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c. Thin layer of material glued to a real ﬁnger,

including real skin cells grown in a laboratory

3. Original ﬁnger:

a. Cut out

b. Belonging to a dead person

c. Alive person under threat

Significant Developments in Fingerprint

Spoofing

In the early 1990s, Ton van der Putte developed and

improved a technique to fool the available biometrical

ﬁngerprint recognition systems. But when he con-

tacted the manufacturers and showed them the secu-

rity breach in their systems, it was ruled unimportant

and nothing was done to solve it. In 2000, van der

Putte and Jeroen Keuning decided to raise people’s

awareness and published an article [4]‘‘as a warning

to those thinking of using new methods of identiﬁcation

without ﬁrst examining the technical opportunities for

compromising the identiﬁcation mechanism.’’ Using

duplication with and without cooperation and materi-

al such as silicone rubber, van der Putte and Keuning

fooled four optical sensors and two silicon-based

capacitance sensors.

In 2001, Ka

kona [5] described how to spoof an

optical ﬁngerprint sensor using a printed ﬁngerprint

(Fig. 2) and reactivating latent ﬁngerprints on the

sensor’s surface by breathing on it. In 2002, Thalheim

et al. [6] tested ﬁve solid-state and two optical ﬁnger-

print sensors. Gummy bears were introduced by

Matsumoto [7] in 2002. The experiments involved 11

commercially available ﬁngerprint sensors, both opti-

cal and capacitive, using a new cheap material, gelatin.

Further studies from Kang [8] and Blomme

[9]

extended the previous work. Ste

n et al. [ 10] spoofed

a capacitance sensor using hot glue for the negative

mold and gelatin for the fake ﬁnger. Marie Sandstro

(2004) published her thesis [11], ‘‘Liveness Detection

in Fingerprint Recognition Systems,’’ which gathered

most of the available technologies at that time as w ell

as experiment results on various sensors.

In 2006, Ton van der Putte updated his work [12]

using additional material including silicon gel, acrylic

paint, gelatin, gum arabic. Ongoing attempts to spoof

ﬁngerprint sensors continue to appear on the Internet;

for instance, the Chaos Computer Club [ 13] used

wood glue and published their results online (Fig. 3).

Fingerprint Fake Detection. Figure 2 Printed fingerprint spoofing an optical sensor.

460

Fingerprint Fake Detection

Making a Fake Fingerprint

Making a fake ﬁngerprint always requires a ﬁngerprint

image. The easiest way to get a good ﬁngerprint image

is to have the cooperation of the donor. This is rarely

the case in the real world, except when the latent print

is left on the sensor (Level 1). In that case, the donor

completes a successful acquisition; later, the impostor

‘‘reactivates’’ the latent print by breathing on the

sensor. This happened in the past with some optical

systems and with some capacitance-based sensors.

A simple algorithm rejecting an image previously

acquired is generally enough to avoid this problem,

while swipe-sensing just eliminates this possibility.

The required ﬁngerprint image is not necessarily

exactly the same as the original ﬁngerprint of the

donor. Minutia matching (which is the main matching

technolog y for ﬁngerprints) only requires having the

minutia locations and directions at the right place. It is

possible, in theory, to create a ﬁngerprint image with

the right minutia locations that does not look like the

original. This requires accessing the minutiae locations

stored in the templa te, which should be ciphered.

Work related to some form of automated reconstruc-

tion has been proposed, requiring only access to the

matching score (hill-climbing) [14, 15]. This technique

is far more difﬁcult compared to obtaining the

original ﬁngerprint.

So in general, an impostor will take the easiest way

to obtain the original ﬁngerprint image. We will not

deal here with the Level 3 which requires the original

ﬁnger, cut, or belonging to a dead person. Obtaining

the original image can be done with or without coop-

eration. With cooperation is the easiest way, and most

Fingerprint Fake Detection. Figure 3 Wood glue using a printed fingerprint as negative.

Fingerprint Fake Detection

461

articles dealing with spooﬁng assume that the right

ﬁnger is available to create a negative mould. Without

cooperation will be the most common situation. For-

tunately, stealing the ﬁngerprint of someone else is not

easy. Even for forensic professionals, it is hard to iden-

tify people from ﬁngerprints left in a crime scene.

Moreover, it is very difﬁcult to select which ﬁngerprint

to use. It is likely that the foreﬁnger is the most com-

mon ﬁnger used in a ﬁngerprint system, but selecting

the right ﬁngerprint is not obvious.

Once the right image is obtained, image processing

skills are generally required to enhance the ﬁngerprint.

Printed circuit technologies are often proposed to cre-

ate a negative mould, but sometimes direct molding

techniques, such as a rubber stamp (Fig. 4), can be

used to get a positive.

With a negative mold, you need to create the posi-

tive cast that will be used to spoof the ﬁngerprint

sensor. Glue, latex, gelatin, and other materials have

been proposed (Fig. 5), but the most difﬁcult thing is

to select the right material that properly ﬁts the sensor.

Latex may work for some sensors and not for others.

Understanding the physics of the sensing techniques

will help. So, at the end of the day, making a fake

ﬁnger without cooperation is difﬁcult, but far from

being impossible.

Liveness Measurement

To be able to detect a fake, we must ﬁrst answer the

question of what deﬁnes a live ﬁnger. Some activities

related to liveness are:

1. Cellular metabolism with material transformation

(protein)

2. Movement

3. Heat production (a sub-product)

4. Blood circulation fo r material delivery and heat

transportation (regulation)

These activities have a number of signatures: physical,

chemical, mechanical, nervous, geometrical, to name a

few. Moreover, signiﬁcation changes with the observa-

tion scale.

Detection methods can be active or passive. Active

techniques involve a response to a stimulu s, and can

be voluntary or involuntary. It could be seen like a

challenge-response as used in regular cryptographic

techniques. Involuntary are reﬂexive challenge res-

ponses (removing your ﬁnger when you feel an electri-

cal shock), while voluntary are behav ioral challenge

responses (how many vibrations did you feel?). Active

detection is very interesting, because the nervous sys-

tem up to the brain can be involved, which is a good

marker of aliveness. But generally, active detection

is not very practical from a user point of view, and

nociceptive methods are not acceptable.

Passive techniques are linked to physiological activ-

ity of the ﬁnger. Here are some physiological data

about ﬁngers:

1. Cells, a bone, and a nail make a structure of about

1–10 cm

. Note that there is no muscle (and so

electrical activity is coming from other areas)

2. Arterial blood brings all chemicals, oxygen, and

heat and returns to the body through veins

3. Skin is composed of three layers:

a. Stratum corneum made of dead cells, more or

less hydrated, 100 mm thick, variable electrical

conductivity

b. Blood-free epidermis, 0.05–1 mm thick, made

of proteins, lipids, melanin-forming cells

c. Dermis: dense connective tissues, capillaries

arranged in vertical loops

4. Arteriovenous anastomoses, innervated by nerve

ﬁbers that regulate the blood ﬂow of a factor of 30

in response to heat

Fingerprint Fake Detection. Figure 4 Rubber stamp.

462

Fingerprint Fake Detection

5. Temperature range: 10



–40



C; not regulated

6. Skin emits some speciﬁc molecules (odor)

7. Skin presents some plasticity

Remark: The external layer of the skin is made of dead

cells, which is no t a favorable conﬁguration for liveness

detection!

Any liveness detection reader should read one or

several data related to the previous list. Also, reading

only one characteristic will not ensure that the read

ﬁngerprint is coming from a real ﬁnger: some material

exhibiting the same plasticity than skin exists for

instance.

Fingerprint Sensors with Liveness

Detection

Few ﬁngerprint sensor manufacturers claim to have

some kind of liveness detection; and whenever

claimed, little or evasive information is given. But,

new techn iques and ideas are being explored:

1. Maybe the most common liveness detection

method is based on electrical measurements, using

the conductivity and/or impedance of the skin.

Some sensors can acquire ﬁngerprints using electri-

cal properties of the skin (RF-ﬁeld, capacitance, elec-

tro-optical), and so require a conductive material

to be spoofed. Non-conductive latex cannot work

2. Light transmission properties of the skin and/or the

blood. Hospitals are using pulse oxymetry to mea-

sure the blood oxygenation, i.e., the percentage of

oxyhemoglobin compared to deoxyhemoglobin.

Two LEDs send infrared light through the ﬁnger

to a photo diode, so it is some additional material

aside the regular ﬁngerprint sensor. Skin spectrum

has also been proposed [16], using a wider range

of colors

3. Perspirati on induces detectable changes in time

when looking at a series of images [17]

4. Distortion of the skin depends a lot on its

plasticity [18]

5. Skin emits some speciﬁc molecules that can be

detected (odor) [19]

Fingerprint Fake Detection. Figure 5 Some moulded fakes: gelatine, plastic (negative), alginate, silicon.

Fingerprint Fake Detection

463

Faking the Counter Measures

Any measurement can be faked:

1. Electrical method can be faked by the appropriate

voltage applied on the sensing area (or even a

simple connection to real skin while a fake is

applied)

2. Optical methods can be faked by the appropriate

plastic with the correct absorption characteristics

3. An optical sensor is made of photodiodes; it is

always possible to send the appropriate light, syn-

chronized with the light sent by the system

4. Cardiac pulse can be faked with the appropriate

pump and pipes

But it is possible to make things very hard to spoof.

For instance, the latest immigration control systems

acquire the two foreﬁngers at the same time, and

so trying to spoof both sensors at the same time will

be much harder.

Conclusion

Fake ﬁngerprint detection will be an important feature

of ﬁngerprint sensors in the future, likely mandatory.

We already know that a no ﬁngerprint system will be

100% spoof-proofed, but several different sens ors

reading different information at the same time will be

very hard to deceive. The ‘‘Swiss cheese’’ model applies

here: each slice of cheese is not 100% secure, some

holes exist. But more slices will stop most of threats...

at the cost of each slice!

Related Entries

▶ Anatomy of Fingerprint

▶ Forensic Science

▶ Security

References

1. Danjaq, S.A.: DIAMONDS ARE FOREVER Copyright ß (1971)

2. Transplantation des deux mains dans le service de chirurgie

de transplantation de l’Ho

pital Edouard Herriot/Ho

pitaux

de Lyon. January 13, 2000 http://www.chu-lyon.fr/internet/

relations_medias/2005/5ans_double_greffe/dossier_presse_5ans_

double_greffe.pdf

3. US Department of Justice’s US Attorney’s ofﬁce for Arizona

press release, May 3 (2006)

4. van der Putte, T., Keuning, J.: Biometrical ﬁngerprint recogni-

tion don’t get your ﬁngers burned. In: Proceedings of IFIP TC8/

WG8.8 Fourth Working Conference on Smart Card Research

and Advanced Applications, pp. 289–303. Kluwer, Dordecht

(2000) (http://cryptome.org/fake-prints.htm)

5. Ka

kona, M.: Biometrics: yes or no? (http://home.i.cz/kakl/

biometrics/Biometricsyesorno.htm). Accessed Feb 11, (2009)

6. Thalheim, L., Krissler, J., Ziegler, P.M.: Body check: biometric

access protection devices and their programs put to the test

(http://www.heise.de/ct/02/11/114/)

7. Matsumoto, T., Matsumoto, H., Yamada, K., Hoshino, S.: Im-

pact of artiﬁcial gummy ﬁngers on ﬁngerprint systems. In:

Proceedings of SPIE on Optical Security and Counterfeit Deter-

rence Techniques IV, San Jose, CA, vol. #4677 (2002) (http://

cry ptome.org/gummy.htm)

8. Kang, H., Lee, B., Kim, H., Shin D., Kim, J.: A study on performance

evaluation of the liveness detection for various ﬁngerprint sensor

modules. http://www.springerlink.com/content/0df29gectgdkwrkl/

9. Blomme

, J.: Evaluation of biometric security systems against

artiﬁcial ﬁngers (http://www.ep.liu.se/exjobb/isy/2003/3514/

exjobb.pdf). Accessed Feb 11, (2009)

10. Ste

n, A., Kaseva, A., Virtanen, T.: Fooling ﬁngerprint scanners –

biometric vulnerabilities of the precise biometrics 100 SC

scanner. In: Proceedings of the Fourth Australian Information

Warfare and IT Security Conference, Adelaide, Australia (2003)

http://www.stdot.com/pub/ffs_article_asten_akaseva.pdf

11. Sandstro

m, M.: Liveness detection in ﬁngerprint recognition

systems. Ph.D. thesis, Linkoping University, Sweden (2004)

12. van der Putte, T.: Workshop spooﬁng ﬁngerprints, SAFE-NL,

University of Twente http://wwwes.cs.utwente.nl/safe-nl/

meetings/08-06-2006/ton.pdf

13. Chaos Computer Club, How to fake ﬁngerprints? October 26,

2004 http://www.ccc.de/biometrie/ﬁngerabdruck_kopieren.xml?

language = en

14. Martinez-Diaz, M., Fierrez-Aguilar, J., Alonso-Fernandez, F.,

Ortega-Garcia, J., Siguenza, J.A.: Hill-climbing and brute-force

attacks on biometric systems: a case study in match-on-card

ﬁngerprint veriﬁcation. In: Proceedings of the 40th Annual

IEEE International Carnahan conferences security technology,

Lexington, Kentucky, pp. 151–159 (2006)

15. Ross, A., Shah, J., Jain, A.K.: Towards reconstructing ﬁngerprints

from minutiae points. In: Proceedings of SPIE Conference on

Biometric Technology for Human Identiﬁcation II, Orlando, FL,

pp. 68–80 (2005)

16. Nixon, K.A., Rowe, R.K.: Multispectral ﬁngerprint imaging for

spoof detection. In: Jain, A., Ratha, N. (eds.) Proceedings of

SPIE on Biometric Technology for Human Identiﬁcation II,

Bellingham, WA, vol. 5779, pp. 214–225 (2005)

17. Parthasaradhi, S., Derakhshani, R., Hornak, L., Schuckers, SAC.:

Time-series detection of perspiration as a liveness test in ﬁnger-

print devices. IEEE Trans. Syst. Man Cybern. C Appl. Rev. 35,

335–343 (2005)

464

Fingerprint Fake Detection

18. Antonelli, A., Cappelli, R., Maio, D., Maltoni, D.: A new

approach to fake ﬁnger detection based on skin distortion.

International Conference on Biometric Authentication

(ICBA’06), Hong Kong, China (2006)

19. Baldisserra, D., Franco, A., Maio, D., Maltoni, D.: Fake ﬁnger-

print detection by odor analysis. International Conference on

Biometric Authentication (ICBA’06), Hong Kong, China (2006)

Fingerprint Features

JOSEF BIGU N

Embedded Intelligent Systems Center

Halmstad University, IDE, Halmstad, Sweden

Synonyms

Fingerprint analysis; Fingerprint characteristics;

Fingerprint signatures

Definition

Fingerprint features are parameters in epidermis images

of a ﬁngertip (the ﬁngerprint) that can be utilized to

extract information which is exclusively speciﬁc to a

unique person. These parameters can be measured by

computational techniques applied to a digital image

obtained by a ﬁngerprint sensing method, e.g ., using

live optical or solid-state scanners, and digitizing ink-

rolled or latent ﬁngerprint images. Such identity char-

acterizing parameters include one or more speciﬁcs of

ridge–valley direction and frequency, minutiae, and

singular points. The ﬁngerprint features should be re-

producible and resilient to variation in the face of

external factors such as aging, scars, wear, humidity,

and method of collection.

Introduction

Fingerprints consist of ridges alternating with valleys

that mostly run in parallel but also change direction

smoothly or may terminate abruptly. Other patterns in

nature that resemble ﬁngerprints include Zebra skins,

corals, and shallow sea-bottom. Such pattern variations

can be parametrized and used to characterize the

ﬁngerprints of individuals and to distinguish them

from others. Identity establishment by ﬁngerprint

matching has been used by human experts long before

the computer era, e.g., the nineteenth century contribu-

tors to the advancement of ﬁngerprints, Jan. Purkyne

William Herschel, Alphonse Bertillon, Francis Galton,

Edward Henry, Aziz-ul Haque, Chandra Bose, to nam e

but few [1].

Caused by a foray of factors, low contrast and noisy

images can compromise the reproducibility of ﬁnger-

print feature severely. Although the reason of poor

image quality might be known , a better data acquisi-

tion is sometimes not a practicable option, e.g., latent

ﬁngerprints at a crime-scene, aging, scars and bruises,

professional wear, etc. Accordingly, reproducibility is

an important property of ﬁngerprint features to be

used. Another issue is their computational efﬁciency,

if lacking it can hinder a practice of a ﬁngerprint

recognition method altogether, e.g., AFIS systems

used in border-control, altogether.

Minutiae, to be discussed below in further details,

represent the most widely used feature type by machine

as well as human experts to determine if two ﬁnger-

prints match. The geometric interrelationships of

extracted minutiae, the spatial frequency between

them or in their vicinity, and the local direction, con-

tribute all to the strength of a minutiae based feature set

so as to uniquely characterize a ﬁngerprint. Another set

of well-localized points is singular points. As will be

detailed later, these are few , and one need larger neigh-

borhoods to determine them in comparison to minutiae.

An important tool to characterize ﬁngerprints is

their direction ﬁelds since they are used in many opera-

tions of ﬁngerprint processing. In the coming sections,

we discuss direction ﬁeld estimation, followed by min-

utiae, and singula r points.

Direction Fields

The ﬁngerprint direction ﬁelds are dense vector ﬁelds

representing dominant local directions. A direction of

an image-point (a pixel) is thus a property of its

neighborhood; by itself no pixel can deﬁne a direction.

Early direction ﬁelds were associated with local edges

or lines and were approximated by the gradient of

the image, rf ¼ (∂f∕∂x, ∂f∕∂y)

where f is the local

image, on di gital lattices. Direction in this sense is the

angle of the gradient and has already been used in

Fingerprint Features

465

1960s, including in ﬁngerprint applications. However,

this concept hinders the use of effective signal proces-

sing tools, because a sinuso idal wave pattern (the local

ﬁngerprint) has a unique direction whereas half of its

gradient directions in a ﬁngerprint patch differ w ith

180

∘

from the other half, resulting in a neither unique

nor continuous representation if gradient angles would

have deﬁned feature spaces representing ridge direc-

tions. In turn this hinders efﬁcient signal processing

and inference which require rotation, scale-space, and

interpolaton operat ions.

Direction Fields by Structure Tensor

An effective cure to representation ambi guity of ridge

and valley direction is to use the concept of iso-curve

(points having the same gray-value), which suggests

the use of 2  2 tensors naturally, in the quest of an

optimal direction estimation in the total least squares

sense. This is summarized next, where the notion of

image refers to a local patch of a ﬁngerprint.

If all iso-curves of an image has a common direc-

tion the image is said to be linearly symmetric, e.g .,

sinusoidal planar waves resembling most neighbor-

hoods of ﬁngerprints. Ideally, the unknown direction

k is optimal for an image f(r) if the image is invariant

to a translation in the amount of e along the line k

where e is small and can be positive as well as negative,

and ||k||¼1. Then the total translation error E

EðrÞ¼ f ðr þ EkÞf ðrÞ

¼ E½rf ðrÞ

k þOðE

Þ¼EeðrÞ¼0

ð1Þ

will be zero for all r if the gray-value patch f is trans-

lation invariant in the direction k. Here e(r) is the

unit-error. Ignoring the quadratic term OðE

Þ, because

e represents small translations, if and only if the uni t-

error of translation in the (ﬁxed) direction k

eðrÞ¼½rf ðrÞ

k ¼ 0 ð2Þ

vanishes, (1) will vanish for all r of the patch. Evi-

dently, the unit-error will even vanish on a discrete

sub-set of the points of the patch, as below



¼ Dk ¼ 0 ð3Þ

where D

¼ ∂f(r

)∕∂x and D

¼ ∂f(r

)∕∂y with r

being a node of a grid having M nodes on the patch.

The matrix D is the set of gradients on the grid nodes,

as indicated on the left in Eq. (3). using the continuous

2D Gaussian

ðx; yÞ¼

2ps



þy

ð4Þ

the elements of D, such as D

and D

, can be prefer-

ably obtained by convolving the original discrete image

with the discretized partial derivatives of the Gaussian.

The parameter controlling the amount of smoothing

the thus obtained derivation ﬁlter can apply is ﬁxed by

a certain s ¼ s

in x and y directions as standard

deviation, to avoid nonisotropic artiﬁcial bias. How-

ever, asking for nil (inﬁnitesimal translation) error at

every r

with a common k may not be possible to fulﬁll

in practice because f may not be perfectly linearly

symmetric. The next be st thing one can do is to solve

the problem in the total least squares error sense such

that ||Dk||

is minimized for a direction k. The solu -

tion is given by the least signiﬁcant eigenvector of the

structure tensor, S ¼ D

D, which is easy to obtain

analytically as discussed in the following section. Alter-

natively, one can apply SVD numerically to D yielding

the same solution obtained by an eigenvalue analysis of

S. Before computing the direction, in practice one needs

to incorporate a window function m

¼ m(r

) into the

solution as well because the patch must be cut-out of a

larger image. This can be conveniently done in the

tensor-space (at the level of the outer-product of the

gradients) and via a Gaussian, to obtain a mathemati-

cally tractable optimization [2, 3].

S ¼ D

ðD

ÞðD

Þm

ðD

ÞðD

Þm

ðD

ðrf

Þm

ð5Þ

¼ l

max

þ l

min

¼ðl

max

 l

min

Þk

max

þ l

min

ð6Þ

Here m

is a discrete Gaussian with a certain

that deﬁnes the extension of the local ﬁngerprint

patches, l

max

, k

max

are the most signiﬁcant eigenvalue

of S and its corresponding eigenvector, delivering the

largest error and the maximum variation direction,

respectively. Similarly the l

min

, k

min

yield the

466

Fingerprint Features

corresponding quantities for the least error and the

direction of least variation respectively. Notice that

max

and k

min

are always orthogonal (S is symmetric),

have unit lengths, and sum to identity tensorially,

max

þ k

min

¼ I. Thus to represent the

direction we could relate it to k

max

, the normal of

the ridges/valleys, as well as to k

min

because knowing

one determines the other. The representation of the

direction is made by the tensor k

max

rather than

max

because the tensor representation will map the

two possible n umerical representations o f the normal

k and k to the same (tensor) quantity avoiding the

ambiguity inherent to vectors as representations of

axes/directions.

Complex Representation of the Structure

Tensor

There is a mathe matically equivalent but a more con-

venient way of representing the structure tensor, by

use of complex gradients [ 2, 4],

ðD

þ iD

¼ðl

max

 l

min

Þe

i2’

max

ð7Þ

þ iD

¼ l

max

þ l

min

ð8Þ

with ’

max

being the direction angle of k

max

and

i ¼

ﬃﬃﬃﬃﬃﬃﬃ

1

The ﬁrst beneﬁt of complex representation is that

the direction of the eigenvector is delivered by averag-

ing (summation) squares of complex gradients,

Eq. (6), in the ar gument of I

, though in double-

angle representation [5], and both eigenvalues are easily

obtained by computing, jI

j and I

. However easy to

obtain, eigenvalues will not be necessary for many

applications, as it is more useful to work with the

sums and differences of them. This is because if l

min

is very small, an acceptable way to conclude upon this

fact is to compare it with l

max

. Accordingly, when we

obtain a large (magnitude) complex number I

for a

patch, it means that we have a good direction ﬁt

(linearly symmetric patch) and a reliable estimate

of the common direction will be found right in the

argument of I

(in ▶ double angle representation),

with the reservation that jI

j must be close to I

By contrast, if the error of the worst direction is not

much worse than the best direction then the direction

ﬁt is poor, making the corresponding argument angle

meaningless automatically. Notice that jI

j I

and equality holds between the two quantities if and

only if the iso-curve directions are aligned (linearly

symmetric patch).

The next beneﬁt is that the complex representation

allows effective scale-space operations, including com-

putation by subsampling, band-pass pyramids,

extracting speciﬁc ridge frequencies (by changing s

and s

), and coarse-to-ﬁne reﬁnements, etc. by using

the complex image (D

þ D

)

and its (realvalue)

magnitude image, jD

þ D

Direction Fields as Features

The fact that scalar products on complex number ﬁelds

is well deﬁned makes direction ﬁelds descriptive fea-

tures which can be used as complements to other

descriptive features. If two ﬁngerprints are registered,

meaning that the query image f

and the reference

image f

are rotated and translated such that they are

aligned, then the scalar product between the

corresponding direction ﬁelds of the query, I

and the reference, I

), ﬁngerprints

bðf

; f

Þ¼

j <I

ðf

Þ; I

ðf

Þ> j

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðf

Þ; I

ðf

Þ>< I

ðf

Þ; I

ðf

Þ>

ð9Þ

can be used as a belief in the match. Here the scalar

product is

ðf

Þ; I

ðf

Þ> ¼



ðf

ÞI

ðf

Þð10Þ

and the summation is applied either to a region, possi-

bly weighted by some quality index [6–8], e.g. the

common region of the ﬁngerprint pair to be matched.

The star as superscript denotes complex conjugation.

Direction Decomposition

A concept, i.e., closely related to direction ﬁelds is

the decomposition of the original ﬁngerprint in a set

of images representing the (local) energy in quantized

directions (typically 6–8 angles) and scales (typically 1–3

frequencies). Such decompositions can be obtained by

a suitable Gabor ﬁlter bank independent of the direc-

tion ﬁeld computations discussed earlier. Although the

Gabor ﬁlter-bank ﬁltered images can be interpolated to

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467

generate accurate and dense direction ﬁelds [9], these

have been mainly used to enhance ﬁngerprints, and to

estimate texture properties of ﬁngerprints. The meth-

od suggested by [10] assumes that a landmark in each

ﬁngerprint of a pair to be matched is available or the

pair is somehow registered with the corresponding

landmarks. In regular concentric sectors of a circle (de-

ﬁned by a uniform polar grid of 5 radii and 16 angles)

around the landmark, the average absolute deviations of

Gabor-cosine ﬁlter responses (single frequency, eight

directions) over the patch are computed. Called Finger-

code, this set of texture measures constitutes a 640

dimensional (5  16  8) integer valued feature vector

that can be used as a descriptive vector on its own or in

conjunction with other features, Fig. 4.

Segmentation

In addition to their auxiliary or direct use to deﬁne

descriptive features, the direction ﬁelds are also used

in segmenting ﬁngerprints. The latter refers to separat-

ing the image area that contains an acceptable quality

of ﬁngerprints, from the rest, typically the bac k-

ground. Because the ﬁngerprint regions have a

dominant orientation, meaning that there is a direc-

tion along which the gray-values change singiﬁcantly

faster than the orthogonal direction, the absolute

and/or relative differences of the structure tensor

eigenvalues, l

min

, l

max

have been used to achieve

segmentation [6, 11].

Minutiae

Minutiae are end-points of ridges or valleys of a ﬁn-

gerprint, occupying typically 0.1–0.5 mm on the skin,

and are visible as 2–10 pixels in images captured at 500

dpi resolution. Minutiae are the most widely used

features to match two ﬁngerprints , for a variety of

reasons, including that there is a great amount of

human expertise in their use, and that it is difﬁcult

to reconstruct the original ﬁngerprints only by the

knowledge of minutiae, mitigating privacy concerns.

A minutia can be of the ty pe termination or bifurcation.

A bifurcation of a ridge exists in conjunction with

termination of a valley and vice-versa because the

former engulfes the latter, by deﬁnition. This is

known as duality. However, one must bear in mind

that ridges appear as valleys and vice-versa depending

on the sensing conditions, i.e., whether the dark pixels

or the white pixels are ridges. Accordingly, the minu-

tia-ty pe, i.e., bifurcation or termination, as a descrip-

tive feature is meaningful only if the interpretation

ambiguity caused by sensing can be accounted for.

Because from these two types of minutiae it is possible

to derive other constellations, e.g., lake, spur, cross-

over, Fig. 2, several national agencies relying on

Fingerprint Features. Figure 1 Commonly used classes to categorize fingerprints [27]. (a) Arch, (b) Tented Arch,

468

Fingerprint Features

minutiae for their ﬁngerprint processing base their

taxonomy only on termination and bifurcation, e.g.,

FBI in USA [12]. Before minutiae extraction, ﬁnger-

print enhancement is applied if ﬁngerprints are deemed

noisy, usually according to an automatically extracted

quality measure [7, 8, 13, 14].

Two main ways of minutiae extraction can be

achieved by (1) by binary image processing operations,

(2) by using gray-value image processing techniques.

Assuming that the binary image of a ﬁngerprint

can be obtained and it has a reasonably high ﬁdelity

w.r.t. ridges,

▶ ﬁngerprint thinning can be achieved by

morphological operators (errosion and dilation) or by

distance transforms [15–17]. A number of algorithms

to extract minutiae from skeletonized binary image s

exist. It is common that at the beginning, there are

several thousands of minutiae candidates of which

only approximately 50 are real. Various criteria for

validating the endpoints, including the duality, a min-

imum length of the ridge or valley , are used to sup-

press spurious false minutiae [18].

However, minutiae detection based on binary

images has a shortcoming, lack of robustness when

used for low quality ﬁngerprint images. Because ridge

skeletons are obtained by applying a thinning method

to the binarized ﬁngerprint, the binary ridges should

correspond to real ridges accurately if thinning proce-

dure is to be successful. This puts high demands on

the quality of the ﬁngerprints, as well as the adaptive-

ness of the binarization since the resulting binary ridges

might not represent the real ridges sufﬁciently well.

Extracting minutiae from gray images, without pass-

ing through binarization, offers better opportunities

in this respect. The ridges can be directly followed in

the gray-value image by use of the direction ﬁeld,

and the gray-value ridge proﬁles [6, 11], Fig. 3.

Fingerprint Features. Figure 2 Illustration of minutiae types and duality. (a) a ridge termination engulfed in a valley

bifurcation; (b) vice-versa. (c) basic ridge types in green (termination, bifurcation) and derived types in red (lake,

spur, crossover) (d) the direction of a minutia exempliﬁed at a ridge-bifurcation.

Fingerprint Features. Figure 3 Illustration of thinning and minutia detection by ridge following in gray-images [11]. On

the left, a segment of a ridge is represented. Gray-value proﬁles, like the one in green, are regularly sampled and

tracked along the ridge, until a termination or a bifurcation is found. On the right, the result is shown where the white

circles and squares represent terminations, and bifurcations respectively. The black circles and boxes are

improvements of a postprocessing.

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