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and DWT coefﬁcient scaling. In the work presented

here those explicit control mechanisms such a s the

MAXSHIFT tool were not used, but rather the same

pixel substitution method as described earlier for ROI

was used, for comparison purposes. Three JPEG2000

compression factors (CF) of 20, 50, and 60 were cho-

sen, which yielded ﬁle sizes of 5,100, 2,000, and 1,700

bytes, respectively. The three images in the second

column of Fig.1 were created with a JPEG2000 CF of

50 and thus have a ﬁle size of only about 2,000 bytes.

Whereas JPEG generates widely varying ﬁle sizes to

deliver any given QF, JPEG2000 creates ﬁle sizes that

are closely predictable from the speciﬁe d CF. In the

authors’ experience of compressing several thousand

iris images with JPEG2000, the standard deviation of

the distribution of resulting ﬁle sizes was usual ly only

about 1.6% of the mean [2], for any given CF. Predict-

able ﬁle size is an important beneﬁt for ﬁxed payload

applications [19].

Finally, it is interesting to compare visually some

examples of the iris images after compression to a

constant data size of 2,000 bytes using each of the

three different scheme s for image compression that

have been discussed here. In Fig.2, each column is

from the same NIST iris image; the rows represent

the different schemes. The top row is a simple JPEG

compression of a cropped (320  320) image but

without ROI isolation. Most of the 2,000 byte budget

Iris Recognition Performance Under Extreme Image Compression. Figure 2 Visual comparison of three schemes

for iris image compression, for images all severely compressed to the same data size of 2,000 bytes. First column uses NIST

image 239230; second column uses NIST image 239343. Top row: simple JPEG compression of the cropped (320  320)

images. Middle row: JPEG compression of the cropped images after ROI isolation. Bottom row: JPEG2000 compression

of the cropped and ROI-isolated images. At severe compression levels, JPEG2000 is vastly superior to JPEG.

830

Iris Recognition Performance Under Extreme Image Compression

is wasted trying to encode eyelashes, and the cost on

iris texture is horrendous. The middle row shows im-

provement after ROI isolation, so most of the JPEG

budget is allocated to the iris, but the result is still very

poor. The bottom row shows the result of combining

the cropping, ROI isolation, and JPEG2000 compres-

sion for the same iris images. The improvement is

visually remarkable, and it is conﬁrmed by very good

iris recognition performance as summarized by the

purple ROC curve (CF = 50) in Fig.5 in the next

section.

Tools for Evaluating the Effects of Iris

Image Compression

Biometric recognition performance is usually measu-

red by generating Receiver Operating Characteristic

(ROC) curves, which plot the trade-off between two

error rates (False Accept and False Reject Rates, FAR

and FRR) as the decision threshold fo r similarity

scores is varied from conservative to liberal. It is com-

mon to tabulate speciﬁc points on such trade-off

curves, such as the FRR when the decision threshold

causes an FAR of 1 in 1,000 or of 1 in 10,000, and the

point at which the two error rates are equal, FRR =

FAR = EER, the Equal Error Rate. Such ROC curves

and tabulations are presented in Fig.3 for the NIST

[12] ICE-1 gallery, both for baseline performance (un-

compressed and uncropped: black curve), and for the

three QF quality factors (coloured curves) used with

the simplest JPEG compression approach described

earlier. The coordinates of the ROC curves are semi-

logarithmic: the ordinate plots 1-FRR linearly, over

just the upper 5% of its possible range, while the

abscissa logarithmically spans many factors of 10 in

FAR, to nearly as low as 1 in a million. The number of

images and the mix of Subjects in this NIST iris

Iris Recognition Performance Under Extreme Image Compression. Figure 3 ROC curves in semi-logarithmic

coordinates for the NIST [12] ICE1Exp1 iris database, showing the impact of simple data reduction methods on

performance. Black curve shows baseline performance on the original database of full-size images. Red curve shows the

effect of simple cropping to 320  320 pixels after automatically locating and centering each iris, followed by JPEG

compression at QF¼70. Blue and green curves show the effects of more severe JPEG compression at QF¼30 and QF¼20.

Iris Recognition Performance Under Extreme Image Compression

831

database allows 12,214 same eye matches to be tested,

and it allows 1,002,386 different eye comparisons to be

done, which means that one cannot measure a False

Match Rate (or FAR) between 0 and 1 in a million; this

determines the limit of the ROC curves on the left

extreme of these graphs.

The red ROC curve in Fig.3 shows that at a JPEG

quality factor of 70 and an overall data reduction factor

of 25:1, no performance loss relative to the baseline

(black) ROC curve is detectable. (Indeed there is even

some suggestion of a small beneﬁt from compression,

possibly due to de-noising.) The blue and green ROC

curves show that for this scheme based only on imag e

cropping and JPEG compression, using a QF in the

range of 20–30 produces image ﬁle sizes in the range of

5,000 bytes but at the cost of roughly doubling the

FRRs and EER compared to the error rates for uncom-

pressed images.

The additional impact of the ROI isolation (JPEG +

ROI) on iris recognition performance is gauged by the

ROC curves in Fig.4. These show that for each QF

studied, iris recognition performance remained about

the same as before the ROI isolation (Fig.3), but with

the achievement of a further twofold reduction in

image data size, even dow n to the range of just

2,000–3,000 bytes per image.

Figure 5 presents the ROC curves generated by the

JPEG2000 + ROI compression scheme, together for

comparison with the black ROC curve for the baseline

gallery (uncropped, uncompressed, not ROI-isolated).

It is clear that compression as severe as 0.156 bpp

(CF = 50, ﬁle size 2.0 KB, purple curve) still allows

remarkably good iris recognition performance. For

example, the FRR remains below 1% at an FAR of 1

in 100,000. It seems extrao rdinary that image arrays

recovered from as little as 2,000 bytes of data are still so

Iris Recognition Performance Under Extreme Image Compression. Figure 4 ROC curves and data size statistics

showing the consequences of ROI isolation prior to JPEG image compression, so that the available information budget

is allocated almost entirely to the iris texture itself. The same quality factors were specified as in the corresponding

curves of Fig.3, and the recognition performance is generally comparable, but now the data reduction factors achieved

in each case are twice as great.

832

Iris Recognition Performance Under Extreme Image Compression

serviceable for iris recognition. It is possible that part

of the explanation lies in the similarity between the

Daubechies wavelets used for the DWT in JPEG2000

coding, and the Gabor wavelets used in the creation

[10] of the IrisCode itself, so that informati on lost in

such severe compression is not used in the IrisCode

anyway. However, a watershed seems to exist at 2,000

bytes, since a pronounced degradation becomes evi-

dent when images are further compressed to 1,700

bytes (CF = 60, blue-green ROC curve in Fig.5).

As with all biometrics, ROC curves as plotted in

Figs.3–5 reﬂect the overlapping tails of the two distri-

butions of similarity scores computed for images from

same or different eyes. For the present work, the simi-

larity score is a normalized Hamming Distance (HD),

which is the fraction of bits disagreeing between two

IrisCodes among the bits compared [10]. It is also

informative to see the full distributions of HD scores,

which are presented in Fig.6 for two of the compres-

sion schemes. In each panel, two different ordinate axis

scales are used to facilitate visualiz ation since there

are 1,002,386 counts in the ‘‘all against all other’’ dis-

tribution (magenta) created by comparing different

eyes, but only 12,214 counts in the distribution

(olive) made by all same eye comparisons across the

database. The upper panel shows the distributions

obtained with ROI+JPEG compression at QF¼70,

which created an average ﬁle size of 5,700 bytes. The

recognition performance obtained with that compres-

sion sch eme was almost indistinguishable from the

baseline performance (black ROC curve: no compres-

sion, ROI, or cropping). The lower panel shows the

distributions obtained with ROI+JPEG2000 compres-

sion at CF = 60, which created an average ﬁle size of

just 1,700 bytes and generated the blue–green ROC

curve in Fig.5. It is remarkable that such extremes

of compression do not have catastrophic effects on

the separability of the pair of distributions. Instead,

as seen in Fig.6, the distribution obtained from differ-

ent eyes (mag enta) is v irtually unchanged, whereas the

Iris Recognition Performance Under Extreme Image Compression. Figure 5 ROC curves and data size statistics

showing iris recognition performance when the cropped and ROI-isolated images are compressed using JPEG2000 at

various compression factors. Performance with file sizes of merely 2,000 bytes (CF¼50, purple curve) remains remarkably

unimpaired compared to baseline (black curve); but further compression begins to exact a high toll (blue-green curve).

Iris Recognition Performance Under Extreme Image Compression

833

distribution obtained from same eye images (olive) is

shifted to the right by a small amount, corresponding

to an increase in the mean HD score from 0.1080 to

0.1424 as indi cated by the two dots and a projected

vertical line for comparison.

Information theory provides certain metrics for

deﬁning the ‘‘distance’’ between two random variables

in terms of their entire probability distributions. When

both random variables are distributed over the same set

of possible outcomes, such as the HD scores that were

tallied in the histogram s for same and for different eyes

in Fig.6, then the relative entropy or Kullback–Leibler

distance is a natural way to measure the overall dis-

tance between the two distributions. As a measure of

separation, it is also called the ‘‘information for dis-

crimination.’’ Unfortunately, this measure becomes

undeﬁned if there are so me values that only one ran-

dom variable can have while other values are accessible

only to the other random variable. Since the distribu-

tions of HD scores obtained from comparisons

Iris Recognition Performance Under Extreme Image Compression. Figure 6 Distributions of Hamming Distance scores

comparing same and different eyes in the NIST database, for two of the image compression schemes bracketing the

range of schemes studied. Even in the most severe case (lower panel) using images compressed to only 1,700 bytes, the

dual distributions have little overlap and so decisions about identity remain robust.

834

Iris Recognition Performance Under Extreme Image Compression

between different eyes in Fig.6 vanish for scores smal-

ler than about 0.3, and likew ise the score distributions

for same eyes attenuate to zero over much of the other

distribution, the calculated Kullback–Leibler distance

between these distributions is inﬁnite and meaningless,

unless based on nonvanishing theoretical models for

them or by adding arbitrary quantities that then be-

come decisive for this metric. An alternative family of

distance metrics, encompassing the Fisher ratio and

Z-scores, deﬁne distance in terms of the difference be-

tween the means of the two distributions, normalized by

some function of their standard deviations. One such is

the d

metric of decidability in signal detection theory,

deﬁned as d

¼jm

 m

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ðs

þ s

, where m

and

are the means and s

and s

are the standard

deviations. A limitation of this metric is that by con-

sidering only the ﬁrst two moments of the distribu-

tions, it makes no explicit use of skew, kurtosis, and

higher moments that are more sensitive to mass in the

tails. Thus d

might be said to take a ‘‘Gaussian v iew’’

of the world, whereas the skewed distributions in Fig.6

are clearly not Gaussian. Nonetheless, the d

scores for

each underlying pair of distributions obtained with

each of the compression schemes studied here have

been included within the ROC graphs in Figs.3–5.

They show a small but systematic trend of deteriora-

tion with more aggressive levels of image compression.

But as is clear from the two bracketing extremes pre-

sented in Fig.6, the separability of the two underly ing

distributions remains remarkable, despite the massive

compression factor reaching 180:1 reduction from the

original images.

Another metric system often used in decision the-

ory to summarize overall performance by a single

scalar statistic is the area under the ROC curve. Clearly

a value of 1.0 represents perfection since it arises only

from the complete absence of overlap between the two

distributions. The ten different ROC curves plotted in

Figs.3–5 appear to have signiﬁcant amounts of missing

area, but this is an illus ion due to the loga rithmic

abscissa and the magniﬁed ordinate ranging just be-

tween 0.95 and 1.00. In fact the area under the baseline

black ROC curve (present in all three ﬁgures) is

0.999985, and the areas under most of the other nine

curves are reduced from this value in only the sixth

decimal place.

Summary

From studying the effects of three schemes for image

compression on iris recognition performance, one is

drawn to the surprising conclusion that even images

compressed as severely as 150:1 from their original full-

size formats, to just 2,000 bytes, remain very service-

able. It is important to use region-of-interest isolation

of the iris within the image so that the coding budget is

allocated almost entirely to the iris texture rather than

to costly irrelevant structures such as eyelashes; and it

Iris Recognition Performance Under Extreme Image Compression. Table 1. Summary of the compression schemes,

resulting file sizes, and their effects on computed IrisCodes, expressed as entropy per code bit and as the fraction (HD) of

bits that were changed from those computed for the original full-size images

Strategy

Compression

parameter

Average image

size

Entropy/code

bit

Interoperability

Cropping (320320) þ JPEG

compression

QF¼70 12.4 KB 0.053 bit 0.006

QF¼30 5.7 KB 0.087 bit 0.011

QF¼20 4.2 KB 0.147 bit 0.021

Cropping + ROI + JPEG compression QF¼70 5.7 KB 0.112 bit 0.015

QF¼30 2.7 KB 0.147 bit 0.021

QF¼20 2.1 KB 0.199 bit 0.031

Cropping + ROI + JPEG2000

compression

CF = 20 5.1 KB 0.130 bit 0.018

CF = 50 2.0 KB 0.179 bit 0.027

CF = 60 1.7 KB 0.219 bit 0.035

Iris Recognition Performance Under Extreme Image Compression

835

is important to use JPEG2000 instead of JPEG as the

compression protocol. Advantages of this overall ap-

proach from the perspective of Standards bodies and

interoperability consortia are that the compact image

data (when decompressed) are a native rectilinear

arrays; no proprietary methods are required; and the

distortions that can arise from alternative coordinate

transformation methods such as polar unwrapping or

polar sampling are avoided.

As concluding measures, the IrisCodes genera-

ted under each scheme were compared with those

generated for the corresponding original uncom-

pressed images. The entropy H ¼

log

ðÞor

uncertainty per code bit caused by each compression

scheme is tabulated in Table 1. For reference, the en-

tropy associated with the states of bits in IrisCodes

calculated from different images of the same eye, due

merely to variation in image capture, is typically 0.506

bit; Table 1 shows that the corrupting effect of the

image compression schemes is much less than this

native uncertainty in the bits of IrisCodes for a given

eye. The ﬁnal column of Table 1 tabulates, as interop-

erability scores, the average HD (fraction of disagree-

ing bits) between the IrisCodes obtained before and

after image compression for each scheme and for each

compression parameter. They indicate that only about

2–3% of the IrisCode bits change as a consequence of

image compression even as severe as to 2,000 bytes.

When considered in the context of Fig.6 showing the

HD distributions for same and different eyes, it is clear

that an increment of 0.02–0.03 in HD score is a negli-

gible impact indeed. In conclusion, it app ears that

rough convergence between data length and standard

description length for this biometric system is possible.

These observations appear to vindicate the applica-

bility to biometrics of the fundamental insig hts of

Shannon [3] and Kolmogorov [4] and the relevance

of their analyses of asymptotic compressibility.

Related Entries

▶ Iris Encoding and Recognition Using Gabor Wavelets

References

1. Bradley, J., Brislawn, C., Hopper, T.: The FBI Wavelet/Scalar

Quantization standard for grayscale ﬁngerprint image compres-

sion. Proc. SPIE (Applications of Digital Image Processing XIX)

2847 (1996)

2. Daugman, J., Downing, C.: Effect of severe image compression

on iris recognition performance. IEEE Trans. Inform. Forensics

Secur. 3, 52–61 (2008)

3. Shannon, C.: A mathematical theory of communication. Bell

Syst. Tech. J. 27, 379–423 (1948)

4. Kolmogorov, A.: Three approaches to the quantitative deﬁnition

of information. Probl. Inform. Transm. 1, 4–7 (1965)

5. Terzopoulos, D., Waters, K.: Analysis and synthesis of

facial image sequences using physical and anatomical

models. IEEE Trans. Pattern Anal. Mach. Intell 15, 569–579

(1993)

6. Cappelli, R., Maio, D., Maltoni, D.: Synthetic ﬁngerprint-

image generation. Proc. Int. Conf. Pattern Recognit. 15,

475–478 (2000)

7. Cui, J., Wang, Y., Huang, J., Tan, T., Sun, Z.: An iris image

synthesis method based on PCA and super-resolution. Proc.

17th Int. Conf. Pattern Recognit. 4, 471–474 (2004)

8. Zuo, J., Schmid, N., Chen, X.: On generation and analysis of

synthetic iris images. IEEE Trans. Inform. Forensics Secur. 2,

77–90 (2007)

9. Daugman, J., Downing, C.: Epigenetic randomness, complexity,

and singularity of human iris patterns. Proc. R. Soc. B Biol. Sci.

268, 1737–1740 (2001)

10. Daugman, J.: How iris recognition works. IEEE Trans. Circuits

Syst. Video Technol. 14, 21–30 (2004)

11. Rakshit, S., Monro, D.: An evaluation of image sampling and

compression for human iris recognition. IEEE Trans. Inform.

Forensics Secur. 2, 605–612 (2007)

12. National Institute of Standards and Technology. Iris challenge

evaluation. http://iris.nist.gov/ice/

13. Wallace, G.: The JPEG still picture compression standard. Com-

mun. ACM 34, 30–44 (1991)

14. International Organisation for Standards: Information technology –

Digital compression and coding of continuous-tone still images.

ISO/IEC 10918 (1994)

15. Bradley, A., Stentiford, F.: JPEG2000 and region of interest

coding. In: Digital Imaging Computing Techniques and Appli-

cations. Melbourne, Australia (2002)

16. International Organisation for Standards: Information

technology – JPEG2000 image coding system. ISO/IEC 15444-1

(2004)

17. Christopoulos, C., Skodras, A., Ebrahimi, T.: The JPEG2000 still

image coding system: an overview. IEEE Trans. Consum. Elec-

tron 46, 1103–1127 (2000)

18. Hsu, R., Grifﬁn, P.: JPEG region of interest compression for face

recognition. IDENTIX Doc. RDNJ-04-0102 (2005)

19. Registered Traveler Interoperability Consortium (RTIC): Tech-

nical Interoperability Speciﬁcation for the Registered Traveler

Program. http:///www.rtconsortium.org/

Iris Recognition Systems

▶ Iris Acquisition Device

836

Iris Recognition Systems

Iris Recognition Using Correlation

Filters

YUNG-HUI LI

,MARIOS SAVVIDES

,JASON THORNTON

B. V. K. V

IJAYA KUMAR

Language Technolog y Institute, Carnegie Mellon

University, Pittsbu rgh, PA, USA

Department of Electrical and Computer Engineering,

Carnegie Mellon University, Pittsburgh, PA, USA

Synonym

Iris Recognition with deformation and occlusion

estimation

Definition

Algorithms for iris recognition usually consist of apply-

ing feature extraction on raw iris pattern, then match-

ing against features. However, two important techniques

in machine learning and pattern recognition, namely

probabilistic graphical model, and advanced correla-

tion ﬁlters, have not been used for iris recognition. By

using probabilistic graphical models for iris texture

deformation, with the observation being the correla-

tion output derived from applying correlation ﬁlters

to local iris regions, problems of iris pattern local

deformations and occlusions can be handled and

recognition performance can be improved over that of

the conventional iris recognition algorithms.

Introduction

In the past two decades, iris recognition has emerged

as one of the most promising modalities for biometric

recognition. Many algorithms have been proposed

to improve the recognition performance of iris recog-

nition. However, there are still some obstacles which

keep us from achieving near-perfect recognition

results. Those obstacles incl ude:

1. Local deformation in iris texture: iris texture may

deform locally because of the dilation, contraction,

or motion of the pupil, as shown in Fig. 1. Note

that these deformations appe ar locally, not globally.

Therefore, a simple image global transformation

can not solve this problem. A more advanced mod-

eling technique is needed.

2. Occlusion: very often, iris texture is occluded by

many different objects, for example, eyelid, eye-

lashes, or eye glasses. Proper estimation of occluded

region is important for achieving high recognition

rate iris recognition.

The problem of deformation and occlusion estimation

is seldom addressed in iris recognition literature.

In this article, this problem is addressed by two advanced

techniques in the ﬁeld of pattern recognition and

Iris Recognition Using Correlation Filters. Figure 1 Example images to show local deformation of iris texture.

(a) original iris texture (b) iris texture after local deformation. There are four regions where local deformation is observed.

Every anchor point is marked with a white star, and local anchor points are connected with white lines. Note that the

deformations are irregular with different direction in different region. Therefore, it cannot be solved by a simple image

global transformation.

Iris Recognition Using Correlation Filters

837

machine learning: probabilistic graphical models and

advanced correlation ﬁlters. Interested readers are re-

ferred to the original publication for more details [1–3].

Data Preprocessing

Iris images have to be preprocessed before going into

the framework of deformation and occlusion estima-

tion. The stage of data preprocessing includes iris

segmentation and coordinate transformation, as de-

scribed in the entry ‘‘Iris Overview.’’ After preproces-

sing, the iris texture map is transformed to the polar

coordinate plane, as shown in Fig. 2.

Deformation and Occlusion

Estimation

We can model the deformation and occlusion in iris

pattern with a probabilistic graphical grid, as shown in

Fig. 3. In Fig. 3a, an iris texture image is shown. The

iris texture is dissected into smaller patches in order to

observe the local deformation in more detail. In

Fig. 3b, another iris texture image from the same

class, is compared with Fig. 3a. The comparison is

done in a patch-wise fashion. Every local patch is

compared against the patch in the same location in

the other image. The vectors in the center of each

patch show how much and in what direction the

patch is deformed. In Fig. 3b, we can see that the

distance and the direction of the deformation vector

is distributed randomly, and there is no global con-

sistency among t hem.

In order to model such local deformation and

occlusion, a probabilistic graphical model, arranged

in a grid structure, is proposed, as shown in Fig. 3c.

Suppose the number of patches in an iris imag e is N

Each node d

in the model, i ¼ 1, ..., N

, represents

a 2-D discrete-valued shift vector, the true value of

which is hidden. The components of d

are the vertical

and horizontal shifts (in pixels) of the template region

relative to the corresponding query region. The nodes

are hidden binary-valued occlusion variables, where

=0 and =1 denote that the region is occluded and

un-occluded by the eyelid, respectively. Nodes O

represent the observations, which include the match

score of each local patch, and the occlusion statistics p

Match Score Computed from

Correlation Filters

Computation of the match score has to be robust to

the noise. At the same time, s ince we are e stimating

local deformation (relative shift) of each patch,

it would be even better if the match score itself

incorporates the information about the relative

in-plane translation of the compared pattern.

Advanced correlation ﬁlter is one of the techniques

in pa ttern recognition ﬁ eld that can meet such

requirement.

Theories of advanced correlation ﬁlters have been

developed in the last two decades and they have

been successfully applied in the ﬁeld of biometrics

[4–6]. There are many different versions of correlation

ﬁlters and each of them is designed according to dif-

ferent criteria [7–11]. The one which is introduced

in this article is the Optimal Trade-off Synthetic

Discriminant Function (OTSDF), one of the most

robust correlation ﬁlters [12]. The process of creating

and using OTSDF is illustrated in Fig. 4. During train-

ing stage (i.e., creation of OTSDF), a few training

images are given. From those training images,

Iris Recognition Using Correlation Filters. Figure 2 The data preprocessing stage. First row: the raw eye images with iris

boundary. Second row: the iris texture map after segmentation and coordinate transformation.

838

Iris Recognition Using Correlation Filters

OTSDF can be computed using a closed form expres-

sion in 2D Fourier domain. The expression is designed

to minimize both the

▶ average correlation energy

(ACE) and the

▶ output noise variance (ONV), but

at the same time, make the output of the peak to be

the preset value if the test image is one of the training

images itself. Let h represent a vectorized form (e.g., by

lexicographic scanning of the array into a column

vector) of the correlation ﬁlter H(u, v), x

represent

the vectorized form of the

▶ Fourier transform of

training image i, D represent a diagonal matrix

with the average squared magnitude of all x

along its

diagonal, and N is the power spectral density of the

input noise lexicographically re-ordered along its diag-

onal. The ACE and ONV can be represented as

ACE ¼ h

ONV ¼ h

ð1Þ

where + denotes complex conjugate transpose.

As stated above, the criteria of the ﬁlter design is to

minimize both ACE and ONV subject to the linear

peak constraints for the input training images. This is

equivalent to minimizing a linear combination of the

two terms (determined by a parameter a), subject to

the same linear constraints. Lagrange optimization

yields a closed from solu tion

h ¼ A

1

XðX

1

XÞ

1

u ð2Þ

where

A ¼ aN þ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1  a

D ð3Þ

Iris Recognition Using Correlation Filters. Figure 4 Left: The training stage of OTSDF; Right: the testing stage of OTSDF.

Iris Recognition Using Correlation Filters. Figure 3

Probabilistic graphical model for deformation and

occlusion estimation. (a) the iris pattern dissected into

patches (b) another iris pattern of the same class, dissected

into patches. The vectors in the centers of the patches

indicate the relative deformation of that patch. (c) the

graphical model used for deformation and occlusion

estimation.

Iris Recognition Using Correlation Filters

839