A study of iris recognition methods

3.1 Iris contour extraction The first step in an iris recognition scheme is segmentation which is an essential step in many image processing algorithms, and consists in finding areas of

BENOIT MORTGAT

NATIONAL UNIVERSITY OF SINGAPORE

2009

BENOIT MORTGAT

(joint degree Télécom SudParis)

A THESIS SUBMITTED FOR THE DEGREE OF

MASTER OF ENGINEERING

DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2009

In the context of an increasing demand of biometric solutions and growing market for security and authentication applications, iris recognition has potential for a wider use The iris is particularly good for biometric purposes due to the high randomness of its texture, thus making each eye highly unique Iris offers other various advantages such as universality and feeble intrusiveness In our iris recognition process, the iridian region is first isolated using mathematical tools to find circles in images The iris image is then passed through a set of Gabor filters, that offer a good localisation both in frequency and in space Depending on the outputs of these filters, each pixel in the iris image is assigned to a class by a clustering program with a required number of classes Comparison between two irises can be performed by measuring similarity between class repartition of the pixels This algorithm gives out

promising results that allow for future enhancements.

*

**

Keywords — Iris recognition ? Iris segmentation ? Clustering algorithm ? Automatic

classification ? Gabor filter ? Biometrics

I would like to thank many in this thesis My thoughts are first for the different people who supervised my work, namely Assoc Prof Ashraf, Kassim and Prof Venkatesh, Yedatore Venkatakris For their advice, support all along the duration of my research work They provided significant help and gave me directions for my research I owe them warmest thanks.

The research work that is presented in this thesis has been made possible by the use of the UBIRIS database, from the University of Beira Interior, Portugal.

I appreciated this precious help and express my most sincere gratitude to its creators This iris database provided excellent data for this work.

The present thesis and its data, graphics, etc have been produced by ous computer software, and I would like to particularly thank the creators of the CImg software library In addition, creators of the TikZ-PGF library for LATEX did

numer-a work thnumer-at pnumer-articulnumer-arly helped me.

Eventually, I address my thanks to all the people who encouraged me out my work, those whom I am indebted to, my family and friends.

1.1 About biometrics 1

1.2 Iris as a biometric feature 4

1.2.1 Anatomy of the iris 4

1.2.2 Biometric features 6

1.3 Overview of thesis 8

2 Previous works 10 2.1 On textures 10

2.2 On iris recognition 11

3 Recognition 15 3.1 Iris contour extraction 15

3.1.1 Overview of the problem 15

3.1.2 Problems to overcome 16

3.1.3 Our algorithm 17

3.2 Iridian meshwork filtering 26

3.2.1 Gabor filters 26

3.2.2 Gabor filter sets 28

3.3 Clustering 29

3.3.1 The algorithm 30

3.3.2 Example 32

3.4 Measuring similarity 34

4 Results and discussions 36 4.1 About The database UBIRIS 36

4.1.1 Advantages of UBIRIS 38

4.1.2 Drawbacks of UBIRIS 38

4.2 Segmentation results 39

4.2.1 Hough transform 39

4.2.2 Finding the location of the sclera (outer circle) 41

4.2.3 Finding the location of the pupil (inner circle) 43

4.2.4 Global segmentation results, and discussion 45

4.3 Filtering results 46

4.4 Clustering results 51

4.5 Matching 53

4.6 Performance 56

5 Conclusion 57 Bibliography 60 Appendices 63 A Source code 63 A.1 Segmentation source code 63

A.1.1 ChangeGeometry.H 64

A.1.2 ChangeGeometry.C 65

A.1.3 Common.H 66

A.1.4 Drawing.H 67

A.1.5 Drawing.C 68

A.1.6 FindCircles.H 69

A.1.7 FindCircles.C 71

A.1.8 Hough.H 74

A.1.9 Hough.C 75

A.1.10 Segment.H 76

A.1.11 Segment.C 76

A.1.12 Makefile 79

A.2 Filtering source code 80

A.2.1 filters.conf 80

A.2.2 Gabor.H 81

A.2.3 Gabor.C 83

A.2.4 Makefile 88

A.3 Clustering source code 89

A.3.1 Makefile 89

A.3.2 ClassesC.H 90

A.3.3 ClassesC.C 92

A.3.4 Clustering.H 96

A.3.5 Clustering.C 97

A.4 Matching source code 102

A.4.1 Makefile 102

A.4.2 Matching.C 103

B Example of use 106 B.1 Segmentation 107

B.2 Filtering 109

B.3 Clustering 110

B.4 Matching 111

C The PGM file format 112

Index 113

List of Tables

List of Figures

1.1 Several fingerprint readers 1

1.2 Steps in biometrics applications 2

1.3 Several figures, from [ 2 , section X-1c] 5

3.1 Segmentation of the eye 16

3.2 Zoom on the border of an iris 18

3.3 Y (x, y, ρ) is roughly the integral of γ(∆I)dθ where ∆I is the inten-sity difference 20

3.4 Non-linear filter on luminance to diminish the effect of light re-flection 22

3.5 Pixel interpolation for storage of segmentation results 26

3.6 A Gabor filter 27

3.7 2D Gabor filters 27

3.8 Sample chequerboard 29

3.9 Running the clustering algorithm on a random set of 2D vectors 33 4.1 Sample images from the UBIRIS database 37

4.2 A successful segmentation example 39

4.3 A Hough transform can detect circles efficiently 40

4.4 The parameter pocontrols the desired radius 43

4.5 Some typical segmentation outputs 46

4.6 View of the masks of the different filter sets 48

4.7 Reconstruction of a chequerboard image with the five filter sets 49 4.8 Progressive reconstruction of the chequerboard with nine filters 50 4.9 Clustering results after filtering with filter set 3 52

4.10 Different clustering outputs for different photographs of the same eye 52

4.11 Clustering of raw RGB data 53

4.12 Density of similarity measures within pairs of images 55

B.1 Original images 106

B.2 Circles1.jpg 107

B.3 Segmented images 107

B.4 Classified images 110

 Introduction

1.1 About biometrics

Biometrics is the art of identifying an individual by measuring some feature This feature can be of various types; it can be a physical (fingerprint, iris, hand shape ) or behavioural (handwriting, gait ) characteristic Biometrics is nowadays widely used as many governments gather individual features for identification of people on their territory Biometric information is stored on chips in passports issued by more than 50 countries Also, private companies encourage the use of systems based on biometrics for security enhancement.

(a) A fingerprint reader for a

desktop computer

(b) A fingerprint reader for a laptop computer

(c) A fingerprint reader for an out- door system

Figure 1.1: Several fingerprint readers

A biometric system is a partially or fully automatic system that measures a man feature and uses it to authenticate or identify a person This system is based

hu-on pattern recognitihu-on theory, using generally a significant load of informatihu-on provided by a single feature Such systems exist, for example, for authentication

by fingerprint on recent computers, and are used to log in Figure 1.1 on the ceding page shows several fingerprint readers; the last one is sometimes used to deliver access to a part of a building.

pre-Capture Segmentation Feature Extraction Database

(a) Training

Capture Segmentation

Comparison Classification

(b) Identifying

Figure 1.2: Steps in biometrics applications

As any pattern recognition system, the biometric based recognition system

depending on the goal Registering a person or class in a database of features

is called training, whereas the identification operation consists of using training data to determine whether it matches a measure.

The different steps shown on Figure 1.2 are detailed here:

Capture: the step in which data is obtained from an individual Capture can

be realised with the help of an optical system like a camera in the case of fingerprint, iris or gait recognition, or a microphone in the case of voice, for example.

Segmentation: the removal of all useless information obtained in the capture.

In the case of gait recognition, for example, all environment should be nored, in order to exclusively retain the morphology of a walking person.

ig-Extraction: could be roughly described as a succession of algorithms that try to describe the segmented data in a reliable way Yet the description has to contain less information than the data, it should be sufficient to make a distinction between individuals.

Comparison: the process during which multiple descriptions are taken as puts and that attempts to determine a correlation ratio between them Com- parison can be used in order to enhance the description of an individual’s features in a database during the training stage, but it is mostly used while identifying a user of the system There are two sorts of applications for biometrics:

in-Authentication: the system has to check the measured feature against a single description in its database, and to decide whether the descrip- tion match It is similar to providing a password on a web site, but no user name.

Identification: the system has to check the measured feature against all descriptions in its database, and to decide that there is a description against which it matches the best, or to decide that it does not match any of the descriptions This is similar to providing both user name and password on a web site.

Classification: the final decision using all evaluated probability in the ison step, and taking into account the costs in case of error.

compar-Extended description of the steps of pattern recognition machines can be found on [ 1 ] in the introduction and in the chapter called “Bayesian Decision Theory”.

1.2 Iris as a biometric feature

A complete description of the iridian anatomy is out of the scope of this thesis, this section provides a short attempt to describe it.

Iris is a part of the eye, which is a circular and contractile membrane around the pupil1 Contractions of the iris allow more or less light to pass through the lens to the retina Many muscles embedded in the iris can either constrict or dilate the pupil.

A description of the iris surface, its layers and its pigmentation can be found

in [ 3 ].

Causes of uniqueness

The possibility that the iris may be used as a kind of optical fingerprint for sonal identification was suggested originally by ophthalmologists, who noted from clinical experience that every iris had a highly detailed and unique texture,

In citing Davson’s Physiology of the Eye [ 5 ], Daugman [ 4 ] highlights that since the iris’ detailed morphogenesis depends on initial conditions in the em- bryonic mesoderm from which it develops, the phenotypic expression even of two irises with the same genetic genotype (as is identical twins, or the pair pos- sessed by one individual) have uncorrelated minutiæ.

In another article[ 6 ], Daugman explains that the structures that form the ian pattern are “largely complete by the eighth month” of gestation, “although pigment accretion can continue into the first postnatal years” This is the reason why iris is a very stable feature.

irid-1Certain persons affected by polycoria may have two or more pupils This affection will not

be covered in this thesis.

(a) A horizontal section of the eyeball (b) Vessels of the

As an example, voice is not a good feature in terms of uniqueness, because

it is not uncommon that two individuals have similar voices.

Stability is also of very high importance for long-term applications A feature that is stable is a feature that will not change much over time Voice is still

a good example of non-stable feature: illnesses, breaking of voice during adolescence, and age, have an influence on the tone of every individual.

Universality is a concern about potential non-existence of the given feature for certain persons Voice is non-existent among people with speech impair- ment, therefore it is not universal.

Social acceptability should be taken into consideration It is most certainly related to intrusiveness The presence of a microphone would probably not cause much inconvenience or embarrassment to people whose voice is recorded; hence voice is an acceptable biometric feature.

Iris and uniqueness

The iris texture is formed during morphogenesis of the eye, which is a chaotic process[ 4 ] The appearance of the iris is due to a layered anatomy Those factors result in a very strong uniqueness; even monozygotic twins have uncorrelated

ran-domly scattered on its surface, thus meeting the requirements of uniqueness.

2A minutia is a point of interest that can occur at the intersection, bifurcation or ending of ridges.

Iris and stability

As noted in the previous section, the iris is located behind the cornea and the aqueous humour; these parts offer a protection from external factors to the iris, which therefore is well-preserved and is not subject to changes in its structure Iris is therefore of extremely good stability over time.

Iris and universality

Although it is not uncommon for a person to wear a plastic or glass eye3, it is very rare to find a person who does not have at least one real iris (ie, who has two glass eyes)4 Therefore the iris is an almost universal feature.

Iris and social acceptability

It is probable that iris recognition would be more accepted in certain cultures and not in other cultures because it is related to an organ of the visual system, thereby constituting a form of embarrassment in front of a machine perceived as

“looking” into one’s eye.

Deployment of an iris recognition machine

It is possible to scan the iris of an individual provided the iris is not artificial, and

is visible Sunglasses or coloured lenses have to be removed, and illnesses of the cornea such as keratitis can obstruct recognition Those cautionary measures apart, iris appears to be a very convenient feature for performing biometrics Iris recognition should work with wearers of vision correction systems (glasses

iris recognition without becoming too invasive, for example by requesting the subject to use a chin rest Moreover illumination should be sufficient but not disturb the subject.

A way to achieve this was imagined by John G Daugman, pioneer in iris recognition, who designed a system using a beam splitter to send the eye im- age to a camera and simultaneously show the image to the subject; this more interactive way of taking the picture, similar to a photo booth, can be felt as less intrusive In addition the subject can participate and adjust his position and an- gle of view upon seeing what is being captured With this system, with a typical distance of 15 cm between the subject and the capture device, a captured iris can easily reach 200 pixels in diameter This system uses a LED source of light to have a good luminosity.

present algorithms that perform segmentation, feature extraction and son on templates The results and discussion is provided in Chapter 4 on page 36

compari-and the concluding remarks are presented in in Chapter 5 on page 57

Appendices will mostly contain the developed source code as well as an ample of use of the programs for a full understanding of the working scheme.

ex-Contribution of this work

This thesis presents a set of methods that can play a major role in iris recognition machines The methods enable further analysis and improvements While every

variable has tentatively been optimised for a database in particular, with a deep explanation of the used method The tools that are provided here, based on liter- ature and entirely self-developed, offer a good starting point for further research for other extraction methods for example and the results section provides useful observations on the influence of some variables.

meth-ods of texture analysis, with the help of several mathematical tools (statistics

of the image, frequency analysis, use of Peano curves and local trajectories, or description by characteristic matrix of the patterns) and evaluates performance using a texture database and classifying his segmentation results with the k- nearest-neighbours method[ 1 ] In a second part, an application to segmentation

is investigated, so as to obtain an algorithm to extract “visual entities” of an age by decomposing it into regions This involves segmenting an image into several homogeneous zones, in a certain sense A uniformity measure has to

im-1A tentative translation for its title could be “Texture characterisation and Segmentation for Content-Based Image Retrieval”.

be developed, and several segmentation algorithms, from the most basic one to

a fully enriched version, are detailed (C-Means (CM), Fuzzy C-Means (FCM), Fuzzy C-Means with Spatial Constraints (SCFCM), Fuzzy C-Means with Spatio- pyramidal constraints (SPCFCM) An index of segmentation quality is built, and segmentation results of all these algorithms are compared both on natural and artificial images In a next part, Hafiane applies these results to Content-Based Image Retrieval (CBIR) The main issues with CBIR are explained (including what it requires in terms of spatial layout of the image elements) Different search techniques are presented with performance evaluation The complete automated chain of algorithms developed in this thesis is dedicated to analysis

of satellite images for geographic systems.

reproduce the set of treatments applied to images in the human visual system Texture recognition is very efficient for humans and such a work provides details

on the use of Gabor filters in the cortical system and their interest The method

is able to satisfactorily classify images representing a mountain scene, an urban scene or a forest scene.

Since the introduction of Gabor filters, several works have attempted to find good filter sets, notably a paper by Fischer et al.[ 9 ], in which an “optimal” filter set is applied to image denoising.

con-More specifically, this paper details creation of an iris code which is a 256-byte

code (2048 bits), that is computed from each iris and with which recognition can

code and a database iris code.

A study of the repartition of the Hamming distances measured on a icant number of iris codes led Daugman to approximate the number of binary degrees of freedom in an iris code as approximately 173, which means that the likelihood for two iris codes from different people to match in their entirety is

2173 that is approximated as 10−52 Daugman extended his research, writing several papers which present more results and statistics with recent data[ 10 ], and implement new features like ro- bustness against rotation[ 6 ].

new techniques including active contours, correction for off-axis gaze, tion of interfering eyelashes and several methods to correct geometry and pre- process the image in order to achieve less intrusive systems.

detec-In parallel, strongly based on Daugman’s research, some researchers have developed their own methods for iris recognition:

• Wildes[ 3 ] uses an alternate approach for capture of the iris; the subject does not see the camera output but is helped for self-positioning The seg- mentation of the iris is tweaked with a thresholding of gradient magni- tude and help of the Hough transform Moreover a registration technique

is used to compensate for scaling and rotation The feature extraction is not done with the help of Gabor filters, but with Laplacian of Gaussian filters Similarity to data base is measured with a correlation definition Both Wildes and Daugman systems have been awarded with US patents Wildes paper[ 3 ] emphasises on the differences between these two systems step by step.

2the Hamming distance between iris codes A and B is measured as H = 1

2048

P2048i=1 Aj? Bjwhere ? represents the XOR operator.

• Boles and Boashash[ 12 ] usex a radically different technique for iris tion: the iris “ring” is viewed as a periodic signal (as the normalised image represents a rotation around the pupil centre), therefore its wavelet trans- form is invariant to rotation The wavelet transform at low resolutions en- sures noise does not affect too much the results The zero-crossings of the wavelet transform constitute the biometric template A method to classify these templates (for matching) is proposed Results seem to be very good, even though few results are presented.

recogni-• Huang et al.[ 13 ] refine the original Daugman segmentation process by ducing its computational complexity (rescaling), converting the image to

re-a binre-ary mre-ap for re-a better speed, re-and providing re-a rough detection for lids and eyelashes But their feature extraction method is based on inde- pendent component analysis contrary to Daugman-based methods This

lower complexity ICA is performed on small windows, and its results, once quantised, constitute the iris encoding Recognition is done with an Average Euclidean distance It is regrettable, however, that few results are provided; the authors conclude observing a need for optimisation of the choice of the ICA coefficients used in encoding.

• Ma et al.[ 14 ] use a variant of Gabor filters, named “circular symmetric ters”, with a radial oscillation, and use a classification method (notion of iris code is not present here) Refining an older algorithm by themselves, they obtain almost perfect results.

fil-Ritter and Cooper[ 15 ] developed in 2003 a method for iris localisation using active contour models Internal and external forces applied to the contour adapt

it to the iris border The algorithm presented can report its own failures to detect iris boundaries Statistics of the image, and not only local gradients, are there-

3Principal Component Analysis, see [ 1 ].

fore used to detect the iris This paper does not propose further tools for iris recognition.

In 2007, Ganorkar and Gathol[ 16 ] created a chain of image treatments on the

CASIA database4 This thesis roughly consists of the same type of work, but with the UBIRIS database.

In 2006, Lim Mei Ling, Doreen[ 17 ] wrote a thesis with development of tools for recognition with Matlab, namely segmentation, filtering, classification and encoding This work is strongly based on her work, but the classification method

is different.

4

CASIAdatabase: http://www.cbsr.ia.ac.cn/IrisDatabase.htm

 Iris recognition using Gabor filters

This chapter presents our iris recognition algorithm based on pattern analysis The algorithm transforms the eye data into a more stable and recognisable in- formation map which is used for recognition.

3.1 Iris contour extraction

The first step in an iris recognition scheme is segmentation which is an essential step in many image processing algorithms, and consists in finding areas of rele- vant information in the initial data In iris recognition, segmentation consists of finding the region in which the iris is located in a photograph.

The iris has a ring shape, could be roughly modeled as an annulus (two centric circles) In this model, there are two circles that delimit the iris:

con-• the interior circle represents the inner boundary, between the pupil and the iris.

• the exterior circle represents the outer boundary, between the sclera (white part of the eye) and the iris.

In standard iris databases (like UBIRIS [ 18 ]), both upper and lower eyelids occlude some parts of the iris Thus, these frequently occluded regions (the up- permost and the lowermost parts), are properly ignored (i.e., not segmented).

Figure 3.1: Segmentation of the eye.

The resulting segmented region consists of two parts, the first one being on the left and the second one on the right, as shown on Figure 3.1 The segmented zones are represented in light grey surrounded by a thick black line The pupil has been represented in darker grey and is not segmented.

The annular geometry of the iris provides a natural intrinsic polar nates system If the location of the iris centre can be determined as well as the inner and outer radii (which will be denoted as r and R), then the segmented area corresponds to all points (x, y) = (ρ sin θ, ρ cos θ) so that:1

Nevertheless, many aspects can be questioned, that are tentatively listed

1In the formula, the angular values are arbitrary and can vary.

Of the shape of the iris

The circular shape of the iris can be questioned Actually, it is more generally assumed that the shape is rather elliptic The reasons for this include gravity, and camera positioning.

Of the concentricity of the two boundaries

Much work on recognition state that the centre of the pupil is not always exactly

at the same location as the centre of the iris[ 11 , 4 ] Therefore, the shape of the iris

is not mathematically an annulus, but could be rather defined as a “doughnut”.

Of the horizontality of the head

A biometric system must ensure that the information that is captured is stable If

a person is tilting his or her head while the iris is being photographed, then the area that will be segmented will not correspond to the same portion of iris once

it would be unfriendly to ask a person to keep head perfectly upright, it should

be more advisable to find a solution to overcome this problem.

Of the exact position of the outer boundary

The outer boundary, that separates the iris on one side, and the sclera (white part) on the other side, is, as can be seen on Image 3.2 on the following page, difficult to locate with precision, because of a “fading zone” inside which the colour of the iris progressively shifts from its dominant colour to white.

A simple but efficient algorithm has been developed to segment database ages; the different questions presented in previous part have been answered as

im-Figure 3.2: Zoom on the border of an iris follows:

• The shape of the two borders are considered perfect circles, in order to improve the computing speed, hence the algorithms performance.

• The two circles are not considered to have the same centre, but their two centered should not be “too far” A pseudo-polar coordinate system will

be used.

• It is assumed that the original image consists of a single eye and was tured while the head was not tilting (databases used did not provide larger

• The outer boundary is assumed to be located where the gradient is the most important This aspect will be presented in more detail in the follow- ing.

• The intensity of a pixel at location (x, y) will be denoted as IR(x, y), IG(x, y)

or IB(x, y) ;

• The coordinates of the centre for the outer circle will be denoted as (xo, yo) , and the coordinates of the centre for the inner circle will be denoted as (xi, yi)

• The radii for those two circles will be similarly denoted as ρo and ρi.

Overview of the algorithm

The algorithm handles typical RGB images in the JPEG format It attempts to locate the two circles that delimit the iris, with three parameters for each circles: two location parameters, and the radius.

Once the six parameters are determined, it builds a new image that has a fixed size by transforming the pseudo-polar coordinate system into a Cartesian coordinate system, and scaling Interpolation has to be done, as both original and output images are in raster format (JPEG) This step could be interpreted as

a type of normalisation.

Outer circle

Basically, the first circle that is “looked” for is the outer circle, that separates the sclera and the iris There are several reasons to choose this circle first, that are tentatively listed here:

• The border between the sclera and the iris has a better contrast The irises are heavily pigmented, and even in cases of albinism, an iris area will be seen as red because of blood vessels irrigating it Since the sclera is always white, this border should be always visible.

• The border between the sclera and the iris is a large circle Therefore, it is more visible on an image.

• The border between the sclera and the iris has a longer perimeter, and therefore the coordinates of the iris centre can be estimated with a better precision.

In order to locate this outer circle, a “quality index” is measured for each set

of parameters xo, yo, ρo An extensive search on different combinations of these parameters is performed in to select the parameters that give the best index For this search, each individual parameter will take a certain number of quantised values.

A good quality index Y must measure the likeliness for the three parameters

to match a circle in the image Given x, y and ρ, the goal is to detect sufficient radial variation:

In this integral, S represents an interval of radial directions that are most highly suspected to be visible on iris images The interval [0; 2π] is not chosen because it is frequent that eyelids occlude the iris In the implementation, S will typically be equal to −π

2 + ν; π2 − ν ∪ π

2 + ν;3π2 − ν  where the choice of the angular parameter ν will prevent certain radial directions from being explored The choice of ν will be explored in the results section.

The function γ is a positive function that is used to control that the variation

is as desired, given prior knowledge on what is looked for: for this application,

on every channel (be it red, green or blue), the sclera, which is white, is brighter than the iris Therefore, the function x 7→ x · H(x), with H being the Heaviside function (which equates to 1 over all positive values and 0 elsewhere), is a good candidate for γ.

The function β is a positive function that is used to control the order of nitude of the desired radius Actually, since the perimeter of larger circles is longer, the values of Y would tend to increase with ρ Setting β(ρ) = 1

mag-2πρensures larger radii would not be privileged, but since locating the outer circle requires not to match the pupil border, β has been set to 1 for this step.

This integral has to be adapted for a discrete use: using ICx,y(ρ, θ) to denote

sam-• dark coloured-irises are not always easy to segment; for example on photos

of brown eye, even a human is not always able to estimate this border because the pupil does not have sufficient contrast with the iris.

In a similar way, the inner circle is found by maximising an integral; this time, a rough estimation of xiand yi is given by (xo, yo) , and the radius should

be meaningfully smaller than the outer radius By observing many images, the pupil diameter, in case of large dilation, was found to be approximately 50 % of the iris outer diameter.

original luminance output luminance

Figure 3.4: Non-linear filter on luminance to diminish the effect of light reflection Differences between this step and the previous one are:

• The Y (luminance) channel of the image, in the (Y,Cb,Cr) colour mode, is passed through a non-linear filter, the goal of which is to diminish the hin- drance created by bright reflections An example of such a filter is shown

on Figure 3.4

• The interval S is [0, 2π] because the entire pupil is assumed to be visible.

• The expression of β(ρ) is still to be determined, but it must privilege smaller radii.

• The function γ has been slightly tweaked; as the pupillary contour is cult to distinguish, as explained, two radial intensity differences are mea- sured The first intensity difference is measured between two adjacent pix- els, the second one is measured between two pixels that are 5 pixels far from each other This security measure ensures that the detected circle is inside the pupil and that there is a brighter region outside with two mea- sures to confirm it A minimal intensity difference may also be required.

diffi-Increasing the processing speed

The presented methods to find the two circles have a drawback, that is cessing speed On large images, it would take a very long time to perform an extensive research of each circle centre and radius, because the number of possi- bilities is large Even on a 300 × 300 image, there would be 90 000 possible circle

pro-centres, and for some of those pro-centres, integrals along circles of which the radii would spread from 1 to 150 would have to be calculated.

For this reason, a method to accelerate these image processing steps has been developed; we present it here:

• The original image is downscaled with a scale factor of 50 % Each new pixel is computed as the average of four original pixels in a natural way If height or width of the original image were odd, some pixels are lost in this step.

• The downscaling operation is repeated until the image size is sufficiently small (in the implementation, either width or height (or both) has to fall below 30 pixels).

• Potential location of the iris centre is estimated thanks to a Hough form, which will be detailed in Section 3.1.3 on the following page.

trans-• The outer and inner circles are located as has been detailed, with the help

of the Hough transform.

• The centre positions and circle radii are refined on each resized version of the image, from the smallest to the biggest (which is the original); each refinement step consists in optimising the previously introduced integrals

on a restricted set of possible parameters.

This algorithm significantly improves on the processing time because each refinement step requires only a few integrals to be calculated Each upscaling step induces an error margin on the centres locations and their radii, that can

be estimated of ± 1 pixel Actually, the implementation that was realised uses a larger error margin of ± 3 pixels Then, at each step, there will be 7 possible val- ues for each circle centre coordinate and radius, and the number of refinement steps will be logarithmically dependent on the original size of the image.

For these reasons, this algorithm has a significantly lower computational complexity.

Hough transform

The Hough transform is a mathematical tool that can help detecting geometrical shapes in images It deals with available information to organise a poll and elect parameters that are the most consistent with it.

As an example, circles can be fully described with three parameters, which are the centre x-coordinate, the centre y-coordinate and the radius At each pixel, the gradient gives information that can be used to determine which triplets are consistent with it, typically triplets for which the potential circle centre is in the direction indicated by the gradient and the radius is the distance between the centre and the point where the gradient was measured.

Notations Let Ω be the set of all possible combinations of parameters and n

be the number of parameters desired; n is also the dimension of Ω Let f be a function mapping Ω to R+, this function will be called the vote count function.

At start, f (ω) = 0 for each ω ∈ Ω.

Let Ξ be the set of information available; each piece of information ξ ∈ Ξ will

be consistent with a subset Φ ⊂ Ω, and the value of f (ω) will be incremented for each ω ∈ Φ.

At the end of the poll, the elected combination of parameters is

ω0 = arg max

ω∈Ω f (ω)

Use in this algorithm In this algorithm, the Hough transform has been used

to determine only the iris centre, but not its radius There are two reasons porting this choice:

sup-• Since there are two circles with two different radii (pupil and sclera ders), f would have had two local maxima; if radii are ignored, as the centres of these two circles are approximately at the same location, f will have only one global maximum.

bor-• n falls from 3 to 2, reducing the complexity of the implementation.

As n = 2, the vote count function can be graphically represented as an greyscale image that will be called the Hough map; since the desired parameters are positional (centre of a circle), the Hough map represents the plausibility for each pixel to correspond to the iris centre.

It is known that in an image, the direction of the gradient is the direction of greatest rate of luminance increase, and is orthogonal to the direction of lowest rate of increase As the radius of a circle is perpendicular to its tangent at any point on the circle, if there is a circle standing on an image, the gradient should theoretically indicate the radial direction at any point situated on the circle Each pixel on the radial line is a possible circle centre.

As the pupil is darker than the iris and the iris is darker than the sclera, possible circle centres are assumed to be situated only on a half-line according

to the gradient at each point, and each vote is weighted with the value of the gradient Before choosing the elected pixel, the Hough map is blurred with a Gaussian filter in order to remove parasites.

of the grid is 60 × 60 for the left part as well as the right part.

This means that for 60 angular values between −π/2+ α andπ/2− β, 60 values have to be interpolated between the two borders in a linear way, for the right part, and as well for the left part The radial directions are passing through the pupil centre and do not reach the outer circle in a perpendicular way.

β

α

β

Figure 3.5: Pixel interpolation for storage of segmentation results

3.2 Iridian meshwork filtering

A Gabor filter is basically the product of a Gaussian envelop and a sinusoidal wave A simple Gabor filter can be represented as a function of one variable as

In two dimensions, Gabor filters have the following form:

G(x, y) = e−

x2 σ2x−y2 σ2y · cos (ωxx + ωyy)

coor-dinates system is represented, as this graph does not aim to represent one Gabor filter in particular.

f (x)

G(t) = cos(ωx) × e−x2σ2

Figure 3.6: A Gabor filter

(a) Three dimensional view of a Gabor

frequency of ω = pω2

x+ ω2

y and a principal direction given by θ = arctanωy

ωx Gabor filters can be written in a complex form; in this case, the imaginary part is a sine.

G(x, y) = e−

x2 σ2x−y2 σ2y · ei(ωxx+ωyy)

Gabor filters are interesting because they are quite well-located both in the spatial domain and in the frequency domain The Gaussian window, although never equal to zero in mathematical terms, is still almost equal to zero beyond some width The Fourier transform of a Gaussian is a Gaussian that have an inversely proportional width; therefore, as the Fourier transform of a product is

a convolution, the Fourier transform of a Gabor function is a Gaussian that has been shifted to be centered on the central frequency of the oscillating component.

In the case of a real Gabor filter, given that the Fourier transform of a cosine is

a pair of Dirac impulsions centered on two opposed frequencies, the Fourier

In the work presented here, the method to extract relevant information derives from work by J Daugman The segmented image is processed with a set of filters, that form a pseudo basis for a wavelet transform As the filters do not overlap much in the frequency domain, they are almost orthogonal In addition, the sum of their outputs, which will further be referred to as reconstruction, is not far from the original input The frequency coverage should be sufficient, such that loss of frequencies is minimised.

The filtering operation is done by convolution: the Fourier transform of a filter output is therefore the product of the Fourier transform of the filter, and the Fourier transform of the input As a result, when summing the outputs

of different filters, the Fourier transform approximately approaches the Fourier

transform of the original input as soon as the Gaussians are well-spread over the whole map of frequencies, and large enough not to leave any frequency uncov- ered.

If this requirement is met, then the chosen filter set offers possibilities for curately describing the image in the frequency domain with a good localisation and the outputs of the filters will provide much information that could be of great use for recognition.

ac-Figure 3.8: Sample chequerboard

In order to measure the quality of a filter set, reconstruction is performed

on a variety of chequerboard patterns like on Figure 3.8 Then, the resemblance between the reconstruction and the original image is evaluated with human eye without mathematical measurement; this evaluation is sufficient to be sure that filters capture small details and can restore them.

Filtering the segmented image has mapped each pixel to several real bers For example, if the original image has three layers (red, green and blue),