Detection of Iris in Image by

Brightness Gradient Projections

Ivan A. Matveev

Dorodnicyn Computing Centre of Russian Academy of Sciences

Vavilov str, 40, Moscow, 119333, Russia

Abstract. A method is proposed to detect a human iris location and size in digital

image given some point lying inside the pupil. Method is based on construction of

histogram projections of local brightness gradients and interrelating local maxima

of these histograms as probable positions of pupil and iris borders. Method has

low calculation cost.

1 Introduction

Recognition of human by iris is one of the most demanded biometric technologies.

Algorithm of iris size and position estimation is an essential part of iris registration

systems. At that the following characteristics of algorithm are important:

— reliability (understood as algorithm’s ability to detect iris in images where it

really presents and reject images without iris)

— precision (difference between real and detected iris coordinates is small)

— performance (processing of standard video stream 640 ∗ 480 ∗ 30 fps)

— robustness against noises (including parasite reﬂections and occlusions by eye-

lids and eyelashes)

— ability to process images obtained by various sensors and in various environment

conditions (one of such requirements here is an ability to detect irises differing in size

by several times).

Since outer borders for both pupil and iris can be approximated by circles with

good precision, circle detection is a central element of any system of iris detection in

image. There are plenty of methods of circle (or circumference) detection implemented

and tested for this task: detecting of mass center of an object selected by thresholding

function [1], detection of a point most remote from borders of such selected object [2],

maximizing of integro-differential circular symmetric operator [3], generalized [4], [5],

[14] and split [6] Hough transform, Hough transform using brightness gradient [7], [8],

brightness gradient projection method [9], paired gradient vectors [10], circular shortest

path construction [11], restoring centers of circles passing through randomly selected

points [12]. But none of these methods does conform to all of the above conditions.

Thresholding and image morphology methods are fast but fail if specular reﬂection is

present inside pupil. On the other hand, generalized Hough transforms and Daugman’s

A. Matveev I. (2010).

Detection of Iris in Image by Brightness Gradient Projections.

In Proceedings of the Third International Workshop on Image Mining Theory and Applications, pages 45-50

DOI: 10.5220/0002962100450050

 SciTePress

operator give stable results but are calculation intensive and inadequate for real-time ap-

plications. More elaborated later methods [10,11,12] give better robustness/time com-

promise.

However, so far the fact was not employed that iris border contains two circles

(pupil-iris and iris-sclera borders) with interrelated parameters. Synchronous detection

of two circles with parameters subject to certain mutual restrictions, implied by na-

ture of iris allows substantially enhance algorithm characteristics in comparison with

search of single circle. A proposed algorithm of iris location is based on construction

of histograms (local brightness gradient circular projections) and comparisons of their

maxima as possible positions of iris borders.

2 Construction of Circular Projections of Brightness Gradient

As in majority of recognition tasks the problem of iris location can be treated as a prob-

lem of selection of best positions of the two circles from a set of alternatives. These

alternativesare given by positions of maxima of circular projections of brightness gradi-

ent. These projections are constructed relative to an approximate iris center, as detected

in [9].

Input data for the algorithm are monochrome eye image and an approximate po-

sition of eye center. Irises with diameter not exceeding image size (i.e. minimum of

image width and image height) can be detected.

Denote: c = (c

)

be a point of approximate center position. Method [9]

guarantees its distance to real pupil center is not greater than half of pupil’s radius. For

simplicity consider this point as a coordinate origin. x = (x y)

is a point vector,

b(x) is a brightness (intensity) in this point, g(x) = ∇b(x) is a brightness gradient.

Gradient for discrete digital image is calculated using Sobel mask.

Only points with certain gradient value and direction can belong to iris border. This

set is described by indicator function:

(x) =







1, if kgk > T

and T

x · g

kxk kgk

and U,

0, otherwise,

(1)

where T

and T

are thresholds, U is an additional condition selecting a sector (quad-

rant) of the coordinate plane. T

is set to reject image noise (including quantization

noise) and is calculated as 6

√

2 max{σ, 2} , where σ is a dispersion caused by the

noise. T

is set to include only points where brightness gradient has approximately

same direction as the point vector: T

= arccos(π/6). Following conditions are used

for selecting of left, right, upper and lower quadrants respectively:

U =











L : |x| > |y|, x < 0,

R : |x| > |y|, x > 0,

B : |x| < |y|, x < 0,

T : |x| > |y|, x > 0.

(2)

Fig.1. Sample of circular projection and local maxima positions.

Taking one of above conditions, for instance, U ≡ R for v

(x) one can obtain

a histogram of number of points satisfying the conditions as a function of radius. For

example the following is a histogram of right quadrant normalized to radius:

(r) =

2πr

r−0.5<kxk<r+0.5

(x). (3)

The histogram may have several local maxima. Denote n-th local maxima value as

loc max

n,r

(r) and its position as arg loc max

n,r

(r).

Fig.1. represents eye image and its right quadrant histogram Π

(r). Eight local

maxima positions arg loc max

n,r

(r), n = 1 . . . 8 are outlined in the histogram. After

detecting local maxima positions for all four quadrants one can obtain distances to

hypothetic circle borders from central point in appropriate direction.

Combining these values one can obtain coordinates of centers q = (q

)

and

radii ρ of these circles:

n,m



arg loc max

n,r

(r) − arg loc max

m,r

(r)



, (4)

u,v



arg loc max

u,r

(r) − arg loc max

v,r

(r)



, (5)

n,m,u,v





arg loc max

n,r

(r) + arg loc max

m,r

(r)+

arg loc max

u,r

(r) + arg loc max

v,r

(r)





. (6)

Quality of circle obtained for four given positions of local maxima (n, m, u , v) (in

right, left, top and bottom projections respectively) may be estimated as sum of projec-

tion function values in these positions:

n,m,u,v

= loc max

n,r

(r) + loc max

m,r

(r) + loc max

u,r

(r) + loc max

n,r

(r). (7)

3 Selection of Interrelated Histogram Maxima

So, various hypothetic circles are constructed by a method of circular projections. The

circles can be hypothetic pupils (index P is used further) or irises (index I). Circles can

be deﬁned by their parameters, center position and radius: (q

, r

) (q

, r

). If two

circles are the borders of an iris the following limitations due to human iris nature [13]

are necessarily true:

1) r

(iris radius cannot exceed pupil radius more than six times);

2) r

(pupil radius cannot be bigger than 75% of iris radius);

3) d < r

, d = kq

− q

k iris center lies inside pupil circle;

4) 2(r

− r

− d) > r

− r

+ d, or after reduction d <

− r

(lengths of

segments between pupil and iris borders cut by a line passing through pupil and iris

centers do not differ by more than two times).

From all pairs of circles satisfying (1–4) the one is selected with maximum sum of

quality values.

Thus algorithm in whole consists of three steps:

1. Calculation of local gradients in image. Each of two gradient components require

six memory reads, ﬁve additions, one subtraction, three bit shifts and one memory write,

that is totally 24 integer operations per one image point.

2. Building circular projections (histograms) for four quadrants selecting local max-

ima in histograms. This requires evaluating indicator function (1) in each point. Check-

ing condition kgk > T

requires two memory reads for obtaining g

and g

, two mul-

tiplications, one addition and one comparison operations, totally six integer operations.

Most of image points do not have enough brightness gradient to pass this check and

are not involved in the following calculations. Checking condition T

x·g

kxk kgk

is split

to checking x · g > 0 and (x · g)

> T

to avoid square root calculation. First

of these conditions takes six integer operations and rejects half of points. Second takes

additional four multiplications and one comparison. Summing to projection histogram

is a single memory write operation. Totally, processing of each image point in this step

takes from 6 to 18 integer operations, and the major share of points is processed in 6

operations.

3. Enumeration of circle combinations searching most likely (with biggest quality)

pair. The computational cost of this step depends on the number of local maxima se-

lected rather than on source image size. Typical number of local maxima is around ten,

and there could be dosens of thousands of combinations from four maxima positions,

however most of them do not pass the limitations (1)-(4). Only less than hundred hy-

potheses are sensible and require quality calculation and comparison. Hence the amount

of calculations in this step is negligible compared to the previous ones.

Totally, from 30 to 42 integer operations per one image pixel are required, and

majority of pixels are treated with 30 operations. Image of the typical size of 640 ∗480

pixels is processed in 10 million operarions.

4 Experiments

The following databases from public domain were used for performing experimental

study:

— UBIRIS (http://www.di.ubi.pt/∼hugomcp/doc/ubiris.pdf),1207 im-

ages

— CASIA Iris Image Database (http://www.sinobiometrics.com),16213im-

ages

— Iris Challenge Evaluation (http://iris.nist.gov/ice/), 2954 images

Size of these images is 640 ∗ 480 pixels, iris radii vary from 50 to 200 pixels.

Testing method. Eye images were reviewed by human expert who indicated pupil

and iris borders in each of them. These data were then considered as true and were used

for method veriﬁcation. Then images were processed automatically. The approximate

eye center was detected by method [9] (this point rarely matches true pupil center or

true iris center, but is always close to them). With the help of method proposed here

pupil and iris were detected. Their parameters were compared with those indicated by

human operator. Table below gives numbers of rude errors (difference in any one of

center coordinates or radii exceeds 10 percents of iris radius) and moderate (difference

in any one of center coordinates or radii exceeds 5 percents of iris radius) errors. If

all parameter values differ from true one not more than by ﬁve pixels, detection is

considered correct.

Table 1. Results of algorithm for test databases.

Data base Image

count

Number of

moderate

errors in

pupil

detection

Number

of rude

errors in

pupil

detection

Number of

moderate

errors in

iris

detection

Number

of rude

errors in

iris

detection

UBIRIS 1201 296 3 31 1

CASIA 16213 2070 48 274 43

ICE 2954 116 17 18 5

Execution of the algorithm takes not more than 0.01 second in PC with P-IV 3GHz

CPU for an image of 640 ∗480 pixels. Main share of calculation time is taken by Sobel

gradient estimation.

Proposed method of iris location may be applied for preliminary determination of

pupil (with precision up to 5 pixels) and iris (with precision up to 10 pixels) positions

if a point lying inside pupil is known. Method is useful for real-time applications.

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