of 10-print records asfollows. Six of the records, selected at random, were discarded,leaving 12,090 prints that were assigned randomly into 1209groups of 10. Each group of 10 was randomly ordered from 1 to 10,where the 10 integers were taken to correspond to the fingers ofthe hand according to the convention shown in Table 2.

We are not claiming that this reference collection would besuitable for operational use. Indeed, it incorporates unsubstanti-ated assumptions about the uniformity of minutiae configurationsand patterns across the 10 fingers of the hand. Nevertheless, itremains one of the largest non-governmental fingerprint datasets,and it serves adequately to illustrate the principles of our approach

Table 1Structure 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

and to provide the reader with a feel of the range of magnitude ofthe LRs that can be expected with our model.

4. Extension to incorporate observations made on the generalpattern

We are now interested in expanding the possibilities forfingerprint examiners to inform the model with observations madeon the mark and the print. We extend our analysis and nowincorporate observations on the pattern of the ridge flow that canbe made on the mark and on the print.

We define t as the general pattern of the ridge flow of afingerprint. Although this is essentially a continuous quantity, wetreat it as a discrete type for now. In our model, it can take fivevalues: 1 = arch; 2 = whorl; 3 = right loop; 4 = left loop; 5 = un-known. In any control print, we consider that t would be assignedwith certainty to any of the first four types, or would be a complexcombination of any of the four basic types and thus deemedunknown.

We also introduce the term R that summarises, in some fairlyinformal and discrete way, the observations that an examinermakes regarding the pattern of the ridge flow in the mark. Forexample, R would capture the presence, or absence, of delta(s) andcore, or the curvature of the ridge flow.

When it comes to minutiae, in [1,2] we have consideredquestions such as ‘‘what is the probability density of observing theconfiguration y(k) on the mark, if it was left by finger that also leftthe configuration x(k) (or zi

(k) – in the case of the denominator)’’.In the case of the pattern of the ridge flow, which we are

treating as a discrete variable, we consider ‘‘the probability ofobserving this ridge flow R in the mark, if the mark was left by afinger with an arch (respectively a whorl, a loop, etc.)’’. In otherwords, we aim to elicit personal probabilities on PrðR tÞj from theexaminer.

After introducing R and t into the numerator of the LR proposedin [1] and [2], and after some simplification, we obtain:

numpers ¼X10

g¼1

pðyðkÞ; RjxðkÞmin:g ; tgÞPrðG ¼ gjIcsÞ (2)

Expanding the first term, we write:

numpers ¼X10

g¼1

pðyðkÞjR; xðkÞmin:g ; tgÞPrðR xðkÞmin:g ; tg

����

PrðG ¼ gjIcsÞ (3)

We can simplify Eq. (3) further if we make the followingassumptions:

Assumption 1. The probability of the observation made on thepattern of the ridge flow on the mark (R) depends only on thepattern type tg.

�Þ

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

Corresponding minutiae are indicated by white dots.

C. Neumann et al. / Forensic Science International 214 (2012) 195–199 197

Assumption 2. The probability density of the configurations on themark depends only on xðkÞmin:g: we have already defined this aspðyðkÞjxðkÞmin:gÞ.

Then:

numpers ¼X10

g¼1

pðyðkÞjxðkÞmin:gÞPrðR tg

�� �PrðG ¼ gjIcsÞ (4)

Eq. (4) is very similar to the one of the LR in Eq. (1), with anadditional term capturing the additional information of the patternof the ridge flow.

Realistically, we assume that, if the prosecution proposition istrue, then the mark will display considerably more similaritieswith one of the suspect’s fingers than with any of his/her otherfingers. Therefore, one of the pðyðkÞjxðkÞmin:gÞ terms will besubstantially larger than the others – let this be for finger g0.Then it is a conservative approximation to write:

numpers ¼ pðyðkÞjxðkÞmin:g0ÞPrðR tg0

�� �PrðG ¼ g0jIcsÞ (5)

Eq. (5) implies that if the pðyðkÞjxðkÞmin:gÞ term is, for example,maximum for the right index finger, then it is necessary for thefingerprint examiners to address two questions:

Question 1. Given the circumstances in which the mark was laiddown (represented by Ics), what is the probability that it was madeby a right index finger?

Question 2. Given that the pattern type of the suspect’s right indexfinger is t, what is the probability that the ridge flow in the markwould have been observed?

The former of the two questions was already addressed in [2].We believe that the latter would most appropriately answered bya pre-assessment: the examiner would be asked for theprobability of the observed ridge flow given that the patterntype was 1, 2, 3, 4 or 5. Note that these probabilities do not sum toone and note also that, rather than their absolute magnitudes it istheir relative magnitudes that matter, as will be seen in Eq. (7).Subjective assignment of these probabilities under these circum-stances will be presented in an example below and should not be aproblem.

For the denominator, we assume that there is a referencecollection of N ten-print forms, such as the one described earlier,and then, making assumptions analogous as Assumptions 1 and 2above:

denpers ¼1

N

XN

i¼1

X10

g¼1

pðyðkÞjzðkÞi;min:gÞPrðR tj gÞPrðG ¼ gjIcsÞ (6)

Combining Eqs. (5) and (6), and rearranging slightly, we have:

LRpers ¼pðyðkÞjxðkÞmin:g0

ÞPrðG ¼ g0jIcsÞ

ð1=NÞPN

i¼1

P10g¼1 pðyðkÞjzðkÞi;min:gÞPrðG ¼ gjIcsÞðPrðR tj gÞ=PrðR tg0

��(7)

This is very similar to Eq. (1). The additional ratio in Eq. (7) canbe seen as a weighting of the similarities between the ridge flows ofthe mark and the suspect’s print, versus the ones between the markand any other reference print.

Therefore, we observe that the presence of the ratio in thedenominator of the LR naturally regulates the contribution of eachgeneral pattern to the denominator of the LR. For example, if themark has been left by a finger with an arch pattern, the PrðR tgÞ

��terms for all other general patterns are going to be negligible; thusonly pðyðkÞjzðkÞi;min:gÞ terms for reference fingers with an arch aregoing to contribute to the denominator of the LR. Since N remains

constant, the denominator of the LR is dependent on the respectivedistribution of the various general patterns for the different fingernumbers.

5. Example

In this example, we use our third example from [2] as a startingpoint. The circumstances of this example are repeated below. Fig. 1presents an example of the comparison between a crime scenemark and the ring finger of the right hand of a given individual. Weconsider that the mark was recovered from under the right handleof a sash window (when looking through the window from insidethe room). The window was used as the exit point during aburglary (Trace A in Fig. 2). The crime scene examiner has also

Fig. 2. Schema of the sash window in the example. 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.

Table 3Correspondence between pattern and pattern number; ratio used in Eq. (7);

probability assigned to the various Pr(Rjtg).

tg General pattern Pr(Rjtg) PrðR tg ÞjPrðR tg0

Þj

1 Arch 0.1 0.167

2 Whorl 0.6 1

3 Right loop 0.9 1.5

4 Left loop 0.9 1.5

5 Unknown 1 1.667

C. Neumann et al. / Forensic Science International 214 (2012) 195–199198

observed a smudged mark on the right of the recovered mark(Trace B in Fig. 2). No ridge detail information is present on thatsmudge; however, it led the examiner to consider that somebody,who was opening the window, left the mark and the smudgesimultaneously.

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 two questions reported above.

The answer to the first question (that of the finger number) hasbeen addressed in [2]. We proposed that a fingerprint examiner,based on the information Ics, might assign the probabilitiesPr(G = gjIcs) as in Table 2.

In this paper, we are concerned with answering the secondquestion, which is the assignment of probabilities in the PrðR tgÞ

��terms. When considering the ridge flow of the mark in Fig. 1, weimagine that the fingerprint examiner might consider it morelikely if the mark had been left by a loop or a whorl and less likely ifleft by an arch. Following the examination of the ridge flow, theexaminer might assign the probability proposed in Table 3. Notethat these probabilities do not add up to one. Note also that wehave set, by convention, PrðR tgÞ ¼ 1

�� when tg = 5 (patternunknown); this implies that the absence of information, or

Table 4Comparison of the results obtained in [2] with the ones obtained in this paper.

Numer

Example with Eq. (1) and Pr(G = g|Ics) as in Table 3 1.68 �

Example with Eq. (7), Pr(G = g|Ics) as in Table 3

and accounting for PrðR tgÞ�� as in Table 4.

1.68 �

decision, on the pattern of the control print will result in aconservative denominator of the LR.

Then the examiner proceeds to perform the comparison andfind 8 corresponding minutiae (Fig. 1). The examiner is also able toexplain all the slight differences between the mark and the print byeffects of distortion, matrix and development technique.

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 2, we see thatPr(G = 4|Ics) = 0.2. We observe that the general pattern of the ridgeflow of the control print in Fig. 1 is a whorl: from Table 3, we seethat PrðR tg0

Þ ¼ 0:6�� .

For the denominator, the values in Tables 2 and 3 are used toweight the contributions for each finger, from each databasemember, to the overall sum. The outcome of the calculations isshown in Table 4. The results from [2], computed with Eq. (1), havebeen reported to assess the effect of the general pattern on the LR.

The numerator of both LRs is equal; this was expected since thenumerator of Eqs. (1) and (7) is the same. The denominator ischanged, but not greatly, as a result of the weighting applied to thedifferent general patterns. Greater changes might be observeddepending on:

(a) the extent of information observed on R. For example, in ourexample, loops and whorls represent approximately 94% of theridge flows observed on fingers [3]. A better resolution of thecategories for t will lead to a greater impact of thedetermination of the ridge flow on the denominator.

(b) A more accurate representation of the distribution of eachgeneral pattern on the different finger numbers.

6. Discussion

To simplify our analysis, we made two assumptions. Both arerooted in the same argument, however the first assumption is morerobust than the second one. The first assumption – that theprobability of the observation made on the pattern of the ridgeflow on the mark (R) depends only on the pattern type tg – is alwaysreasonable since the observation of t is overwhelmingly moreinformative with respect to R than any observations made on theconsidered minutiae configuration.

The second assumption – that the probability of the config-urations on the mark depends only on xðkÞmin:g (or zðkÞmin:g for thedenominator) – is always reasonable, except when (a) the markconfiguration is directly on a core or a delta and (b) the considered t

is an arch. In this case, the assumption is wrong, since theobservation on the mark configuration in a delta or a core is clearlyincompatible with the observation of the arch pattern on the print.At most, this can occur in 6% of the cases [3]; however, in mostcases we can expect the minutiae configuration on the mark to bein the periphery of the ridge flow. Therefore, we consider that ourassumption is valid in most cases.

We have seen that the introduction of the general patterninformation did not have a major effect between the LRs computedin [2] and in the above example. We chose to classify t in fivecategories. We have seen that apart from t = 1 for arches (6% of theobserved general pattern [3]), these categories are not very

ator Denominator LR

10�3 2.11 � 10�12 7.92 � 108

10�3 2.06 � 10�12 8.12 � 108

C. Neumann et al. / Forensic Science International 214 (2012) 195–199 199

specific. A higher resolution is needed to define these categories ina more useful way. The complete National Crime InformationCenter (NCIC) system [3] might be used; however, we might reachthe opposite situation: the NCIC system is so complex thatobservations on R will be too limited to narrow down accuratelythe class of the mark. A more elegant solution would be to design asystem that would assign PrðR tÞj (semi-)automatically by usingimage recognition and comparison algorithms. PrðR tÞj would thenbecome a probability density function.

7. Conclusion

Initially, our research aimed at providing a quantitativeassessment of the weight of evidence provided by fingerprintcomparisons [1]. While the original model could realistically beemployed to complement existing procedures for formingopinions, it was only considering ‘‘finger’’ propositions. Further-more, it was exclusively considering information related to theposition, direction and type of minutiae.

In [2] we recognised that ‘‘finger’’ propositions were generallynot best suited in most cases. We have thus extended our model toconsider ‘‘person’’ propositions. In the current paper, we address acommon challenge from the fingerprint community: that currentstatistical models do not account for all level of details consideredby fingerprint examiners when comparing fingerprints. The modelproposed in this paper now considers together general patterns,finger number and minutiae configurations. We have shownthrough an example how the proposed model can easily beimplemented in casework using examiners’ training and experi-ence as a means of assigning the required probabilities.

We realise that our model still does not account for all level ofdetails considered by fingerprint examiners. However, we believethat such a model, based on the more robust fingerprint features, canalready be implemented in practice, while it is improved to take intoaccount the more volatile characteristics, such as pores and ridgeedges. Indeed, our method provides a strong basis for a quality

assurance tool that will help convergence towards a commonreporting standard within the community and will contribute to thereduction of variability between individuals and organisations.

Our work needs to be extended beyond the development of thefundamentals of the model. The use of such model to supportfingerprint examination in operation will require the completion ofa number of critical stages. The dataset supporting the assignmentof the probability density in the denominator of the model needs tobe completed and validated; however, the owners of large datasets(local and national governments), which would be representativeof populations, are currently not making them available toresearchers. More generally, the sensitivity of the model to variousparameters (mostly user-related) needs to be studied: e.g., impacton the LR of the onscreen selection of the minutiae, and theassignment of probabilities for the finger number or the generalpattern.

In addition, further work needs to be performed on thepresentation of numerical weights of evidence in court, and on thebusiness and operational benefits of the use of the model incasework [4]. Finally, the complex mathematics of the model needsto be implemented in a user-friendly software package, and itsusers need to receive appropriate training (basic statistics,interpretation of forensic evidence, use of software package) inthe newly proposed approach.

References

[1] C. Neumann, I.W. Evett, J. Skerrett, Quantifying the weight of evidence from aforensic fingerprint comparison: a new paradigm, J. R. Stat. Soc. A 175 (2012) 1–26.

[2] C. Neumann, I.W. Evett, J.E. Skerrett, I. Mateos-Garcia, Quantitative assessment ofevidential weight for a fingerprint comparison. I. Generalisation to the compari-son of a mark with set of ten prints from a suspect, Forensic Sci. Int. 207 (2011)101–105.

[3] National Crime Information Center (NCIC) fingerprint pattern classification, http://www.dermatoglyphics.com/mfre/ (last visited 28.5.10).

[4] C. Neumann, I. Mateos-Garcia, G. Langenburg, J. Kostroski, J.E. Skerrett, M. Koolen,Operational benefits and challenges of the use of fingerprint statistical models: afield study, Forensic Sci. Int. (2011), doi:10.1016/j.forsciint.2011.05.004.