Location of Pupil Contour by Hough Transform of Connectivity

Components

Ivan Matveev

1,3

, Nikolay Chinaev

and Vladimir Novik

Computing Centre of Russian Academy of Sciences, Vavilov str., 40, Moscow, 119333, Russia

Moscow Institute of Physics and Technology, Institutsky per., 9, Dolgoprudny, 141700, Russia

Iritech Inc., B.Tatarskaya str., 21, 115184, Russia

Keywords:

Iris Segmentation, Hough Transform.

Abstract:

A method for determining the pupil boundary in the image of eye is proposed. The method is based on image

binarization followed by a search of the pupil as one of the connectivity components. The pupil boundary is

determined as a part of boundary of the connectivity component. Hough transform is used for separating pupil

in the case of its merging in one connectivity component with other objects, as well as to verify the likelihood

of solution.

1 INTRODUCTION

Iris region segmentation in eye images is an interest-

ing and actual task for biometric identiﬁcation and

medical applications. An important sub-task is de-

tection of pupil boundaries that is in fact search for

rounded dark object. Circle detection is one of the

most popular problems in image processing ﬁeld.

Numerous different methods have been developed,

some of which are applicable in the particular case of

pupil border detection. One can outline morphology

methods (Bowyer et al., 2008), projections of bright-

ness and its gradient (Matveev, 2010; Mohammed

et al., 2010), optimal contour construction (Ritter and

Cooper, 2003). Big share of methods (Matveev, 2012;

Chen et al., 2012; Ma et al., 2002; Pan et al., 2011)

relies on Hough transform (Hough, 1959) ideology.

The essence of this transform is the following:

when searching for parametrically deﬁned object (cir-

cle, straight line, ellipse, etc.) the space of parameters

is considered, called accumulator. For instance, ar-

bitrary circle is given by an equation (x− x

)

+ (y−

)

= r

with three parameters (x

,r) = ~p. Conse-

quently three-dimensional accumulator is considered.

A counter function A(~p) is deﬁned in the accumula-

tor, initially zero in all its points. The pixels which

can be part of the searched ﬁgure are determined in

the processed image, call them candidates. For ex-

ample, when searching for circles pixels with high

brightness gradient can be assumed as belonging to

the circle border and marked as candidates, whereas

pixels with low gradient belong to circle border less

likely. A voting procedure is conducted: for each can-

didate a set of points in the accumulator is treated,

corresponding to all possible parameters of the ﬁg-

ures, which may include this candidate, the counter

value at these points is incremented. Then maximum

(or several local maxima) of the counter are deter-

mined, its position in the accumulator space deﬁnes

the parameters of the searched ﬁgure. The advantage

of Hough transform is its stability against partial oc-

clusion of the ﬁgure, for example, it can be used to

ﬁnd the circumference by one of its arcs. The draw-

back is a relatively high computational cost arising

from complex processing of candidates.

Morphology and brightness projection based ob-

ject detection methods often apply brightness thresh-

olding (or more elaborate techniques) as the ﬁrst step

to create binarized image, which is then processed.

This is done under assumption that pixels of object

region have uniform characteristics, which are dis-

tinct from those of background. Pixels with similar

characteristics usually form several blobs in image,

call them connectivity components. As a rule, pupil

is a darkest object in eye image that prompts to ap-

ply binarization by brightness level and then detect

roundish black connectivity component in black-and-

white binarized image. Since binarization and ex-

tracting connectivity components are computationally

simple procedures, the advantages of this method is

the execution speed. It should be noted that the bor-

ders of objects appearing in binarization consist of a

Matveev I., Chinaev N. and Novik V..

Location of Pupil Contour by Hough Transform of Connectivity Components.

DOI: 10.5220/0005456100140021

In Proceedings of the 5th International Workshop on Image Mining. Theory and Applications (IMTA-5-2015), pages 14-21

ISBN: 978-989-758-094-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

relatively small number of pixels. However, quite of-

ten binarization generates several connectivity com-

ponents, as the brightness of the eyebrows or eye-

lashes may be a little different from the brightness of

the pupil or even be lower. Also eyelashes and eyelids

may merge with the pupil to form one component of

inadequate form. Therefore, the disadvantage of this

class of methods is a signiﬁcant share of errors associ-

ated with the distortion of the shape of object, arising

from merging with stranger objects or removing parts

of genuine object.

The presented work attempts to combine the ad-

vantages of the method of binarization, which re-

trieves a small number of pixels of interest in the im-

age, and Hough transform, which extracts the shape

of a given type from very noisy data. On the binarized

image connectivity components are outlined, bound-

ary of each is subjected to Hough transform to ﬁnd

the rounded contours. This combination of methods

is not known to the authors from literature.

2 PROBLEM STATEMENT AND

SOLUTION METHOD

Image of eye with the surrounding parts of the face

(eyebrows, nose, cheeks part) is considered. Image

is grayscale, i.e. contains only one luminosity chan-

nel. Typically it is registered in IR range. It is neces-

sary to ﬁnd a circle, which is the best approximation

of the boundary between pupil and iris. The border

can be partially occluded by eyelashes, eyelids, re-

ﬂections. Pupil is dark but not necessarily darkest ob-

ject in image, see Fig.1. Deﬁne source raster image

Figure 1: Samples of eye images.

I(x,y) = I(~p), its size is W × H pixels. It is necessary

to ﬁnd coordinates and radius of circle, which approx-

imates pupil.

The workﬂow of method is presented in the block

diagram, see Fig.2. Now we describe it brieﬂy and in

the following subsections more details are given.

Several thresholds of binarization B

are calcu-

lated from image brightness histogram (block 1).

Connectivity components corresponding to the dark

areas are outlined by binarization (block 2). For each

component its boundary and inertia moments are de-

termined (block 3). Moments of the component are

used to calculate the likelihood that pupil belongs to

a this component, then components are sorted so as

to process ones with highest likelihood ﬁrst (block 4).

The boundary of each component is a cyclic sequence

of edges, see more details in section 2.7. It should be

noted that the number of border edges is substantially

smaller than their total number in the image or the

number of pixels with high brightness gradient, which

could be considered as parts of boundary. The pupil

not always has border with lighter iris only, but is of-

ten covered with eyelids and / or eyelashes that causes

distortions of two kinds: the boundary of the pupil

is visible partially; connectivity component of pupil

merges with eyelids or eyelashes (see. Fig. 1 (b)).

In this case only a small part of detected boundary

belongs to pupil, however it is necessary to deter-

mine visible part of the boundary. Hough transform

is performed (block 5), which includes construction

of beams in the accumulator starting from each pixel

of boundary perpendicular to it. As a result, if the

boundary contains circular arc, signiﬁcant local max-

ima arise in the accumulator at the center of hypo-

thetical circle containing these arc. Global maximum

of accumulator corresponds to the most likely posi-

tion of the circle. To determine the radius of the cir-

cle histogram of distances from the found center to

the boundary pixels is built (block 6). Maximum of

the histogram gives the radius. Following subsections

describe steps of the method in more detail.

2.1 Estimating Binarization Thresholds

As the pupil is dark image area, it can be outlined as a

connectivity component when the binarization thresh-

old value exceeds pupil brightness and is below iris

brightness. Boundary of this connectivity component

is a pupil border. As levels of brightness of pupil and

iris are unknown a-priory, and hence the threshold di-

viding them is also unknown, several passes (denoted

their count as K) of algorithm with different thresh-

olds are performed. The values of applied thresh-

olds are determined so that the number of pixels with

brightness below the threshold is a certain fraction of

the total pixel number. For this purpose brightness

histogram is used:

h(b) = |{~p : I(~p) 6 b}| . (1)

Pupil is a dark object, so histogram part correspond-

ing to the low brightness is analysed. Shares of pix-

els α

, determining the binarization thresholds, are set

LocationofPupilContourbyHoughTransformofConnectivityComponents

Figure 2: Block diagram of method functioning.

uniformly in range from 0 to 1/4 of total pixel count:

,k = 1,...,K . (2)

Binarization thresholds B

are calculated by his-

togram (1) and shares (2):

: h(B

) = α

WH . (3)

2.2 Binarization

Binarization with threshold B is performed to zero

brightnesses over the threshold and outline the pixel

with lower intensities so as to generate objects from

dark regions:

(~p) =



1, I(~p) 6 B ,

0, otherwise .

(4)

Samples of binarized images I

are given in Fig.3

Figure 3: Samples of binarized images. (a) — image ob-

tained from Fig.1a with share of pixels α

= 0.14; (b) —

image, obtained from Fig.1b with share of pixels α

= 0.08.

2.3 Determining Borders and Moments

of Connectivity Components

In the binarized image dark (the brightness is less than

the threshold) and light areas form several connec-

tivity components. Here 8-connectivity is used i.e.

dark pixels ~q are considered connected with pixel ~p,

(~p) = 1, if~q: I

(~q) = 1, |p

− q

| 6 1, |p

− q

| 6 1.

For each connectivity component C ordered list of

border edges L(C) =

and moments of zero or-

der M(C), ﬁrst order M

(C), M

are calculated:

M(C) = |C| ≡ |{~p : ~p ∈ C}| ,

∑

~p∈C

, M

∑

~p∈C

∑

~p∈C

, M

∑

~p∈C

∑

~p∈C

(5)

Moments (5) are determined by enumerating all pix-

els of the component by the ﬂoodﬁll method (Glass-

ner, 1990). List of border edges is determined by a

special algorithm described in the section 2.7.

2.4 Rejection and Sorting of

Connectivity Components

Components detected by binarization are subjected to

Hough transform. However, some of them can be

discarded before the processing merely by the statis-

tical characteristics as obviously not containing the

pupil, and the remaining can be sorted, so that the ﬁrst

processed components contain pupil with the highest

probability. To remove components, obviously not

containing the pupil parameters of equivalent ellipse

are considered. They are calculated as:

IMTA-52015-5thInternationalWorkshoponImageMining.TheoryandApplications

a =



+ 2pqM

+ q



1/2

b =



− 2pqM

+ p



1/2

p = cosϕ , q = sinϕ ,

ϕ =

arctan

−M

−





−





(6)

where a, b, ϕ are big and small half-axes and direction

of big half-axis respectively. Connectivity component

containing pupil should have a sufﬁciently large area,

and the ratio of the major and minor semi-axes must

lie within a certain range. Furthermore, if eyelashes

/ eyelids have same or smaller brightness than the

pupil, induced distortion of the connectivity compo-

nent extends it horizontallybut not vertically. Accord-

ingly, the objects with equivalent ellipse having large

eccentricity and major axis located closer to the verti-

cal should be discarded. These conditions are written

as:

ab > ρ

min

< T





> T



∩



ϕ ∈



;

3π



(7)

where ρ

min

is minimal possible radius of pupil in pix-

els. Optimal values of thresholds T

= 5, T

= 2.5 are

determined experimentally.

To sort residual components the following quality

criteria is calculated:

Θ(C) =

M(C) − l(C)

(C)

, (8)

where l(C) = |L(C)| is a length of connectivity com-

ponent border. This feature increases as the shape of

the region approximates to the circular, and also in-

creases with the size of the area. Thus, connectivity

components are sorted by descending characteristic

(8), which favours rounded components of signiﬁcant

size.

2.5 Hough Transform

Voting procedure is performed as follows: inner nor-

mals to each pixel

∈ L are constructed, a segment

of normal enclosed in range [ρ

min

;ρ

max

] is selected,

counter function in appropriate accumulator points is

increased.

A(~p) := A(~p) + v(~p,

v(~p,

) =







1, if ~p = r

η+

r ∈ [ρ

min

;ρ

max

];

0, otherwise .

(9)

Constructing normal vector

η is done as follows: clos-

est neighbours of pixel

in list L are selected, deﬁne

them as

, where negative index corresponds to mov-

ing backward in the list and positive is forward. Tan-

gent direction

τ is estimated from the neighbour pixel

coordinates:

τ =

−1

∑

j=−n

−



−



∑

j=1

−



−



, (10)

where n is a size of pixel neighbourhood and is

equal to ρ

min

/2. From two possible normal direc-

tions

= (η

,η

) = (−τ

,τ

) and

= (τ

,−τ

) in-

ner normal is selected according to direction of bor-

der enumeration. Segment for voting is constructed in

rastered accumulator by Bresenham algorithm (Bre-

senham, 1996). After the voting the accumulator is

smoothed by the low-pass ﬁlter and center of the hy-

pothetical circle is determined as the global maximum

in smoothed accumulator:

~c = argmax

(A(~p) ∗ G) , (11)

where G is a low-pass ﬁlter. Fig. 4 (a) depicts a results

of Hough transform for biggest connectivity compo-

nent of image Fig. 3 (b), which contains pupil. This

is the only component for processing, others were re-

jected at the previous stage.

2.6 Building Histogram of Distances to

Border Edges

A histogram h(r) of distances from center ~c and all

edges of the border L =

is constructed:

h(r) =



∈ L, r − 0.5 6 k~c−

k < r+ 0.5



(12)

Histogram has a speciﬁc properties in case when pupil

belongs to the component and its center is correctly

detected. For instance in Fig. 4 (b), a histogram

for component Fig. 3 (b) is given. One can see a

peak corresponding to the radius of pupil in image:

= argmax

h(r). The ﬁnal conclusion about pupil

presence is based on analysis of h(r). Mass of the

histogram is calculated in window of width w cen-

tered at r

, which is position of histogram maximum.

The resulting value is an estimate of the length of the

visible contour of the pupil, and is compared with r

Is is considered that pupil is detected if

∑

r=r

−w

h(r) > πr

, (13)

i.e. sufﬁcient condition for pupil detection is visibil-

ity of half of its border. the width w of the summing

LocationofPupilContourbyHoughTransformofConnectivityComponents

Figure 4: Processing of connectivity components. (a) —

result of voting by component ofimage 3 (b) with maximum

Θ value and satisfying conditions (7); (b) — histogram of

distances (12) from hypothetical center of circle to border

edges.

window depends on precision of center detection, it is

set here to w = 2 according to numerical tests.

So, the method includes the following steps:

S t e p 1. Building brightness histogram (1). Cal-

culating binarization thresholds B

according to (3).

For each k steps 2− 3 are carried out.

S t e p 2. Image binarization (4) with threshold B

S t e p 3. Determining moments (5) and borders of

each connectivity components, rejecting those unﬁt to

(7).

S t e p 4. Sorting of residual components accord-

ing quality criterion (8).

Following steps 5 − 6 are executed subsequently

for elements of sorted list, until an element satisfying

conditions is met (as a rule it is the ﬁrst one in the list)

of the list is exhausted.

S t e p 5. Hough transform (9) for borders, maxi-

mum (11) is detected.

S t e p 6. If maximum is sufﬁciently large, his-

togram (12) is built. If peak (13) exists in the his-

togram, it means that roundish segment of border ex-

ists with center close to detected accumulator maxima

and radius equal to coordinate of the peak. If no com-

ponent satisﬁes these conditions, it is declared that no

pupil is present in the image.

2.7 Algorithm of Border Edges

Enumeration

Here the algorithm of building list L of border edges

of connectivity component C is presented. It works

in binarized image and treats the object and its bor-

der under 8-connectivity assumption. The algorithm

is executed by a ﬁnite state automaton, which diagram

is given in Fig. 5. Binarized image (4) is scanned

as a raster until non-zero pixel ~p: I

(~p) = 1 is de-

tected. It means new connectivity component is en-

countered. The enumeration of border edges starts

followed by enumeration and zeroing of all object

pixels by a ﬂoodﬁll procedure (Glassner, 1990). Dur-

Figure 5: Automaton diagram for border pixel enumeration.

ing the ﬂoodﬁll procedure the object is cleaned from

the image. Enumeration of border edges is done se-

quentially, starting from ﬁrst detected one. At each

step of automaton work there is one currently pro-

cessed pixel

f, call it focus pixel. When ﬁrst pixel

of object is encountered during raster scanning it

has conﬁguration “A”.Finite automaton has four states

corresponding to four border orientations and direc-

tions of movements along the border. Border enu-

meration is done clockwise. Four states are: “A” —

left border, movement upwards; “B” — upper border,

movement rightward; “C” — right border, movement

downwards; “D” — low border, movement leftwards.

In each state there are four possible conﬁgurations of

neighbourhood, denoted by numbers from 0 to 3 and

three directions of subsequent movement: turn to the

right (executed in conﬁguration 0), continue moving

without changing direction (conﬁguration 1) and turn

to the left (conﬁgurations 2 and 3). Automaton state is

changed according to new direction in case of turns or

remains unchanged in case of direct movement. Fo-

cus pixel is changed for conﬁgurations 1, 2 and 3 or

remains the same for conﬁguration 0. Each new edge

is added to the list L. If new edge coincide to the ﬁrst

one in the list, it means that the enumeration of border

is completed and the automaton is stopped.

The sample of object is given in Figure 6. The ﬁrst

detected pixel of object is border pixel number “1”,

which is set as initial focus pixel and the ﬁrst enumer-

ated edge is “a”. The automaton is set to conﬁgura-

tion “A”. Neighbourhood conﬁguration is 0, thus the

automaton changes state to “B” (right turn) and pro-

IMTA-52015-5thInternationalWorkshoponImageMining.TheoryandApplications

Figure 6: Sample of object, its border pixels and edges.

ceeds to edge “b”, focus pixel remains unchanged at

this step. Proceeding further will ﬁnally enumerate

edges from “a” to “x” as shown in alphabetical order

and pixels in order 1,2,3,4,5, 6,7,8,9, 8, 10,11.

2.8 Estimation of Algorithmic

Complexity

Image size if W × H, W H, and the width of image W

can be considered as image linear size, thus number

of image pixels is proportional to W

Estimation of binarization thresholds includes

building and processing brightness histogram with

complexity max





, where L is a number of

brightness levels in image. Grayscale 8-bit images

are used hence L = 256 ≪ W

. Binarization and

connectivity component selection for one binarization

threshold have complexityW

. Number of connectiv-

ity components is limited byW

/ρ

min

, where ρ

min

is a

minimum expected pupil radius. Length of the border

can be evaluated as W. Total complexity of K passes

of binarization is KW

, as a result KW

/ρ

min

connec-

tivity components are extracted. Hough voting for one

pixel has complexity of W, and for whole border it is

. Maxima search in accumulator requiresW

oper-

ations. Thus, considering the above total complexity

of the method comprises kW

/ρ

min

With the increase of image resolution and its lin-

ear size W expected pupil size also grows linearly, so

one can state that ρ

min

W and the complexity of the

algorithm is in fact kW

. It grows linearly with re-

spect to image pixel number. Direct application of

Hough transform to locate circle yields complexity of

. The reduction of complexity in the proposed ap-

proach is producedby using preselected border pixels,

which number is proportionaltoW, instead of treating

all image pixels (or some share of them selected by

thresholding), which number is proportional to W

3 EXPERIMENTS

Four public domain iris image databases were used

for tests, deﬁned as:

• BATH (Monro et al., 2005);

• CASIA (Chinese Academy of Sciences Institute

of Automation, 2005);

• MMU (Multimedia University, 2006);

• NDIRIS (Phillips et al., 2010).

These images were marked by a human expert: in

each a circle approximating pupil border was set. De-

ﬁne center of such circle as (x

) and its radius r

Algorithm detected center (x, y) and radius r of pupil

circle in each image and these data were matched

against expert ones, the deviation of center was cal-

culated as Q

= |x

− x| + |y

− y| and the deviation

of radius as Q

= |r− r

|. Table 1 represents compar-

ison of the method with its analogues. Three methods

were used, which results are known from literature.

They are referenced in the table as

• column 1 (Masek, 2003);

• column 2 (Ma et al., 2004);

• column 3 (Daugman, 2007);

• column 4 - method presented here.

The following characteristics are given: average devi-

ation of pupil center Q

(average value of Q

for all

test set), average radius deviation Q

, both expressed

in pixels, and mean calculation time T, expressed in

milliseconds.

Table 1: Comparison with other methods.

DB Values

Methods

1 2 3 4

BATH Q

5.32 4.29 3.27 4.61

6.72 4.65 3.19 1.59

T 108.26 376.83 26.55 97.28

CASIA Q

3.67 4.79 1.19 2.82

5.15 5.39 3.02 3.26

T 97.52 363.64 29.17 93.95

MMU Q

4.98 3.92 1.14 3.11

5.78 4.67 3.76 0.99

T 99.78 317.18 25.47 25.22

NDIRIS Q

5.59 5.92 1.79 3.94

7.23 7.38 3.11 1.89

T 112.25 378.87 27.61 98.30

LocationofPupilContourbyHoughTransformofConnectivityComponents

Figure 7: Sample correct detection in case of occlusion and

virtually correct detection in case of side gaze.

Figure 7 gives examples of correct detection of

pupil. Most typical error is mistaking iris border for

pupil border, which can result in case of low con-

trast of iris-pupil border (see Figure 8a), and occlu-

sion of the pupil (see Figure 8b). Comparing Fig.8b

with Fig.7a one can note that the share of pupil border

visible in Fig.8b is bigger thn that of in Fig.7a, but de-

tection is wrong due to mistaking iris border, which is

visible in bigger part. The third biggest problem for

Figure 8: Sample incorrect detection in case of low contrast

of pupil-iris border and occlusion.

the algorithm is off-side gazing. When gazing causes

pupil to deform strongly, Hough voting for circle fails

to produce maxima in the contour center. Again, the

most frequent result is mistaking iris for pupil, see

Figure 9a. An interesting case is that of red eye ef-

fect, see Figure 9b.

Figure 9: Sample incorrect detection in case of low contrast

of pupil-iris border and occlusion.

4 CONCLUSIONS

Method of pupil contour detection in eye image is

proposed. Contour is built from pixels of boundary

of connectivity component obtained from a dark re-

gion in source image. To select correct (closest to the

circle) component (or part thereof) Hough transform

of boundary pixels is used, yielding the center of cir-

cular part of border. Radius of the circle is deﬁned as

the maximum of the histogram of distances of bound-

ary pixels to a dedicated center. Then pupil contour

pixels may be selected from the entire set of pixels

of the boundary as being close to that radius distance

to the center. Tests of the algorithm were performed

on sets of images of public domain databases. Using

the Hough transform one can correctly locate the true

center, radius and contour of the pupil, even in the

presence of high interference, provided only partially

visible contour of the pupil. The disadvantage of

this method is potentially great execution time, which

may occur when iterating through many connectivity

components and several binarization thresholds. This

drawback is partially mitigated by using quality mea-

sure of connectivity components.

ACKNOWLEDGEMENTS

The work was funded by RFBR grant No.14-01-

00348.

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LocationofPupilContourbyHoughTransformofConnectivityComponents