SYNTHETIC IRIS IMAGES FROM IRIS PATTERNS BY MEANS OF

EVOLUTIONARY STRATEGIES

How to Deceive a Biometric System based on Iris Recognition

Alberto de Santos Sierra, Javier Guerra Casanova

Centro de Dom

otica Integral, Campus de Montegancedo, 28223 Pozuelo de Alarc

on, Madrid, Spain

Carmen S

anchez

Avila, Vicente Jara Vera

Applied Mathematics Department, ETSIT, Polytechnical University of Madrid, Madrid, Spain

Keywords:

Biometric iris recognition, Synthetic iris images, Iris falsiﬁcation, Security, Evolutionary strategies.

Abstract:

Synthetic Biometric is emerging nowadays as a new research ﬁeld in biometrics. An artiﬁcial iris tissue or a

synthetic ﬁngerprint could compromise the security, allowing a non-registered individual to enter the system.

However, inverse biometric can also improve current identiﬁcation systems, enhancing not only its strength

against fake-based attacks, but also by replicating unavailable or corrupted data, due to a bad acquisition, for

instance. The methods proposed in this document aim to provide a procedure to create a synthetic iris tissue

from a stored biometric template, so that a non-registered user could access the system under a registered

identity. These algorithms will come out with the result that synthetic sample could be so similar to original

as desired.

1 INTRODUCTION

Biometric systems based on Iris Recognition are

known to be one of the most reliable systems in terms

of security (Daugman, 1993; Daugman, 2004). Con-

sidering the fact that Iris is already stable in very early

stages of life and unalterable since that moment, it is

obviously impossible to modify the iris itself. Thus,

any method attempting to deceive a system based on

iris recognition should focus on the acquired image,

which is already stored in the system when captured.

Despite of being suggested that there exists no

previous development of an automated iris recon-

struction, (Yanushkevich, 2006), there is indeed a pre-

vious work on iris synthesis, (Cui et al., 2004), but

focused on creating synthetic biometric databases for

testing purpose, far beyond the scope provided in this

paper, where the aim consists on accessing the system

by means of synthetic iris images. On the other hand,

several attempts already exist in other biometric tech-

niques such as ﬁngerprint (Capelli et al., 2006), face

recognition (Yanushkevich et al., 2007), handwritten

signature (Guyon, 1996; Yanushkevich, 2006), voice

(Cook, 2002), and so forth.

Overall biometric systems relies their strength on

the fact that once the templates are extracted, there is

no function able to ﬁnd an acquisition, whatever its

nature (ﬁngerprint, iris, hand veins), whose template

coincides with the required pattern.

This paper provides two approaches attempting to

implement such a function, i.e., a function able to

come out with an image iris, whose pattern may be

so similar to the desired template as required. Based

on evolutionary strategies, the procedure will provide

the best solution to meet the required goal. There-

fore, this algorithm may be extended to other biome-

tric techniques, and all biometric systems will beneﬁt

of it, since their main applications consider not only

enhancing the system against fakes, but also impro-

ving its performance, by replicating corrupted data or

testing algorithms with synthetic databases.

2 CREATING A SYNTHETIC IRIS

The main problem this approach tackles with is about

creating an artiﬁcial iris tissue. In order to meet this

goal, two approaches have been implemented with a

twofold purpose: ﬁrst, providing two possible solu-

tions, and second, comparing them in terms of visual

aspect and overall performance.

Each approach is based on evolutionary strategies

194

de Santos Sierra A., Guerra Casanova J., Sánchez Ávila C. and Jara Vera V. (2010).

SYNTHETIC IRIS IMAGES FROM IRIS PATTERNS BY MEANS OF EVOLUTIONARY STRATEGIES - How to Deceive a Biometric System based on

Iris Recognition.

In Proceedings of the Third International Conference on Bio-inspired Systems and Signal Processing, pages 194-201

DOI: 10.5220/0002706601940201

 SciTePress

(Eiben and Smith, 2003; Schwefel, 1995), but the

schemes on which they are based are completely dif-

ferent. Nonetheless, before describing the algorithms

in detail, the problem to be solved must be stated.

2.1 Problem Statement

The problem these two approaches attempt to tackle

with can be stated mathematically as a function A ,

whose input is the template of a user already regis-

tered in the database, T

. More in detail, A can be

expressed as:

A : T 7−→ D

T ∈ T 7−→ A(T ) ∈ D

(1)

where T represents the set of all possible tem-

plates in a Biometric System, in other words, T is the

information stored in the biometric database, (Daug-

man, 2004); and D stands for the set of all possible

images of a given database, related to previous T .

Both sets verify to have the same number of elements,

same cardinality, and each element in T corresponds

to only one element in D, and vice-versa.

This paper will suppose that the information of the

database is available, but in most current systems, the

stored information is protected and encrypted, so un-

veiling patterns in T is an arduous, but possible, task.

As an overview, A is a function which provides

an image A(T) ∈ D when being applied to a template

T ∈ T .

Continuing on mathematical representation, Z is

deﬁned as the algorithm responsible for extracting the

template from an image. In other words,

Z : D 7−→ T

I ∈ D 7−→ Z(I) ∈ T

(2)

In fact, Z(D) = T , because each element in T

corresponds to only one element in D.

Furthermore, a measure must be deﬁned in order

to assess how similar two templates are. Let η ∈ R be

a function able to measure to what extend two tem-

plates coincides or not. This measurement can be de-

ﬁned in terms of T as follows,

η : T × T 7−→ R

, T

∈ T 7−→ η(T

, T

)

(3)

For the sake of simplicity, η is implemented by

Euclidean distance in this document, but other mea-

sures can be deployed, (Gonz

alez et al., 2004). In any

case, η(T

, T

) will tend to zero, when T

tends to T

Finally, considering previous equations Eq. (1)-

(3), the main problem can be stated as:

Given T

(a registered user template) and η

(a threshold), implement A in order to verify that

η(

T , T

) ≤ η

, where

T = Z(A(T

)). In other

words, the problem can be deﬁned in terms of func-

tions as:

Attempt to ﬁnd A so that A = Z

−1

Before dealing with the problem of ﬁnding A,

several constraints concerning Z should be made.

First of all, and for the sake of simplicity, Z will

be deﬁned as in previous approaches (S

anchez-

Avila

and S

anchez-Re

ıllo, 2002; de Santos-Sierra et al.,

2007), losing some generality. This approach will

be explained in next section 2.2. However, the main

ideas are suitable not only for other feature extrac-

tors (Boles and Boashash, 1998; Chun and Chung,

2004; Daugman, 2004), but also for other biometric

techniques. Secondly, A has been tested in CASIA

v3 database (http://www.sinobiometrics.com), a low

quality database, so that, Z will provide low resolu-

tion templates. Testing these algorithms in different

databases, remains as a future work.

2.2 Template Description

Evidently, a falsiﬁcation must consider how the tem-

plate is extracted, otherwise the problem could be

unattainable. The extraction step begins after pre-

processing the image, once the iris has been isolated

from pupil, eyelids, and so forth, (Daugman, 1993;

de Santos-Sierra et al., 2007). Furthermore, a ﬁrst

‘raw’ template is extracted from the isolated iris, be-

ing afterwards processed in order to obtain a better

result in identiﬁcation.

This approach regards only these previous ‘raw’

data, for the sake of simplicity. Note these consi-

derations do not lack of generality, since posterior

processing is inherent to each Biometric System, and

furthermore, such post-processing is easily reversible

due to the algorithms involved in that step, (S

anchez-

Avila and S

anchez-Re

ıllo, 2002; de Santos-Sierra

et al., 2007).

The template is extracted by Z, using a circular

section (Fig. 1), averaging the intensities values along

the radius of the crown, ρ, for each angle of the pre-

vious section, α

, ∀i ∈ N ∩ [0, 255], (de Santos-Sierra

et al., 2007).

The circular section provides a template of 256

points, where each point is represented by a double

precision value in [0, 255], due to the grayscale repre-

sentation of the iris image. By the use of a 256

circu-

lar section, eyelids are avoided, although a 360

sec-

tion can be considered when suitable, regarding eye

aperture, (de Santos-Sierra et al., 2007).

SYNTHETIC IRIS IMAGES FROM IRIS PATTERNS BY MEANS OF EVOLUTIONARY STRATEGIES - How to

Deceive a Biometric System based on Iris Recognition

195

Figure 1: Region of Interest in Feature Extraction.

2.3 From Original to Synthetic

Once the template extraction has been presented, the

reader could realize that not the whole image is con-

sidered as a part of the template, but only many pixels.

In fact, those pixels are included in the previous circu-

lar section. Furthermore, a certain image I is consid-

ered as a base image, from which the algorithms will

be able to evolve a fake image. This must be done, if

a close-human fake is required. It is far easier to fake

several points in an image than the whole image.

According to these previous statements, several

deﬁnitions must be considered, before starting with

the explanation of the approaches. First of all, the im-

age I is randomly selected. From now, I will be con-

sidered as a matrix, where X and Y represent the sets

for horizontal and vertical coordinates respectively,

assuming that a pixel of I is represented by its position

within the image, (x, y) ∈ X × Y , and its color inten-

sity, I(x, y) ∈ N ∩ [0, 255], (Gonz

alez et al., 2004).

Let V be the matrix containing all the intensity

values within previous circular section. Matrix V has

256 columns and ρ rows, where ρ is the previous cir-

cular section width. Therefore, Ξ ⊂ X and ϒ ⊂ Y are

deﬁned as those positions, in terms of X and Y , whose

pixels are contained in V . In other words, Ξ and ϒ are

the matricial representation of previous circular sec-

tion.

Matrix V is calculated once for image I, since V

gathers the unique values to be modiﬁed to fake im-

age I. When image I is presented to the system, fea-

ture extraction step will come up with a template read

from those pixels located in Ξ and ϒ, the rest of I is

neglected for template extraction.

In fact, template T associated with image I can be

obtained as:

T ( j) =

∑

V (i, j)

(4)

Once the nomenclature is stated, the two ap-

proaches are presented. First approach regards evo-

lutionary algorithms, (Michalewicz, 1996), ﬁnding

optimal solution by evolving those pixels contained

in V . On the other hand, second approach contem-

plates the possibility of changing the order in Ξ and

ϒ, in other words, changing the position of each pixel,

but not altering its intensity. Both approaches entail

evolutionary strategies, but with different approaches.

The performance of both will be presented in section

2.3.1 Evolutionary Strategies on V

An evolutionary algorithm is a suitable manner of

tackling minimization and maximization problems,

(Michalewicz, 1996; Eiben and Smith, 2003). How-

ever, the problem must be adapted to make it suit-

able for evolutionary strategies. Since each template

T ∈ T veriﬁes to be a 256 components vector, the

strategy involves dividing the problem into 256 in-

dependent problems. The j-component of T corre-

sponds to the average of the components in column j

from matrix V , being the representation for the sub-

problem j a vector called v

=< a

1, j

, a

2, j

, . . . , a

ρ, j

with ρ components and a

i, j

∈ V where i ∈ {1,. . . , ρ}

and j ∈ {1, . . . , 256}.

The procedure deployed under this section con-

templates several steps before meeting the goal of ob-

taining an optimal solution:

• Fitness Function: This function provides the al-

gorithm with a Termination Condition. The evo-

lutionary algorithm will seek the solution until a

certain value of ﬁtness function is achieved. An

appropriate ﬁtness function is as follows in Eq. 5.

|T ( j) − ¯v

| =



T ( j) −

∑

i=1



(5)

This ﬁtness function must be minimized until a

certain extent η

according to previous problem

statement. This function exists for each subpro-

blem.

• Population and Initialization: The population of

each subproblem consists of 50 members, each of

them different to each other, in order to ensure di-

versity property, (Eiben and Smith, 2003). Each

member of the population is created based on a

uniform distribution. Such a distribution is uni-

form in the set formed by minimum and maxi-

mum value of column j for each j-subproblem.

BIOSIGNALS 2010 - International Conference on Bio-inspired Systems and Signal Processing

196

For each subproblem, 50 members of the popu-

lation (vectors) are created. The reason why this

initialization is performed is due to the fact that

they present a previous solution quite close to the

ﬁnal result which still remains unknown.

• Parent Selection: Parent Selection will provide

those individuals in the population most suitable

to mate, without neglecting the fact that less suit-

able individuals should be also considered as pos-

sible parents to create next offspring.

Thus, every individual is selected based on:

= |T ( j) − ¯v

which indicates to what extend the results dif-

fers from aim. According to ξ

, those individuals

more capable (with ξ

→ 0) are more likely to be

selected than those whose ξ

is far from 0. In the

literature, (Eiben and Smith, 2003), the Parent Se-

lection described within this document is similar

to Fitness Proportional Selection.

• Recombination: Having parents selected, a new

offspring emerges as a result of mating previous

parents. However, a recombination must be done

in order to provide more richness to such off-

spring. The algorithm proposed in this approach

is known as Whole Arithmetic Recombination,

(Eiben and Smith, 2003), with its parameters set

to α = 0.3, accordingly to (Eiben and Smith,

2003; Back et al., 2000a; Back et al., 2000b),

where 0 < α < 1 is suggested. On the other hand,

a Uniform Crossover operator is proposed to carry

out such an operation with a p

= 0.7 probability.

Lower values may make the algorithm not to con-

verge in a reasonable time, (Back et al., 2000a;

Back et al., 2000b).

• Mutation: Mutation is an operator capable of

modifying the offspring by changing several el-

ements in the alleles (individuals). For the sake of

an optimal solution, mutation must always be car-

ried out, but with lower probability than Recom-

bination. In this work, mutation probability was

experimentally set to p

= 0.25. Higher values

of p

make the algorithm not to converge, (Eiben

and Smith, 2003; Back et al., 2000a; Back et al.,

2000b).

• Survivor Selection Mechanism: This mechanism

is responsible for managing the process whereby

the population of parents (µ) and the new off-

spring (λ) is reduced to the size of popula-

tion. Concretely, this approach considers Elitism,

(Eiben and Smith, 2003), as the most suitable

mechanism for survivor selection, since it com-

bines Age-based replacement and Fitness-based

Replacement, in the same way parent selection is

carried out.

Finally, the algorithm under this approach will be

indicated as A

, as it is based on V matrix. The per-

formance of this algorithm will be considered in sec-

tion 3.

2.3.2 Evolutionary Strategies on Ξ and ϒ

This approach, namely A

Ξ,ϒ

, despite of being differ-

ent from previous algorithm, attempts the same aim.

Nonetheless, this approach intends to fake the iris, by

rotating rows in matrix V . In other words, this proce-

dure attempts to ﬁnd the right combination for what a

solution is found in terms of problem statement.

Matrix V has ρ columns and 256 rows and is mod-

iﬁed in column directions. In fact, the algorithm A is

conceived in this approach as an operator responsi-

ble for shifting the columns of V , so that the template

T changes as the evolutionary strategies attempts to

ﬁnd the optimal solution. The operator able to carry

out every shift is called σ

with i = {1, . . . , nPop} and

m = {1,. . . , ρ}, where nPop is the number of individ-

uals in the population of the evolutionary algorithm.

This value will be set to nPop = 1000, according to

(Eiben and Smith, 2003; Back et al., 2000a; Back

et al., 2000b).

Despite of considering only shifts in row direc-

tion, there exist the possibility of also shifting in col-

umn directions. The operator responsible for this

strategy is deﬁned as α

with j = {1, . . . , 256} and

m = {1, . . . , ρ}. Although possible, the implementa-

tion of an evolutionary algorithm considering both σ

and α

involves a non-acceptable processing time and

the results compared to an approach using only σ op-

erator, does not differ signiﬁcatively. Thus, σ

opera-

tor is considered, but α

operator is ignored, although

its integration remains as future work.

The description of this approach follows in the

same manner as previous algorithm was described.

Most of the concepts coincide with those above in

section 2.3.1, since most representation has been con-

served, for the sake of simplicity regarding implemen-

tation.

• Fitness Function: Same function as in previous

section is selected. However, several considera-

tions must be taken into account. For instance,

threshold η

cannot be assured to be achieved, but

minimum of ﬁtness function can be obtained, al-

though the performance of the whole algorithm

could not be so promising as previous approach.

Note the constraints of this algorithm are more

restrictive than before, being on the contrary less

complex in terms of processing time. Thus, same

SYNTHETIC IRIS IMAGES FROM IRIS PATTERNS BY MEANS OF EVOLUTIONARY STRATEGIES - How to

Deceive a Biometric System based on Iris Recognition

197

1 2

256

1000

Figure 2: Population structure for A

Ξ,ϒ

function is considered as in Eq. (5) but searching

the minimum, and not a deﬁned threshold η

• Population and Initialization: In this case, 1000

individuals for each population is selected, since

a wider population is require due to the simpli-

city of the operator σ

, (Eiben and Smith, 2003).

Each individual represent a V matrix, where the

operator σ

has been carried out. Fig. 2 intends

to clarify the structure of the population and pro-

vides a visual idea about the population. However,

is the actual operator to be evolved, although

it is easier to think on the problem in terms of ma-

trices Ξ and ϒ.

• Parent Selection: Since this approach slightly dif-

fers from previous approach in the fact that what

is evolved is not the data, but the operators σ

parents must be selected based on those displace-

ments which provide a ξ

(as deﬁned in Eq. (4))

close to zero.

• Recombination and Mutation: Both steps have

been gathered under this section. The operators

evolved are σ

and thus, the operators used be-

fore lack of any meaning in this section. Instead,

permutation operators are involved. More in de-

tail, Partially Mapped Crossover was carried out

for recombination with a probability of p

= .7,

and Swap Mutation was considered as a suitable

operator for Mutation, carried out with a proba-

bility of p

= .25, (Eiben and Smith, 2003; Back

et al., 2000a; Back et al., 2000b). These previous

values were set according to experimental results,

lower values for p

and higher values for p

made

the algorithm not converge.

• Survivor Selection Mechanism: As previously

stated, Elitism is selected as the most suitable so-

lution, based on experimental results.

3 RESULTS

Considering the aim of these algorithms, a function

is required to measure how similar an original and a

fake are. Many different proposals exist in literature,

(Gonz

alez et al., 2004), in order to assess how dif-

ferent two signals are. The selected function, namely

ε, provide with a fast and accurate manner of meet-

ing this goal, and coincides with ﬁtness function in its

deﬁnition. Given two functions, f and g, ε is deﬁned

as follows:

ε =

| f − g| (6)

Notice that this function is the simplest measure-

ment function. Main reason to use this function re-

gards the fact that if with the simplest function the

results are promising and acceptable, (see section 3),

more complicated measurement functions will pro-

vide more thorough and precise results. Nonetheless,

an implementation with more complex functions re-

mains as future work.

Once evaluation function is deﬁned, an experi-

ment comparing deviation in terms of ε was car-

ried out among different samples of same individu-

als, and different samples of their corresponding syn-

thetic copies. Next picture highlights the results ob-

tained in these experiments: horizontal lines indicate

the average (µ

Orig

) and standard deviation range

(σ

Orig

, ) of ε among real samples of a same in-

dividual. On the other hand, dotted lines ( and

) indicate the performance of the algorithms A

and A

Ξ,ϒ

respectively. Notice how horizontal lines

split the space in three different regions: a region

where falsiﬁcations are more similar to original than

real samples of the same user from which original

was taken (‘Best’); a region where fake is similar to

real samples (‘Good’) and a region where falsiﬁca-

tions could not deceive the system (‘Bad’).

Since both implementations of the algorithm, A

and A

Ξ,ϒ

, depends on η, several performance of both

implementations were carried out for each value of η,

(Fig. 3). However, notice that although A

Ξ,ϒ

depends

on η, its aim attempts to achieve the closest minimum

to η

, which might not coincide with η

Several conclusions can be extracted from Fig. 3.

First of all, A

and A

Ξ,ϒ

come out with solutions

more similar to their respective originals (from which

they were copied) than even those samples taken from

the same individual from which original images were

taken. In other words, depending on η, falsiﬁcations

can be ‘Good’ if ε is in the deviation interval among

real samples, better if ε is under that range, or ‘Bad’

otherwise. In this former case, the result provided by

and A

Ξ,ϒ

is not considered as a valid solution.

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198

−20 0 20 40

80 100 120 140

160

180 200 220 240

260

280

130

140

150

Original

Ξ,ϒ

, η = 0

Figure 4: Result of both approaches, A

and A

Ξ,ϒ

, compared to the original pattern.

−20 0 20 40

80 100 120 140

160

180 200 220 240

260

280

120

140

160

Figure 5: Patterns from different samples belonging to the same user.

0 2 4

8 10

η(η)

Orig

Ξ,ϒ

Good

Best

Bad

Figure 3: Comparison between A

, A

Ξ,ϒ

and original sam-

ples in terms of η.

The performance of A

and A

Ξ,ϒ

is presented in

Fig. 4. Notice that A

is almost equal to the ori-

ginal, and therefore, some difﬁculties can arise when

trying to distinguish Original from A

in Fig. 4. A vi-

sual evaluation of the performance of both algorithms

can be seen in Fig. 8 and in Fig. 9, where ( )

represents an original pattern, ( ) represents a per-

formance of A

Ξ,ϒ

with η = 0 and ( ) represents a

performance of A

with η = 0. The performance of

is in general better than A

Ξ,ϒ

due to its own deﬁ-

nition, however both provide optimal solutions when

compared to real data from same individuals.

This statement can be assessed in Fig. 5, where

patterns of the same user are depicted. Notice how

different are two samples from the same user. In fact,

that difference is far more noticeable among original

samples belonging to the same user, than among fal-

siﬁcation of a certain original sample. Furthermore,

the fake provided by A

( ) is extremely similar to

original.

Together with these previous visual patterns, and

important question comes up: How does a fake iris

image look like? Obviously, reader must notice that

a considerable amount of pixel within the image have

been altered, so that the image may look strange to

a human. However, that appearance lacks of mean-

ing for a computer, since the system extracts only that

region suitable for a posterior pattern extraction, ig-

noring how ‘human’ the iris looks like.

Thus, although an altered image by these former

SYNTHETIC IRIS IMAGES FROM IRIS PATTERNS BY MEANS OF EVOLUTIONARY STRATEGIES - How to

Deceive a Biometric System based on Iris Recognition

199

Figure 6: Image where falsiﬁcation will take place.

methods could seem weird at ﬁrst sight, it is totally ac-

cepted by the computer. In the end, the computer will

be responsible of processing the image, not the hu-

man. Actually, providing the synthetic image with a

more human-like appearance remains as future work.

However, the main difference between A

and

Ξ,ϒ

consists of the fact that A

achieves more pre-

cise results and can obtain a solution closer to the tar-

get, but on the contrary, the visual aspect of a fake

image is far from being real, in other words, it is ob-

vious that the image has been altered. On the other

hand, A

Ξ,ϒ

achieves worst results and is more time-

consuming. However, the visual aspect provided by

this latter approach (A

Ξ,ϒ

) does not look very differ-

ent from a human iris, and in fact, this difference is

negligible.

Fig. 6 shows the image used to make falsiﬁca-

tion. This image is chosen randomly, and the algo-

rithm does not depend on this previous image selec-

tion. Moreover, Fig. 7 provides the image to fake. In

other words, the idea is to enter the system where Fig.

7 is registered, using Fig. 6.

The results of the algorithms are shown in Fig. 8

and in Fig. 9, which represent the performance of A

and A

Ξ,ϒ

respectively. Notice how the appearance of

Fig. 8 is slightly different from a human iris, and how

Fig. 9 almost does not differ from Fig. 6. It must

be emphasized the fact that although visually they do

not look ‘standard’ human iris, the system makes no

difference. Furthermore, achieving a more human ap-

pearance in both performance remains as future work.

Figure 7: Image whose template is T

Figure 8: Visual result of A

Figure 9: Visual result of A

Ξ,ϒ

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200

4 CONCLUSIONS

This article presents two approaches for biometric

synthesis. Both provide an accurate performance

when creating a fake copy from an original pattern,

although both compromise accuracy, time and human

appearance. Main conclusion highlights the fact that

copies are better than original samples.

Use cases inferred from synthetic biometric data

regard biometric data reconstruction, synthetic data

for testing biometric systems, or tightening up bio-

metric security.

Regarding future work, stricter constraints will

lead to a more human-like appearance in ﬁnal syn-

thetic image, focusing on the texture. Furthermore,

tests will be carried out in more databases apart from

CASIA v3, once the algorithm is able to deal with

more complex textures. Despite of being far be-

yond the scope of this article, time performance must

be considered for a real time application. However,

reader must notice that time is not a constraint when

doing ‘hacking’ activities.

One more aspect regards performance of

the whole biometric system when identify-

ing/authenticating a certain individual. No efforts

have been done focusing on this aspect, since

synthetic copies are so similar to originals, that the

performance of the biometric system will be obvi-

ously decreased if these images are included within

the database. However, to what extent a biometric

system loses accuracy with these images remains as

future work.

Finally, a more complex algorithm, merged as a

result of both approaches, will be considered as a

more precise and promising procedure, gathering best

characteristics of each algorithm, including also α

operator as described before, (Gonz

alez et al., 2004).

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SYNTHETIC IRIS IMAGES FROM IRIS PATTERNS BY MEANS OF EVOLUTIONARY STRATEGIES - How to

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