ZERNIKE MOMENT-BASED FEATURE EXTRACTION FOR FACIAL RECOGNITION OF IDENTICAL TWINS

International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol.3,No. 6,December 2013

ZERNIKE MOMENT-BASED FEATURE EXTRACTION
FOR FACIAL RECOGNITION OF IDENTICAL TWINS
Hoda Marouf1 and Karim Faez2
1

Department of Electrical,Computer and Biomedical Engineering, Qazvin branch,
IslamicAzad University, Qazvin, Iran
2
Department of Electrical Engineering, Amirkabir University of Technology, Tehran,
Iran

ABSTRACT
Face recognition is one of the most challenging problems in the domain of image processing and machine
vision. The face recognition system is critical when individuals have very similar biometric signature such
as identical twins. In this paper, new efficient facial-based identical twins recognition is proposed
according to geometric moment. The utilized geometric moment is Zernike Moment (ZM) as a feature
extractor inside the facial area of identical twins images. Also, the facial area in an image is detected using
AdaBoost approach. The proposed method is evaluated on two datasets, Twins Days Festival and Iranian
Twin Society which contain scaled and rotated facial images of identical twins in different illuminations.
The results prove the ability of proposed method to recognize a pair of identical twins. Also, results show
that the proposed method is robust to rotation, scaling and changing illumination.

KEYWORDS
Face Recognition,Identical Twins,Invariant Moment, Zernike Moment

1. INTRODUCTION
Human face is considered as a suitable property to identify people from his (her) image. Along
with this property, recognition of facial of identical twin is one of the most challenging problems
in pattern recognition applications because of the similarity between the pair of twin.
In the domain of facial identical twins recognition, previous works are listed as: in[12], Klare and
Jain introduced a face detection algorithm which includes three levels. In the first level, an overall
appearance of the face is constructed; in the second level, exact geometric and structural
embedment of face with differentiating between two similar faces are performed; and finally, the
third level consists of process of skin disorders such as wounds, and so on. Sun et al. [16] utilized
CognitecFaceVACS system to recognize identical twins from CASIA Multimodal Biometrics
Database and they obtained the true accept rate of approximately 90% at a false accept rate
greater than 10%. Park et al.[14] proposed an identical twins recognition algorithm that consists
of three steps: in first step, the proposed method consists of face images which are marked using
normal geometric methods; in the second step, the Euclidean distance between a pair of markers
are measured and compared; and the final step involves finding the strong similarity on the
marked regions. Srinivaset al. [15] studied on distinguishing of twins using marks on the face
image. Martin et al. [3] employed DNA approach to recognize identical twins.
DOI : 10.5121/ijcseit.2013.3601

1


In this paper, we study on a pair of facial images in order to determine whether the images belong
to the same person or to a pair of identical twin. For this purpose, we propose the geometric
moments to extract feature vector from facial images of twins to recognize identical twins.
This paper is organized as follow: feature extraction step of a face recognition system
isintroduced in Section 2. The proposed method is presented in Section 3. Experimentalresults are
described in Section 4 and the paper will be concluded in Section 5.

2. FEATURE EXTRACTION
Each face detection system contains four steps: pre-processing, face localization, feature
extraction and classification. Feature extraction refers to the extraction of useful information from
raw data so that they are suitable for the classification process. The feature extraction stage is
characterized by a series of input patterns. The major problem of feature extraction is that it
depends on application and feature extraction methods are not public.
Feature extraction methods can be divided into two majors: structural features and statistical
features [11][19]. The first group is based on local structure of image. In other words, the
structural features deals with local data. Facial change or change in environmental conditions is
the major problem for the structural features [7].
In the statistics-based feature extraction techniques, global data is employed to create a set of
feature vector elements in order to perform recognition. A mixture of irrelevant data, which are
usually part of a facial image, may result in an incorrect set of feature vector elements. Therefore,
data that are irrelevant to facial portion such as hair, shoulders, and background should be is
regarded in the feature extraction phase [10].The statistics-based feature extraction techniques are
Principle Component Analysis (PCA), Legender Moment (LM) [13] and Zernike Moments (ZM)
[20]. Legendre functions are Legendre differential equation. The main advantage is that Legendre
moments like Legendre basis functions are orthogonal. Legendre moments are independent of
each other and are free of data redundancy.In this study, we use ZM to recognize identical twins
that are presented in the next Section.

3. PROPOSED METHOD
The main goal of this paper is to distinguish the identical twins by face recognition. For this
purpose, AdaBoost[18] technique is used for face localization step and subimage creation. After
that the ZM technique is employed to extract the feature vector from the subimage of test image.
After that the feature vectors inside the subimages of all images in dataset are obtained using ZM
approach. Finally, comparison between the feature vector of test image and the feature vectors of
all images of dataset is done to select the closest image from dataset as the pair of test image. In
the next Section, the AdaBoost face detection, ZM and its task of feature vector creation are
described.

3.1. Face Detection Method
As the mentioned before, face detection step is the second step of this algorithm to recognize
identical twins. This step is based on the combing of successively more complex classiﬁers in a
cascade structure using AdaBoost[18]. Furthermore, the AdaBoost technique is used to select a
small number of Haar-like features [18].
2


After ﬁnding an object in an image as a face candidate, an ellipse is drowning around the main
location of face in an image[8]. For this purpose, an ellipse model is constructed using five
parameters: X0 and Y0 are the centers of the ellipse, θ is the orientation, αand β are the minor and
the major axes of the ellipse, respectively. Before the calculation of theseparameters, geometric
moments are required to describe. The geometric moments of orderp+q of a digitalimageare
defined as
=∑ ∑

( , )

(1)

wherep, q = 0, 1, 2, … and f(x, y) is the grey-scale value of the digital image at x and ylocation.
The translation invariant central moments are obtained by placing origin at thecenter of the
image:

where

=

and

=

=∑ ∑

( , )( −

) ( −

) (2)

yare the centers of the connected components. Thus, centerof gravity

of the connected components is used as the center of the ellipse. The orientationof the ellipse is
computed by determining the least moment of inertia [8].
= arctan(

)(3)

where
shows the central moment of the connected components as described in (2). The length
of the major and the minor axes of the best-fit ellipse can also be computed byevaluating the
moment of inertia. With the least and the greatest moments of inertia of anellipse defined as
= ∑ ∑ [( −

= ∑ ∑ [( −

) cos − ( −
) sin − ( −

) sin ] (4)

) cos ] (5)

Length of the major and the minor axes are calculated from [8] as
=

=

/

/

(6)

(7)

To determine how well the best-fit ellipse approximates the connected components, a distance
measure between the connected components and the best-fit ellipse is calculated as follows [8]
∅ =

∅ =

(8)
(9)

where the Pinside is the number of background points inside the ellipse, Poutside is the number of
points of the connected components that are outside the ellipse, and
is the sizeof the
3


connected components. After drawing of ellipse, a subimage is made according to theellipse and
finally, the ZM is used to extract features inside the subimage.

3.2. Zernike Moment (ZM)
ZM is geometric-based moment that is a two dimensional function of orthogonal polynomials on
the unit disk. The orthogonal moments of ZM are rotation and scale invariants which are suitable
for pattern recognition applications [5][6][8][17]. ZM contains several orthogonal sets of
complex-valued polynomials deﬁned as

where

Where

+

( , )=

( , ) exp

tan

≤ 1,n ≥ 0, |m|≤ n, and the radial polynomials {
( , )=∑

,| |,

(

| |)/

= (−1)

,| |,

|

!

|

(

!

)!

(

|

+

|

)

=

∑ ∑

} are deﬁned as

!

The ZM of order n and repetition m can be computed as

( , )

(10)

(11)

(12)

∗

( , )(13)

( , ) = ∗ ( , ).Center
It should be noted that the PZM is computed for positive mbecause
of the unit disk is located on the origin of coordinates and so ZM technique is independent of
scaling and rotation.In the next Section, ZM approach will be utilized to extract feature vector
elements.

3.3 Creating feature vector
After face localization and subimage creation, the ZM is computed for each subimage as face
features. The feature vector elements are defined according to ZM orders as
={

|

= , + 1, … , }

(14)

where j is interval [1,N−1] and so,
contains all the ZM from order j to N. Samples of feature
vector elements will be demonstrated in Table 1 for j = 3, 5 and 9, and N = 10. As Table1 shows,
increasing of j decreases the number of elements in each feature vector ( ).

4. EXPERIMENTAL RESULTS
The proposed method is evaluated on two datasets: Twins Days Festival [2] and Iranian Twin
Society [1] which contain 520 and 600 pairs of identical twins images, respectively. The used
datasets contain the scaled and rotated faces with different illuminations. Figure 1 shows the
subimages of some twin test images. The results of identical twins recognition using ZM is
compared with the results of LM [13]. Experiments have been carried out in three steps according
4


to order of moment. In the first step, order n is in interval [1,6], in the second step, order n is in
interval [6,8] and for third step, order n is in interval [9,10] (Table 2).
In this paper, N is set 10 (N=10) and j varies from 1 to 9. The misclassification rate of all
geometric moments (LM and ZM) is presented in Table 3. The misclassification rate reported in
the table are computed as
=

.

.

(15)

Table 3 shows misclassification rates of LM and ZM. Comparison between geometric moments
in Table 3 proves that higher order moments of the ZM have most information for face
recognition while low-order moments have no significant effect on the system error. According to
the table, LM achieves high misclassification rate on recognition of twins because the rotation of
face in an image has bad effect on the performance of LM. As Table 3 shows, the
misclassification rate of ZM is lower than the LM because ZM is rotation and scale invariant.
Table 1.Feature vector elements based on the ZM

FV

j value

j

K
4
5
6
7
8
9
10
6
7
8
9
10
9
10

4

6

9

feature elements ( ZM
M
0,2,4
1,3,5
0,2,4,6
1,3,5,7
0,2,4,6,8
1,3,5,7,9
0,2,4,6,8,10
0,2,4,6
1,3,5,7
0,2,4,6,8
1,3,5,7,9
0,2,4,6,8,10
1,3,5,7,9
0,2,4,6,8,10

km

)

Number of
feature element

30

24

11

Table 2. Feature vector elements produced by geometric moments in each experiment.

Cat.

1

2
3

LM feature elements
n=1, m=1
n=2, m=0,2
n=3, m=1,3
n=4, m=0,2,4
n=5, m=1,3,5
n=6, m=0,2,4,6
n=6, m=0,2,4,6
n=7, m=1,3,5,7
n=8, m=0,2,4,6,8
n=9, m=1,3,5,7,9
n=10, m=0,2,4,6,8,10

ZM feature elements
n=1, m=1
n=2, m=0,2
n=3, m=1,3
n=4, m=0,2,4
n=5, m=1,3,5
n=6, m=0,2,4,6
n=6, m=0,2,4,6
n=7, m=1,3,5,7
n=8, m=0,2,4,6,8
n=9, m=1,3,5,7,9
n=10, m=,0,2,4,6,8,10
5


Visual results of ZM on pair of identical twins are illustrated in Figure 2which refers to Twins
Days Festival [2] and Iranian Twin Society [1] datasets, respectively.
According to numerical and visual results, ZM is able to create informative feature vector inside
the subimages of pair of identical twins which is necessary for recognition of identical twins. The
results prove that ZM is scale and rotation invariant.
Table 3. Error rate of each geometric moment in different categories. The bold values means the best
values

LM
Cat.
n=1,2,…,
6
n=6,7,8
n=9,10

ZM

No. of
Feature
Elements

No. of
Misclassificati
on

Error rate

No. of
Feature
Elements

No. of
Misclassificati
on

Error
rate

15

20

10%

15

17

8.5%

13
11

18
12

9.1%
6.1%

13
11

13
8

6.5%
4%

Figure 1. Creating of subimage based on the ellipse formation.

Table 4 shows the second phase of testing where the two geometric moments are compared on
finding a pair of a person as the twin ink-nearest persons. In the other words for a test image, his
(her) pair is found in k-nearest persons. In Table 4, the above comparison is done in several ranks
(k), k=3, 5, 7 and 9. Also, visual results of ZM on the second phase of testing are demonstrated in
Figure 3.The results reported in Table 4 are the percentage of identical twins that the pair ofa
person cannot be found in k-nearest persons (16). According to the results of ZM in Table 4and
Figure 3, pair of input image as the identical twin is detected in 3-nearest persons with the
probability of 95.1% (100%-4.9%) while with LM, the obtained value is with the probability of
91.3% (100%-8.7%). For the other ranks, the ZM approach takes the best error rates. As a result
of Table 4, the detected person as the identical twin using the proposed feature extractor is in knearest persons with high probability.

5. CONCLUSIONS

=

.

.

(16)

This paper is focused on the improving of face recognition systems for distinguishing of a pair of
identical twins. The proposed method is based on the Zernike Moment (ZM) as a feature extractor
to recognize a pair of (identical or non-identical) twins. Also, the location of the face in an image
is detected using the AdaBoost method and then the ZM method is utilized to construct feature
vector elements. Experimental results on two datasets show that the proposed method is superior
6


to the other geometric moment such as Legendre Moment (LM) and also is robust to rotation and
scaling and changing illumination.

Figure 2. Samples of testing identical twins which were correctly classified by ZM. The first row refers to
the results of ZM on the Twins Days Festival dataset [2] and the second row is the results of ZM on the
Iranian Twin Society dataset [1].

Figure 3. Visual results of ZM on the second phase of testing with rank=3.
Table 4. Results of geometric moments on the second phase of testing with rank=3. Bold values refer to

the best scores.

7


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