Quality Assessment of Fingerprints with Minutiae Delaunay

Triangulation

Z. Yao, J. Le bars, C. Charrier and C. Rosenberger

Universite de Caen Basse Normandie, ENSICAEN, UMR 6072 GREYC, Caen, France

Keywords:

Fingerprint, Minutiae Template, Quality Assessment, Evaluation.

Abstract:

This article proposes a new quality assessment method of ﬁngerprint, represented by only a set of minutiae

points. The proposed quality metric is modeled with the convex-hull and Delaunay triangulation of the minu-

tiae points. The validity of this quality metric is veriﬁed on several Fingerprint Veriﬁcation Competition (FVC)

databases by referring to an image-based metric from the state of the art (considered as the reference). The

experiments of the utility-based evaluation approach demonstrate that the proposed quality metric is able to

generate a desired result. We reveal the possibility of assessing ﬁngerprint quality when only the minutiae

template is available.

1 INTRODUCTION

The purpose of ﬁngerprint quality assessment is to

improve or guarantee the performance of a biomet-

ric system (Grother and Tabassi, 2007) by forbid-

ding bad quality ﬁngerprint samples, especially dur-

ing the enrollment session. Existing studies of this

issue mostly deﬁne the quality in terms of the clarity

of ridge-valley pattern, contrast between foreground

and background, smoothness of orientation and etc

(Ratha and Bolle, 1999; Bolle et al., 1999; Chen et al.,

2004). No matter how many aspects are considered

by a ﬁngerprint quality assessment approach, it is all

about features employed for generating the quality

metric. Prior studies in estimating ﬁngerprint qual-

ity had proposed several features (Alonso-Fernandez

et al., 2007), among which some are carried out by

using an unique feature, while some others combine

multiple features together. For instance, Chen et al.

proposed the Fourier spectrum-based quality metric

with the Butterworth function, Zhao el al. (Zhao

et al., 2010) concluded that the orientation certainty

level (OCL) (Lim et al., 2002) also performs well for

high resolution ﬁngerprint image and Tabassi et al.

(Tabassi et al., 2004) proposed NFIQ with multiple

features including minutiae quality. To standardize

the quality metric of biometric sample, the quality has

been deﬁned as a utility property (Staff, 2009), i.e.

sample quality reﬂects its impact on the performance

of the system. However, system performance fully

relies on the matching approach such as minutiae-

based system which is employed most in actual de-

ployments. In this case, it is reasonable to consider

qualifying ﬁngerprint with only minutiae information,

particularly when using for embedded applications.

There are very few quality assessment approaches

that take into account minutiae information, such

as NFIQ. Moreover, none of the state-of-the-art ap-

proaches qualiﬁes a ﬁngerprint from the minutiae

template alone. The main contribution of the pro-

posed study is a black box algorithm that computes

quality score from a minutiae template associated to

the ﬁngerprint. In another word, it could be viewed as

a quality metric for assessing the quality of a minu-

tiae template. The beneﬁt of having this type of met-

ric is related to embedded biometric systems in smart

cards or smart objects where only the minutiae tem-

plate is available due to computational and storage

constraints.

This paper is organized as follows. Section 2

presents the proposed quality metric. Details of the

experimental results are given in section 3. Section 4

concludes the paper and discusses the perspectives.

2 METRIC DEFINITION

Fingerprint matching approaches, according to the lit-

erature (Maltoni et al., 2009), are broadly classiﬁed

as minutiae-based, correlation-based or image-based,

among which minutiae-based is the most widely stud-

315

Yao Z., Le Bars J., Charrier C. and Rosenberger C..

Quality Assessment of Fingerprints with Minutiae Delaunay Triangulation.

DOI: 10.5220/0005235603150321

In Proceedings of the 1st International Conference on Information Systems Security and Privacy (ICISSP-2015), pages 315-321

ISBN: 978-989-758-081-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

ied solution. A minutiae template generally provides

three kinds of information: 1) minutia location, 2)

the orientation and 3) the type of minutia point (ridge

ending and bifurcation), see ﬁgure 1.

Figure 1: A ﬁngerprint and its minutiae template.

These features are sufﬁcient to reconstruct a syn-

thetic ﬁngerprint from a given template (Feng and

Jain, 2011) as the orientation ﬁeld can be estimated.

Another kind of information is the amount of detected

minutiae points, which has been used as one factor

(Tabassi et al., 2004) for quality assessment of ﬁnger-

print samples. However, this information is far from

being enough for generating an effective quality met-

ric. In order to do so, the minutiae template is related

with the foreground of ﬁngerprint because the area of

minutiae indicates an available and useful region for

the so-called ’extractability’ of features. In this case,

this paper proposed to estimate ﬁngerprint quality by

modeling the associated minutiae template with the

convex-hull and Delaunay triangulation (Cf. ﬁgure

2).

Figure 2: A convex hull (left) and Delaunay Triangulation.

The 2D convex hull (Andrew, 1979)

= {(x

, y

)| j = 1, ··· , N

} (where N

is the

minutiae number of the i

ﬁngerprint) is deﬁned as

the smallest convex set that contains all the points of

a given set of minutiae F

in this case (Cf. ﬁgure 2).

The Delaunay Triangulation of a set of points P in 2D

plane is deﬁned as a triangulation DT(P) (Delaunay,

1934) that none of the points of the given set are

inside the circumcircle of any triangle of DT(P), as

illustrated in ﬁgure 2.

With the respective properties of these two geo-

metric structures, an area of the smallest informative

region of the ﬁngerprint and a set of areas and

perimeters of triangles composed by each 3 minutiae

points are obtained. By doing so, one unavoidable

problem is observed that almost all the templates

of bad quality ﬁngerprints contain both correctly

detected minutiae point and spurious points. Based

on this observation, we proposed a quality metric as

described below.

Let a minutiae template F

of a ﬁngerprint con-

taining a set of detected minutiae points represented

by m

= (x

, y

, θ

), where (x

, y

) is the location

and θ

is the orientation of the j

minutia point;

A convex hull denoted by C

and a set of triangles

) formed by Delaunay triangulation, formulated

as DT (F

) = {T

|k = 1, 2, ··· , L

} where L

(< 2N

)

is the number of triangles can be constructed from

. Correspondingly, the convex hull encloses all the

minutiae of F

with the smallest area represented by

, and a set of areas S

and perimeters P

of DT (F

)

are respectively obtained.

In the experiments, we observed that bad quality

samples generate tiny and extremely narrow triangles

(considered as unreasonable) due to spurious minu-

tiae points. The quantitative values of their area and

perimeter are (visually) not proportional to each other,

as observed in Figure 3.

Figure 3: Example of minutiae Delaunay triangulations of 3

different FVC images. NFIQ values are 2, 2 and 1, respec-

tively.

In ﬁgure 3, triangles drew by the pink color indi-

cates the unreasonable minutiae structures. Based on

these observations, the quality metric (abbreviated as

MQF afterwards) is calculated with several steps, as

described by algorithm 1. In the computation of the

ICISSP2015-1stInternationalConferenceonInformationSystemsSecurityandPrivacy

316

proposed quality metric, three thresholds are set for

triangle perimeter, triangle area and the ratio between

the perimeter and area of the triangle, which are rep-

resented by Y

, Y

and Y

, respectively. The details

for choosing the most appropriate parameters are dis-

cussed in section 3. The quality value q is dependent

on the size of the minutiae region so that it is normal-

ized into the range of [0, 100] on each database.

Algorithm 1: Computation of the quality score.

Input:

Minutiae Template F

Output:

Quality index, q;

1: Calculate the area of the convex hull C

, denoted

as A

;

2: Calculate perimeter and area for each triangle T

denoted as P

and S

;

3: A

= area (Search(P

< Y

));

4: A

= area (Search(S

< Y

));

5: A

= area (Search(P

< Y

& S

< Y

));

6: A

= area (Search(P

S

) > Y

);

7: S

area



− A



;

8: return q = S

area

;

Obviously, this algorithm relates the minutiae

template with the area of a region for matching oper-

ations as it has just been mentioned before. However,

this factor is not sufﬁcient so that we consider to re-

move a part of potentially useless area from the infor-

mative region due to the lack of image information.

Delaunay triangulation gives a relatively ideal solu-

tion to this problem thanks to the spurious minutiae of

bad quality images. For example, as it is depicted in

ﬁgure 3, some unreasonable triangles formed by spu-

rious minutiae on the border enable us to remove the

corresponding area. Another case is the tiny triangle

which is mostly happened to the area where the qual-

ity of ridge-valley pattern is relatively bad. The study

also noted that some ﬁngerprint images have several

genuine minutiae clustering in a very small area. This

case is not specially considered in the proposed al-

gorithm just because of the limitation of the template.

The area of each triangle is obtained by using Heron’s

formula (Aufmann et al., 2007).

3 EXPERIMENTAL RESULTS

In order to validate the MQF, we adopt several ap-

proaches to estimate the performance of the quality

metric: 1) the Pearson correlation coefﬁcients be-

tween the MQF and several others (from the state-of-

the-art) are calculated and 2) the MQF is evaluated

by using an utility-based evaluation approach (Yao

et al., 2014). The experiment is performed with a

laptop driving by an Intel Celeron dual-core CPU of

1.73GHz. The experimental protocol is presented at

ﬁrst.

3.1 Protocol et Database

In this study, several FVC databases with dif-

ferent resolutions (Maio et al., 2004) have

been used for experiments: FVC2000DB2A,

FVC2002DB2A, FVC2004DB1A, FVC2004DB2A

and FVC2004DB3A. The ﬁrst database is established

by a low capacitive sensor and the last one relies on a

thermal sweeping sensor, while others are established

by several optical sensors, see table 1 for details.

Table 1: Details of databases.

DB Sensor Type Resolution Image Dim

00DB2A Capacitive 500dpi 256×364

02DB2A Optical 569dpi 296×560

04DB1A Optical 500dpi 480×640

04DB2A Optical 500dpi 328×364

04DB3A Thermal 512dpi 300×480

Each of these databases involves 100 ﬁngerprints,

and 8 samples for each ﬁngerprint. In this case,

the matching scores involved in the experiment have

been calculated by using the NBIS tool (Watson

et al., 2007), Bozorth3. The intra-class scores con-

tain 7×100 = 700 genuine scores, and the inter-

class scores consist of 7×99×100 = 69300 impos-

tor scores for the whole database. Minutiae templates

used in the experiment were also extracted by us-

ing the NBIS tool, MINDTCT. This software gen-

erates a quadruple representation of minutia point,

= {x, y, o, q}, where (x, y) is the location of minutia

point, o indicates orientation and q is a quality score

of minutia point. In the experiment, the location has

been used only for calculating the proposed quality

metric.

3.2 Parameter Settings

Fernandez et al. (Alonso-Fernandez et al., 2007)

and Olsen (Olsen et al., 2012) respectively calcu-

lated Pearson and Spearman correlation coefﬁcients

between different quality metrics to observe their

behavior. Similarly, we investigate the behavior of

the proposed quality metric through the Pearson

correlation coefﬁcients, by which the parameters are

appropriately selected as well.

QualityAssessmentofFingerprintswithMinutiaeDelaunayTriangulation

317

The three thresholds (Y

, Y

and Y

) are all empir-

ical values observed in the experiments and they are

all dependent on the resolution of the image which is

supposed to be over 500 dpi in this study. With the

experiment, we noted that the smallest area of the tri-

angles of each template is generally less than 70 (con-

sidering a histogram of 100 bins). This value is only

a scalar without considering the unit of the measure-

ment. In this case, we ﬁrstly preferred to choose a

value of the area over 70. In addition, it is easy to

observe that a threshold larger than 80 may loose the

signiﬁcance of this parameter. The variation of the

correlation values (larger than 0.3) demonstrates this

problem, see ﬁgure 4.

Figure 4: The variation of correlation between the proposed

metric and OCL as the parameter changes.

Likewise, the smallest perimeter value of the tri-

angles of each template is mostly within the interval

[10, 80], and generally lies around 35 (according to

the histogram). In this case, we further consider the

relation between the area and the perimeter of those

triangles that seemed abnormal. Without considering

the unit of the two measurements (one is 1-D and

another is 2-D), we observed that the value of the

perimeter is generally smaller than the area. In this

case, inspiring by the Heron’s formula, we choose

a threshold to represent the ratio between these two

measurements. We observed that the triangle is

extremely narrow if the ratio between a perimeter

and an area is close to 1. Besides, similarly, it is

also not necessary to consider larger values for the

perimeter. We ﬁrst choose a reference quality metric

among all the others. The correlation of OCL doesn’t

vary so much on variant databases. Therefore, we

simply choose the OCL in the experiment. Figure 4

provides only the graphical result of the variation of

correlation value between OCL and the quality metric

obtained with a series values of two parameters. In

the experiments, the thresholds of the area and

perimeter vary in the range of [40, 100] and [30, 80]

with an interval of 1, respectively.

According to ﬁgure 4, we also observed that the

variation of Y

leads to more impacts on the corre-

lation coefﬁcient than Y

when other parameters had

been set approximately. In order to achieve a general-

ity of the proposed quality metric, the values of Y

, Y

and Y

in this study are 75, 70 and 0.8, respectively.

At last, the behavior of these parameters were esti-

mated by using performance validation approach, and

the variation of the performance measurement (EER)

obtained in a small interval of each of them tends to be

stagnant. With this empirical analysis, the parameters

are set as what had just been mentioned.

3.3 Feature Analysis

To validate the MQF, we calculate the correlation co-

efﬁcients between several quality metrics we have

studied including the MQF. In addition to the two

orientation-based indexes, OCL and the orientation

ﬂow (OF) (Lim et al., 2002), we also employ a

wavelet domain feature carried out via the Pet Hat’s

continuous wavelet (PHCWT) (Nanni and Lumini,

2007). In the literature, it is said that the Pet Hat

wavelet is sensitive to the sharp variations of features

such as ﬁngerprint ridges. Nevertheless, we also use a

pixel-based quality metric which is the standard devi-

ation (STD) of ﬁngerprint local block indicating pixel

information of the image (Lee et al., 2005). The NFIQ

is also involved in this section. Table 2 presents the

correlation results of the trial quality metrics.

Table 2: Inter-class Pearson correlation coefﬁcients.

FVC2002DB2A

OCL OF PHCWT STD MQF NFIQ

1 0.013 0.932 0.892 0.781 -0.503

0.013 1 0.092 0.122 0.070 0.061

0.932 0.092 1 0.954 0.788 -0.474

0.892 0.122 0.954 1 0.678 -0.374

0.781 0.070 0.788 0.678 1 -0.422

-0.503 0.061 -0.474 -0.374 -0.422 1

Table 2 provides only an inter-class correlation re-

sult of the employed quality metrics obtained from

FVC2002DB2A. According to the coefﬁcient values

indicated with the highlighted cells, one can observe

that MQF demonstrates the correlated behavior with

the others except the OF. The correlation coefﬁcients

between the proposed metric and others calculated

from the remaining databases are given in table 3

ICISSP2015-1stInternationalConferenceonInformationSystemsSecurityandPrivacy

318

Table 3: Pearson correlation coefﬁcients between MQF and

others.

MQF of OCL OF PHCWT STD NFIQ

00DB2 0.409 -0.131 0.291 0.301 -0.081

04DB1 0.899 0.253 0.905 0.817 -0.201

04DB2 -0.050 -0.489 0.722 0.650 -0.378

04DB3 0.863 0.021 0.818 0.811 -0.363

According to the results, in addition to

FVC2000DB2A, one can note that MQF shows

a relatively stable correlation with other metrics, i.e.

it exhibits an usability to variant databases. The cor-

relation value between the proposed metric and OCL

for FVC2004DB2A shows an odd value because

a lot of over-inked samples are contained in this

database. This problem results in some difﬁculties

for calculating the OCL and leads to a lot of singular

values. Note that the proposed metric uses only the

set of minutiae location, and the ﬁngerprint image is

considered as unavailable.

3.4 Evaluation

According to the literature (Grother and Tabassi,

2007), the quality measure of a biometric sample is

generally employed within 3 different cases: 1) in-

cluding enrollment phase, 2) veriﬁcation task and 3)

identiﬁcation. Enrollment is known as a supervised

task for getting relatively good quality samples. The

purpose for doing so is to guarantee the performance

or reduce the recognition error as much as possible,

i.e. the typical quality control operation. However,

if the purpose is to validate a quality metric without

considering the testing type (i.e. algorithm testing,

scenario testing and so on.), the variation of the qual-

ity of enrollment sample would generate distinctive

impacts on matching performance and the result is re-

peatable in the experiments. In this case, to estimate

the validity of the MQF, an enrollment phase evalu-

ation approach is applied to the quality metric (Yao

et al., 2014).

We computed the EER values of all the trial

databases by choosing the best quality samples as the

enrollments (in terms of quality value generated by

MQF and NFIQ). A valid quality metric for choos-

ing the enrollment samples should reduce error rates.

Two graphs with the logarithmic curves and the EER

values of two different cases are given in ﬁgure 5 to

illustrate the enrollment selection strategy.

In ﬁgure 5, the EER values of the two datasets

based on NFIQ are 13.2% (02DB2A) and 12.4%

(04DB2A), while the values corresponding to MQF

are: 10.5% (02DB2A), and 13.6% (04DB2A), respec-

tively.

(a) FVC2002DB2A

(b) FVC2004DB2A

Figure 5: The DET curves and global level EER val-

ues obtained by using the evaluation approach. 5a is

FVC2002DB2A; 5b is FVC2004DB2A.

Table 4: The average EER values based-on enrollment se-

lection.

00DB2A 04DB1A 04DB3A

MQF 5.05% 15.03% 6.96%

NFIQ 4.98% 15.33% 7.48%

According to this result, the performance of MQF

is validated with the property that a good quality in-

dex reduces the matching error. However, a further

validation needs to be acquired for making a conclu-

sion that the global EER value is a statistically ob-

jective measurement of the performance. To do so,

we calculate a conﬁdence interval (CI) (Giot et al.,

2013) at 95% level for the global EER values based

on different quality metrics. In biometrics, the CI of

two different measurements are able to indicate the

statistical difference between them if their conﬁdence

intervals do not overlap each other. The CI values of

the EER for each quality metric is calculated via a set

of randomly selected intra-class and inter-class score

QualityAssessmentofFingerprintswithMinutiaeDelaunayTriangulation

319

samples after enrollment selection. The size of each

kind of randomly selected matching scores is 500, and

hence the 95% CI is obtained with 1000 samples of

the EER values, i.e. this random selection has been

performed for 1000 iterations to calculate EER sam-

ples. Table 4 provides the average EER values of the

other 3 databases.

Table 5: The 95% conﬁdence interval of the EERs.

MQF NFIQ

00DB2A (CI) [0.0498 0.0510] [0.0492 0.0502]

02DB2A (CI) [0.1101 0.1118] [0.1323 0.1337]

04DB1A (CI) [0.1493 0.1509] [0.1531 0.1548]

04DB2A (CI) [0.1509 0.1535] [0.1318 0.1340]

04DB3A (CI) [0.0683 0.0694] [0.0742 0.0754]

In table 5, the CI of the EER values based on the

two quality metrics statistically illustrates the validity

of the proposed quality metric. The overlap happened

to FVC2000DB2A, for the EER values obtained from

this database is nearly the same. Moreover, we sim-

ply choose several images to illustrate the differences

between the two quality metrics and their drawbacks.

For instance, the MQF values of the samples given in

ﬁgure 6 are (2.94, 38.61, 38.46, 64.11, 61.2), and

their NFIQ values are all level 2. According to sam-

ple (a), one can ﬁnd that it contains only a partial of

the ﬁngerprint image which is not suitable for match-

ing. In addition, the samples with MQF values under

40 are not as good as a level 2 sample in this exam-

ple. The samples (b) and (c) would result in spurious

minutiae. On the other hand, an obvious shortage of

MQF is the area measurement which would generate

outliers in many cases, such as the samples illustrated

by ﬁgure 6 (d) and (e).

Figure 6: Illustration of the different between MQF and

NFIQ.

The experiments are implemented via Matlab

7.12. The computation takes approximately 0.423

seconds per sample according to a calculation of 1600

samples when the input is image, and 0.122 seconds

for template inputs.

4 CONCLUSION

This study mainly focuses on estimating ﬁngerprint

quality simply with a minutiae template. By investi-

gating the relation between image-based quality crite-

ria and the structure of minutiae template, we calcu-

late the area of minutiae region via a convex hull and

the Delaunay triangulation. The uniqueness of Delau-

nay triangulation provides a possibility that some un-

reasonable minutiae could be further eliminated from

template, and the particular rules for calculating con-

vex hull enables estimating a relatively minimum area

of the detected minutiae. Accordingly, we deﬁne

a simple yet efﬁcient quality metric for ﬁngerprint

and minutiae template. In another aspect, the quality

metric could be affected by some bad samples with

large minutiae region. The lack of image informa-

tion makes this problem inevitable. Correspondingly,

we analyzed the proposed quality metric via Pearson

correlation coefﬁcients and evaluated its performance

with an enrollment phase approach. Therefore, it is

reasonable to conclude that the proposed quality met-

ric is an effective measurement for assessing the qual-

ity of a various of ﬁngerprint samples when their as-

sociated templates are available only.

As ﬁngerprint quality metric is generally deﬁned

with multiple features, this quality metric therefore

could be a candidate for those composite metrics. The

future work of this study tends to concentrate on com-

bining this quality metric with some others extracted

from minutiae template to obtain better performance.

REFERENCES

Alonso-Fernandez, F., Fierrez, J., Ortega-Garcia, J.,

Gonzalez-Rodriguez, J., Fronthaler, H., Kollreider,

K., and Bigun, J. (2007). A comparative study of

ﬁngerprint image-quality estimation methods. Infor-

mation Forensics and Security, IEEE Transactions on,

2(4):734–743.

Andrew, A. M. (1979). Another efﬁcient algorithm for con-

vex hulls in two dimensions. Information Processing

Letters, 9(5):216–219.

Aufmann, R., Barker, V., and Nation, R. (2007). College

Trigonometry. Cengage Learning.

Bolle, R. M., Pankanti, S. U., and Yao, Y.-S. (1999). System

and method for determining the quality of ﬁngerprint

images. US Patent 5,963,656.

Chen, T., Jiang, X., and Yau, W. (2004). Fingerprint image

quality analysis. In Image Processing, 2004. ICIP ’04.

2004 International Conference on, volume 2, pages

1253–1256 Vol.2.

Delaunay, B. (1934). Sur la sphere vide. Izv. Akad.

Nauk SSSR, Otdelenie Matematicheskii i Estestven-

nyka Nauk, 7(793-800):1–2.

ICISSP2015-1stInternationalConferenceonInformationSystemsSecurityandPrivacy

320

Feng, J. and Jain, A. K. (2011). Fingerprint reconstruction:

from minutiae to phase. Pattern Analysis and Machine

Intelligence, IEEE Transactions on, 33(2):209–223.

Giot, R., El-Abed, M., and Rosenberger, C. (2013). Fast

computation of the performance evaluation of biomet-

ric systems: Application to multibiometrics. Future

Gener. Comput. Syst., 29(3):788–799.

Grother, P. and Tabassi, E. (2007). Performance of biomet-

ric quality measures. Pattern Analysis and Machine

Intelligence, IEEE Transactions on, 29(4):531–543.

Lee, B., Moon, J., and Kim, H. (2005). A novel measure

of ﬁngerprint image quality using the Fourier spec-

trum. In Jain, A. K. and Ratha, N. K., editors, Society

of Photo-Optical Instrumentation Engineers (SPIE)

Conference Series, volume 5779 of Society of Photo-

Optical Instrumentation Engineers (SPIE) Conference

Series, pages 105–112.

Lim, E., Jiang, X., and Yau, W. (2002). Fingerprint qual-

ity and validity analysis. In Image Processing. 2002.

Proceedings. 2002 International Conference on, vol-

ume 1, pages I–469–I–472 vol.1.

Maio, D., Maltoni, D., Cappelli, R., Wayman, J. L., and J.,

A. K. (2004). Fvc2004: Third ﬁngerprint veriﬁcation

competition. In Biometric Authentication, pages 1–7.

Springer.

Maltoni, D., Maio, D., Jain, A. K., and Prabhakar, S. (2009).

Handbook of ﬁngerprint recognition. Springer.

Nanni, L. and Lumini, A. (2007). A hybrid wavelet-

based ﬁngerprint matcher. Pattern Recognition,

40(11):3146–3151.

Olsen, M., Xu, H., and Busch, C. (2012). Gabor ﬁlters as

candidate quality measure for NFIQ 2.0. In Biomet-

rics (ICB), 2012 5th IAPR International Conference

on, pages 158–163.

Ratha, N. K. and Bolle, R. (1999). Fingerprint image qual-

ity estimation. IBM TJ Watson Research Center.

Staff, B. S. I. (2009). Information Technology. Biometric

Sample Quality. Framework. B S I Standards.

Tabassi, E., Wilson, C., and Watson, C. (2004). NIST ﬁn-

gerprint image quality. NIST Res. Rep. NISTIR7151.

Watson, C. I., Garris, M. D., Tabassi, E., Wilson, C. L.,

Mccabe, R. M., Janet, S., and Ko, K. (2007). User’s

guide to nist biometric image software (nbis).

Yao, Z., Charrier, C., and Rosenberger, C. (2014). Util-

ity validation of a new ﬁngerprint quality metric.

In International Biometric Performance Conference

2014. National Insititute of Standard and Technology

(NIST).

Zhao, Q., Liu, F., and Zhang, D. (2010). A comparative

study on quality assessment of high resolution ﬁnger-

print images. In Image Processing (ICIP), 2010 17th

IEEE International Conference on, pages 3089–3092.

IEEE.

QualityAssessmentofFingerprintswithMinutiaeDelaunayTriangulation

321