Detecting Precise Iris Boundaries by Circular Shortest

Path Method

Ivan Matveev

and Ivan Simonenko

Computing Centre of Russian Academy of Sciences,

Vavilov str., 40, Moscow, 119333, Russia

Moscow Institute of Physics and Technology,

Institutskii per., 9, Dolgoprudny, Moscow Region, 141700, Russia

Abstract. Modiﬁed circular shortest path detection method is applied for re-

ﬁning pupil and iris boundaries using given approximate pupil and iris circles.

Brightness gradient direction is employed to choose image pixels, which may be-

long to pupil or iris boundary. Using initial approximate circles allows the method

to work in a narrow ring, which contains only single circular contour. Under these

conditions the method allows to correctly handle almost all images used for iris

recognition tasks and appears to be more precise than human expert in mark-

ing the pupil border. The method was tested with public domain iris databases,

containing more than 80000 images totally.

1 Introduction

Iris recognition is one of main biometric identiﬁcation technologies. Detecting iris bor-

ders in image is an important part of this method. Iris pattern in image is represented as

a ring enclosed between two approximately circular and approximately concentric con-

tours: inner border,which is an iris-pupil boundary,and outer border,which is iris-sclera

boundary. Both boundaries are approximated by circles with good precision, however

there are applications demanding more precise shape detection and description [1]. This

particularly concerns inner (i.e. pupil) boundary. As a rule, human pupil is close to cir-

cle in shape, however in most cases it is not an ideal circle and has irregular deviations

with relative magnitude around 5-10% [2]. Thus, a problem appears to detect a contour,

which has approximately circular shape and encloses dark region (pupil) in relatively

brighter background. Apparently, iris can be detected as a dark circular region in a

background of sclera, in case there are no or small occlusions by eyelashes and eyelids.

Problem of detecting shapes modelled by circles and ellipses (i.e. regular shapes) have

attracted much attention and many methods are developed. Rich variability of methods

applied to determining iris boundaries is reviewed in [3,4]. Much less attention is at-

tracted to tracking the boundaries to their irregular (although close to circle) shape that

may allow better recognition performance. Many researchers limit themselves to just

an iteration of same detection algorithm [5, 6] or to applying same detection method

in different scale under multi-scale image processing scheme [7,8]. Special methods

for reﬁnement of the boundaries, which track roundish but irregular shapes with good

Matveev I. and Simonenko I..

Detecting Precise Iris Boundaries by Circular Shortest Path Method.

DOI: 10.5220/0004394501010108

In Proceedings of the 4th International Workshop on Image Mining. Theory and Applications (IMTA-4-2013), pages 101-108

ISBN: 978-989-8565-50-1

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

precision and tolerate noise were developed to much less extent. The authors could ﬁnd

that only one approach of active contours was specially targeted and tested with the

task of iris border reﬁnement [9–11]. Here a method of circular shortest path proposed

in [12] is modiﬁed and applied to the problem of reﬁning pupil and iris borders.

2 Circular Shortest Path Algorithm

There are plenty of methods performing detection of shortest path in images. Speciﬁc

feature of the CSP approach among them is that it starts from an a-priory detected

point that is claimed to be an approximate contour center (or at least is lying inside the

contour). In the reﬁnement task stated here initial data for the method are even more

detailed: center position and radius of approximating circle are given. Since the contour

passes round a given point it is reasonable to perform a polar transformation with the

pole in this point, which simpliﬁes both representation and calculations. (Indeed, polar

transformation is a very common issue in iris image processing.) Polar transformation

renders a ring shape to a rectangle. This rectangle can be positioned so as to have its

top side being a circle enclosing the proposed contour (enough big circle should be

taken), and bottom side is to be enough small circle inside the contour. Then left side

and right side both correspond to a coordinate origin line, let it be OX half-axis. The

radial coordinate of polar system is transformed to abscissa of the rectangle and angle

coordinate becomes ordinate. Image in OXY domain is transformed to Oρφ domain

and is also represented as a rectangular raster. Deﬁne the size of the raster as W ∗ H

pixels. Call it polar representation rectangle, see. Figure1.

After the polar transformation circular path location task is rendered to a problem

of detecting optimal path between left and right sides of rectangle, under the condition

that terminal points at the sides have same vertical coordinate. Since contour is close to

circle in shape and pole of the polar transform is inside it, the polar representation of

contour is univalent, i.e. only one radius of contour corresponds to each angle value, and

the contour can be expressed in terms of function ρ(φ), φ ∈ [0; 2π], ρ(0) = ρ (2π). Fur-

ther, assuming that pole of transformation is not very close to the contour line (in other

words, is near the center of the contour), one can state that derivative of radius by angle

is limited: dρ/dφ 6 1. In raster polar representation rectangle of size W ∗ H this func-

tion becomes a discrete sequence {ρ

} (or accounting for both coordinates {(n, ρ

)}),

n ∈ [0, W − 1], ρ

∈ [0; H − 1]. Limitation to derivative becomes |ρ

n+1

− ρ

| 6 1.

Condition to equal value at ends becomes |ρ

W −1

− ρ

| 6 1. Thus the contour is repre-

sented as a chain of points in rectangular raster, each column of the raster contains one

and only one contour point, the points in adjacent columns belong to same or adjacent

rows, the ﬁrst and last points also belong to same or adjacent rows. Hereinafter this

chain of points is called path S = {ρ

}

W −1

n=0

. Figure2 illustrates the possible paths of a

contour, if tracked from left to right. A path from point with coordinates (φ; ρ) = (2; 3)

can go to points (3; 2) − (3; 4), from point (5; 1) - into points (6; 1) and (6; 2), and if

staring point is (1; 2) ending points can be (8; 1) − (8; 3).

Introduce the cost of transition between points (n, ρ

′

) and (n + 1, ρ

′′

) in adja-

cent columns in polar representation. Deﬁne it as C((n, ρ

′

), (n + 1, ρ

′′

)), or shorter

(ρ

′

, ρ

′′

). It is composed from ”inner” and ”outer” parts: C(ρ

′

, ρ

′′

) = C

(I)

(ρ

′

, ρ

′′

) +

102

Fig.1. Sample of polar transform applied to an iris image.

Fig.2. Possible contour paths in case of limited derivative dρ/dφ 6 1.

(O)

(ρ

′

, ρ

′′

). Inner part conditions the shape of the contour and favours straight hori-

zontal lines (which are circles in original OXY domain):

(I)

(ρ

′

, ρ

′′

) =











0 , ρ

′

= ρ

′′

, |ρ

′

− ρ

′′

| = 1

∞ , otherwise

The constant T

> 0 is the parameter which determines a ”force” compelling the

contour to be a straight line in polar representation (i.e. circle with center in given

103

pole in original image). The value of T

depends on parameters of polar transform,

namely from the scale of polar representation. While inner part depends on contour

shape only, and does not depend on image, outer part is estimated from image charac-

teristics and binds the contour to image. The outer part is the cost of passing through

point (n, ρ

′

) determined from local image characteristics in the point, and does not de-

pend on contour shape: C

(O)

(ρ

′

, ρ

′′

) = w((n, ρ

′

)). For a given path S = {ρ

}

W −1

n=0

total cost is the sum of all transitions between adjacent points in the path: C(S) =

C((0, ρ

), (W, ρ

)) =

W −1

n=0

(ρ

, ρ

n+1

). The optimal contour is the sequence min-

imizing the whole cost:S

∗

= arg min

C(S). This discrete optimization problem may

be solved by some known method, for instance, greedy algorithm as proposed in [12].

3 Application to Pupil Boundary Reﬁnement

Application of CSP method to the problem of iris boundaries detection has speciﬁc is-

sues. First, it is obvious that there are two circular contours in the image of an eye: pupil-

iris boundary and iris-sclera boundary. Sometimes there is a contour of ophthalmic lens

also. This makes it difﬁcult to apply CSP method to initial detection of these borders,

since detected contour can be any of these two and there is no perfect way of discrim-

inating these two cases. This application was treated in [13]. So, feasible task for CSP

method is reﬁnement of already detected pupil and iris borders. Under this condition

initial approximate locations of both iris boundaries is known. Thus the algorithm can

run for a narrow ring containing the target boundary, rather than for the whole image.

For a narrow polar representation rectangle with H < 30 a straightforward exhaustive

search is faster than other elaborated algorithms.

The exhaustive search of optimal circular path is performed recursively as a set of

steps. Each step involves a column of the polar representation raster (points with same

value of φ). The cost of passing from a point (0, ρ

′

), in the ﬁrst (left) column to the

point (n, ρ

′′

), in current column: C((0, ρ

′

), (n, ρ

′′

)) ≡ C

(n)

(ρ

′

, ρ

′′

). Since both ρ

′

and

′′

range in [1, H], it is necessary to calculate H

values C

(n)

. They are calculated

recursively starting from C

(1)

(ρ

′

, ρ

′′

) = 1/δ(ρ

′

, ρ

′′

). For each next column the cost of

arriving to a point in it is a minimal sum of cost of arriving to some point ρ

′′′

in the

previous column and the cost of transition between adjacent columns:

(n+1)

(ρ

′

, ρ

′′

) = min

′′′

(n)

(ρ

′

, ρ

′′′

) + C

(ρ

′′′

, ρ

′′

)) =

= min











(n)

(ρ

′

), ρ

′′

) + w(n, ρ

′′

) ,

(n)

(ρ

′

), ρ

′′

+ 1) + w(n, ρ

′′

+ 1) + T

(n)

(ρ

′

), ρ

′′

− 1) + w(n, ρ

′′

− 1) + T











The incoming path for each point in the column (i.e. which of the three sums gave mini-

mum) is recorded. At the ﬁnal step (which has number W +1) H

valuesC

(W +1)

(ρ

′

, ρ

′′

)

are obtained. Only values with ρ

′

= ρ

′′

correspond to closed contours. So the cost of

optimal closed contour is min

(W +1)

(ρ, ρ) and it starts and ends at ρ

∗

W +1

≡ ρ

∗

104

arg min

(W +1)

(ρ, ρ). From the detected radius ρ

∗

W +1

contour is tracked back easily

from the recorded incoming paths.

Now consider the outer cost of transition via point C

(O)

(φ, ρ) = w(φ, ρ). From the

task formulation it is clear that w(φ, ρ) function should be constructed so as to be small

in the points corresponding to the contour and big in other points. Contour points have

strong brightness gradient value, thus points with small gradient should be rejected.

This is done in the source image by checking the condition kgk > T

in each image

pixel and selecting only pixels, which satisfy this condition as possible contour points.

Here g is is brightness gradient vector and T

is a threshold. The value of T

is selected

so as to suppress false gradients occurring due to image noise. If 3 ∗ 3 Sobel mask is

used for gradient calculation the treshold can be set T

= 6

√

2 max{σ, 2}, where σ is

the brightness standard deviation caused by noise.

Next task-speciﬁc feature is that both pupil and iris are dark regions in brighter

background, hence brightness gradients are directed outwards of the contour, and the

angle between gradient in the point and radius-vector to this point from the center of the

contour is enough small. This condition can be set as: arccos(

x·g

kxk kgk

) < T

. The value

of threshold T

depends on the quality of the center detection algorithm, treated as an

average (or maximum, or percentile) ratio of the distance D between detected center and

true center to the radius R of the contour. It is calculated as T

= arcsin(D/R). Figure3

shows the points of an image from Figure1, satisfying both of the aboveconditions. The

cost of transition is set to zero for these points, and is set to T

for all other points.

Fig.3. Sample of gradient map with direction condition imposed and its polar transform.

With these modiﬁcations CSP method was applied to the reﬁnement of iris bound-

aries

4 Experiments

Tests of CSP performance were done with the following iris image databases from

public domain: UBIRIS.v1 [14], CASIA-IrisV3 [15], ND-IRIS [16]. Eye images were

105

processed by human expert who indicated pupil and iris borders with most likely ap-

proximating circles. Thus each image was attributed with center positions and radii

of pupil and iris circles. These data (call it expert marking) were then considered as

”ground-truth” and were used for method veriﬁcation. Unfortunately, there is no simple

way to obtain reﬁned border contours, that can be treated as ”ground-truth”. Human

operator can manually mark quite a small share of huge image databases with such

contours. This task is much more tedious and error-prone than marking circles.

So, direct tests of comparing reﬁned borders to some ”ground-truth”data and testing

the quality of reﬁnement method are not possible. Indirect methods were used instead.

Reﬁned borders were ”simpliﬁed” back to circle, which has center in the point of mass

center of the area, enclosed to the reﬁned border. Radius of simpliﬁed circle was set to

equate areas enclosed in this circle and in reﬁned border. Call this simpliﬁed represen-

tation of reﬁned border reﬁned circle. Although again circle, reﬁned one does not match

the original approximation, and it can be a better approximation somehow.

Two approaches were used to compare original and reﬁned circles. First approach

is direct matching against expert marking, to estimate which kind of detection is more

precise. Images from all three databases were used [14–16]. Three ways were used to

supply initially detected pupils and irises. First, expert marking data itself were spoiled

with random noise to simulate improper detection. Second, Masek’s algorithm [17]

was used. Third, an approximate method of detection by circular brightness gradient

projections [18] was employed. Mean square deviations of pupil center position and

radius from expert marking were calculated for all three ways for original and reﬁned

circles.

Table 1. Error in pupil detection by various methods.

Method Average error of pupil radius de-

tection in three databases, pixels

Average error of pupil center posi-

tion in three databases, pixels

UBI NDIRIS CASIA UBI NDIRIS CASIA

Spoiled expert 8.16 8.16 8.16 5.77 5.77 5.77

Masek 4.65 7.23 5.15 3.24 5.59 3.67

Matveev 7.78 6.34 5.81 5.13 4.27 4.11

Spoiled expert, reﬁned 5.59 2.52 1.86 3.26 1.63 1.53

Masek, reﬁned 4.07 2.41 1.58 2.88 2.07 1.14

Matveev, reﬁned 4.89 2.09 1.45 3.51 1.52 1.09

CSP reﬁnement makes improvement in precision of initial detection, although it is

not effective for highly noisy images like UBIRIS.v1.

Second approachto estimate the quality and usability of reﬁnement is judging by the

”ﬁnal characteristic”, that is precision of iris recognition. The value of equal probability

of recognition errors of ﬁrst and second kind (equal error rate, EER) was chosen as

such characteristic. CASIA Iris-Lamp database [15] was used for tests, which contains

16213 images of 819 eyes of 411 subjects. The following steps were performed here.

Templates were created from images of database by the algorithm [9]. For its work the

algorithm uses circular approximations of pupil and iris in each image. At ﬁrst, pure

expert marking was used for this purpose. The set of obtained templates was matched

against itself and the EER value was estimated. For original expert marking its value is

106

EER=0.752%. Then expert marking of pupils was reﬁned by the proposed method, and

same operations of template generation, matching and EER evaluation were done, with

resulting EER=0.390%.

So, the reﬁnement of pupil by circular shortest path method appears to reduce the

recognition error. This can be explained by the imprecise marking of human expert.

5 Conclusions

Location of iris borders with high precision is an important task in automatic iris biom-

etry. Though much attention is paid to iris border location in general, only few re-

searchers tried developing special methods for iris border reﬁnement after their initial

detection. The authors have treated this aspect of iris border location problem with the

help of circular shortest path optimization method. The CSP detection algorithm was

modiﬁed to ﬁt the peculiar properties of the task. The results of experiments show that

reﬁnement of pupil-iris boundary by CSP may be a useful addition to general scheme

of iris border location.

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