Fast Complex Gabor Wavelet Based Palmprint Authentication

Jyoti Malik, Ratna Dahiya & G Sainarayanan
International Journal of Image Processing (IJIP), Volume (5) : Issue (3) : 2011 283
Fast Complex Gabor Wavelet Based Palmprint Authentication
Jyoti Malik jyoti_reck@yahoo.com
Electrical Department
National Institute of Technology
Kurukshetra, 136119, India
Ratna Dahiya ratna_dahiya@yahoo.co.in
Electrical Department
National Institute of Technology
Kurukshetra, 136119, India
G Sainarayanan sai.jgk@gmail.com
Maples ESM Technologies
Chennai, India
Abstract
A biometric system is a pattern recognition system that recognizes a person on the basis of the
physiological or behavioral characteristics that the person possesses. There is increasing interest
of researchers in the development of fast and accurate personal recognition systems. In this
paper, Sliding window method is used to make the system fast by reducing the matching time.
The reduction in computation time indirectly reduces the overall comparison time that makes the
system fast. Here, 2-D Complex Gabor Wavelet method is used to extract features from
palmprint. The extracted features are stored in a feature vector and matched by hamming
distance similarity measurement using sliding window approach. Reduction of 74.12% and
90.32% in comparison time is achieved using Sliding window methods. The improvement in time
is indicated by experimental results that makes a system rapid.
Keywords: Palmprint Authentication, Complex Gabor Wavelet, Similarity Measurement, Sliding
Window Method.
1. INTRODUCTION
Biometric identification of a person by his/her physiological or behavioral characteristics, like face,
finger, palmprint, gait, signature, voice etc. has become increasingly popular in modern personal
identification and verification systems [1-3]. In this paper, palmprint biometric is selected for
personal authentication as it is unique and relatively low resolution images (less than 100 dpi) are
sufficient to extract its unique features [4][5].
Palmprint features include line features, geometry features, point features, texture features and
statistical features. In this paper, line features are extracted using Complex Gabor Wavelet
Transform method. A complex Gabor wavelet is defined as the product of a Gaussian kernel
times a complex sinusoid. The line features extracted by complex gabor wavelet [6-15] at various
values of theta is stored in the feature vector. The feature vector is matched by Hamming
Distance similarity measurement using sliding window method.
In this paper, the palmprint authentication system is divided in following two subsystems:
a) Pre- Authentication System
b) Authentication System
In Pre-authentication system, a database of Gabor-Palmprint features is prepared.
Reference threshold values are also identified and stored in database. These values will
be later used by Authentication system.

In Authentication system, the authenticity of a person being genuine or imposter
is identified with the help of Reference threshold values stored in Pre-authentication
system database.
FIGURE 1: Palmprint Pre-Authentication system
FIGURE 2: Palmprint Authentication System
In Palmprint-based personal recognition system matching time plays very important role in
making the real time authentication system. In this paper, we have proposed fast palmprint
authentication system. The reduction in matching time is done using Sliding window methods and
explained later in section 4.
In the following sections, Section 2 defines palmprint feature extraction by our proposed Complex
gabor wavelet method. Section 3 explains the feature matching method by hamming distance
using sliding window method. Section 4 explains Sliding window method (SWM), SWM1, SWM2
and Section 5 defines the reference threshold calculation. Section 6 discusses the experimental
setup with the results. Section 7 concludes the conclusion.
2. FEATURE EXTRACTION
The desired line features are extracted from the palmprint using Complex Gabor wavelet method
which extracts line features from the input palm-print image. The Gabor wavelet is basically a
Gaussian (with variances sx and sy along x and y -axes respectively) modulated by a complex
sinusoid (with centre frequenciesU and V along x and y -axes respectively) described by the
following equation:
( ) ( )fyxM
sy
y
sx
x
sysxpi
yxG ii ,,*
2
1
exp*
***2
1
,
22






























+




−
= (1)
2,1=i
Image
Acquisition
Image Pre-
processing
Gabor
Wavelet
Reference
Threshold
Comparison
Genuine/
Imposter
Hamming
Distance
Image
Acquisition
Image Pre-
processing
Complex
Gabor
Wavelet
Hamming
Distance
Similarity
Database
Reference
Threshold
Reference
Threshold
Gabor-
Palmprint
Features

Complex
Gabor
wavelet
( ) ( )[ ]22
1 ***2cos,, yxfpifyxM +=
( ) ( )[ ]θθ sin*cos****2cos,,2 yxfpifyxM +=
Where sx and sy are the variances along x and y -axes respectively, f is the frequency of the
sinusoidal function, θ is the orientation of Gabor wavelet, 1G and 2G are the output Gabor
wavelets. The sample of Gabor wavelet convolution with the palmprint image is shown in Fig. 3.
FIGURE 3: Feature extraction by Complex Gabor Wavelet
The feature vector contains features extracted by Complex Gabor wavelet at different orientations
i.e. 0°, 30°, 60°, 90°, 120°, 150° and 180° as shown by figure 4.
0° 30° 60° 90°
120° 150° 180°
FIGURE 4: Complex Gabor wavelet features images
The feature vector contains 7 elements at corresponding to each orientation. The Feature vector
matrix is given by (2)
[ ]6543210 ,,,,,, CGWFCGWFCGWFCGWFCGWFCGWFCGWFCGWF = (2)
3. FEATURE MATCHING BY HAMMING DISTANCE AND SLIDING WINDOW
METHOD
The complex gabor wavelet line feature vectors (line information) are matched by Hamming
distance similarity measurement method but firstly the line information (complex gabor wavelet
features) extracted is binarized by the following equation (3):
( )
( )
( )


≤
>
=
0,,0
0,,1
,
jiCGWF
jiCGWF
jiCGWF
n
n
n (3)
where, ( )jiCGWFn , = complex gabor wavelet features corresponding to nth
orientation,
6,....2,1,0=n , i and j are the rows and columns of the complex gabor wavelet features.
Hamming Distance calculates the difference between two binary feature vectors using
EX-OR operation and can be defined as in (4):
( ) ( )( )∑∑ ⊕=
60 60
,,
i j
DBn jiFVjiFVHD (4)
where, HDn denotes the Hamming distance at orientation n, 6,....2,1,0=n , i and j is the row and
column of the complex gabor wavelet feature vector, ⊕ is the exclusive OR operation, FV denotes
the feature vector of the person to be matched, FVDB denotes the feature vector in database.
Here, FV is same as CGWF.

The hamming distance value is calculated by using sliding window method. In sliding window
method, the ROI is reduced by the window size (WS) and the window of ((60–WS)×(60–WS))
slides over the rows and columns out of 60×60 pixels considered for Hamming distance
matching. The minimum value of the hamming distance values is considered. Fig. 5 shows the
sliding window approach.
Column
Row 1….…………...56 57 ……..60
1
:
:
:
56
:
:
:
60
FIGURE 5: Sliding Window Approach with window size 4 and palmprint size 60×60
The modified Hamming distance value at n orientation with window size WS is defined in
(5) as:
( ) ( )( )∑ ∑
− −
⊕=
WS
i
WS
j
DBWSn jiFVjiFVHD
60 60
,, (5)
where, HDWSn denotes the Hamming distance with window size WS and at an orientation n,
6,....2,1,0=n , i and j is the row and column of the Complex gabor wavelet feature vector, ⊕ is
the exclusive OR operation, FV denotes the feature vector of the person to be matched, FVDB
denotes the feature vector in database. The minimum value out of 16 (For window size WS=4,
4×4 = 16) values of Hamming distances is chosen as Hamming distance as calculated in (6).
( )nnnnn HDHDHDHDHD _16_3_2_1 ,.........,,min= (6)
The various steps in sliding window method are shown in figure 6.
(a) Step 1 (b) Step 2

(c) Step 3 (d) Step 4
……….
(e) Step 5 (f) Step 16
FIGURE 6: Various steps in sliding window method
The average of all Hamming distances for n orientations is calculated as shown in (7).
6,....2,1,0=








=
∑
n
n
n
HD
AHD (7)
where, HDn denotes the hamming distance for n
th
orientation, AHD denotes the average value of
hamming distance. The average value will help in finding the reference threshold value.
If, the Hamming distance value of two feature vectors is less than reference threshold
value, feature vectors are considered to be from same hands otherwise different hands.
4. COMPARISON TIME IMPROVEMENT USING FAST SLIDING WINDOW
METHOD
The sliding window method is the basic approach of feature matching and an accurate method
but slow because of window size. The window size is chosen in such a manner to avoid
alignment problem in the palmprint images. Here, two sliding window approaches are proposed.
Sliding window method 1 and Sliding window method 2 is about using palmprint segment in such
a manner so that the matching operation time is reduced. In this paper, complexity of the
algorithm of SWM is reduced in SWM1 and SWM2.
4.1 Sliding Window Method
SWM is the basic technique used for matching two feature vectors. In feature matching, full
image is matched with the image stored in the database. If the image is not aligned properly then
the concept of window size comes into picture. According to (5), the number of calculations
increases by a factor of ( )2
WindowSize . The complexity calculation algorithm of SWM is
explained below.
( ) 1
2
TOWSNMSWMComplexity ××××= (8)

where, ( ) ( )WSWSofRowsNoM −=−= 60. , ( ) ( )WSWSofColumnsNoN −=−= 60.
41toWindowSiseWS == , 7. == ionsofOrientatNoO , ORTimeEXT −=1
According to (5), if WS = 4 and time taken for each EX-OR operation is T1 as shown in (9), then
total time taken for hamming distance calculation is given by:
( ) ( )( ) 1,, TjiFVjiFV DB =⊕ time (9)
Complexity or total sliding window time (TSWM) taken for 6 orientations will be given by (10):
( ) ( ) ( ) 111 3512327165656744460460 TTTTSWM =××××=××××−×−= (10)
where, TSWM specifies time taken to compare feature vectors of two palmprints.
If we consider 100 palmprints the total matching time will be given by:
( )( )11 35123200100351232 TT =×
It is observed that the number of operations is large in number in sliding window method
and will take lot of time. Comparison time need to be reduced by improving sliding window
method.
4.2 Sliding Window Method 1 (SWM1)
In this method, a part of the actual palmprint area is considered and it is named as palmprint
segment. The chosen palmprint area can be any of the palmprint segment mentioned in the Fig.
7.
FIGURE 7: The segmented palmprint.
The complexity calculation algorithm of SWM1 is explained below.
( )( ) OTNMTWSNMSWMComplexity ×××+×××= 11
2
11 (11)
where, ( )WSWSWS
ofRowsNo
M −=





−=





−= 15
4
60
4
.
1 ,
( ) ( )WSWSofRowsNoM −=−= 60. , ( ) ( )WSWSofColumnsNoN −=−= 60.
In (6) minimum hamming distance value using sliding window method is calculated. In
SWM1 method, hamming distance value for o orientations is found out using sliding window
method as shown in (5). The (6) signifies minimum hamming distance in sliding window as the
closest matching between two palmprints.
( )( )WSWS HDindexHDindex min_min_ = (12)
Total time for 6 orientations and window size 4 will be given by (11):
( )( )( )1111 9094475656165611 TTTTSWM =××+×××= .
If we consider 100 palmprints the total matching time will be ( )( )11 909440010090944 TT =× .
The reduction in matching time is given by (13).
( ) %11.74100
351232
90944351232
1
11
=×
−
T
TT
(13)
Palmprint Segment 1
Palmprint Segment 2
Palmprint Segment 3
Palmprint Segment 4

There is 74.11% reduction in matching time using SWM1 than SWM. The reduced matching time
signifies fast authentication system.
The sliding window method on the chosen palmprint area can be shown diagrammatically
as in Fig. 8.
(a) Step 1 (b) Step 2
(c) Step 3 (d) Step 4
................
(e) Step 5 (f) Step 16
FIGURE 8: Various steps in improved Sliding window method
As we can see from the above diagrams that the area of palmprint segment in sliding window
method has reduced considerably and it leads to reduction in matching time.
4.3 Sliding Window Method 2 (SWM2)
In this method, the minimum hamming distance value is not calculated for all the orientations
using sliding window method. The index of minimum hamming distance value is calculated for
one orientation and same index value will be used to calculate hamming distance for other
orientations. The complexity calculation algorithm of SWM2 is explained below.
( )( ) ( ) ( )( )( )1
2
1 12 TONMNMWSNMSWMComplexity ×−××+××××= (14)

where, ( )WSWSWS
ofRowsNo
M −=





−=





−= 15
4
60
4
.
1 ,
( ) ( )WSWSofRowsNoM −=−= 60. , ( ) ( )WSWSofColumnsNoN −=−= 60.
The total time taken given by (14) for window size 4,
( ) ( ) ( )( ) 11112 31808656565656561116 TTTTTSWM =××+××+×××= . If we consider 100
palmprints the total matching time will be( )11 318080010031808 TT =× .
( ) %94.90100
351232
31808351232
1
11
=×
−
T
TT
(15)
There is 90.94% reduction in matching time using SWM2 than SWM. The reduced matching time
signifies fast authentication system.
All the sliding window methods are summarized in table 1.
Method used Number of operations
1. SWM: Hamming distance calculation with
sliding window method with window size WS.
( ) ( )( )∑ ∑
− −
⊕=
WS
i
WS
j
DBWS jiFVjiFVHD
60 60
,,
3512327165656 =×××321 Operations
The )5656( × implies the number of comparisons of the
palmprint with the palmprint in the database.
)165656( ×× signifies sliding window method
comparisons for window size 4, so
16)44( =× comparisons. The total number of
comparisons takes place for seven orientations is
351232.
2. SWM1: Hamming distance calculation with
sliding window method (15×60) with window size
4.
( ) ( )( )∑ ∑
− −
⊕=
WS
i
WS
j
DB jiFVjiFVHD
15 60
,,
The palmprint segment size is )6015( × .
909447)5656165611( =××+×× 321321 Operations
The )5611( × implies the number of comparisons of the
palmprint segment with the palmprint segment in the
database. )165611( ×× signifies to sliding window
method comparisons for window size 4, so
16)44( =× comparisons. )5656( × signifies the
comparison of palmprint at the minimum index value. The
sum of )165611( ×× and )5656( × give the number of
comparison for each orientation. The total number of
comparisons takes place for seven orientations is
90944 Operations.
Assumption: If time taken to do each matching
operation is T1.
Theoretical time improvement
( ) %11.74100
351232
90944351232
1
11
=×
−
T
TT
3. SWM2: Hamming distance calculation with
sliding window method )6015( × with window size
WS.
( ) ( )( )∑ ∑
− −
⊕=
WS
i
WS
j
DB jiFVjiFVHD
15 60
,,
318086)5665()5656165611( =××+×+×× 321321321
Operations
The assumption here is that the minimum hamming
distance values for other orientations will also be at the
same index as it is for one orientation.
)165611( ×× applies to sliding window method
comparisons for window size 4, so

)1644( =× comparisons. )5656( × signifies the
comparison of palmprint and finding the minimum index
value. The sum of )165611( ×× and )5656( × give the
number of operations for one orientation. The number of
comparisons for another 6 orientation is at the minimum
index value as assumed for this method. So, additional
6)5656( ×× comparisons will be added. The total
number of comparisons is31808.
Assumption: If time taken to do each matching
operation is T1.
Theoretical time improvement
( ) %94.90100
351232
31808351232
1
11
=×
−
T
TT
TABLE 1: Reduction in matching operations using various Sliding window method
The number of operations, matching operation time with respect to sliding window size is
tabulated in table 2.
Sliding
Window
Size
Number of
Operations
Matching operation
Time
Percentage reduction
in Matching time
SWM SWM
1
SWM2 SWM SWM1 SWM2 SWM SWM1 SWM2
1 24367 24367 24367 4.48E-03 4.45E-03 4.43E-03 NA 0.67 1.12
2 94192 44660 26564 1.75E-02 8.34E-03 4.98E-03 NA 52.34 71.54
3 204687 65835 28899 3.89E-02 1.23E-02 5.53E-03 NA 68.38 85.78
4 351232 90944 31808 6.53E-02 1.69E-02 6.32E-03 NA 74.12 90.32
TABLE 2: Percentage reduction in matching operation time
From table 2 it is concluded that there is maximum of 74.12% and 90.32% practical reduction in
matching operation time. So it can be concluded from table 1 and table 2 results that with two
different sliding window methods, the authentication system becomes very fast. Figure 9 shows
that with SWM1 and SWM2 the comparison time reduces significantly.

FIGURE 9: Matching time Vs Sliding Window size
5. REFERENCE THRESHOLD
The hand image samples are divided into two groups G1 and G2.
G1 group
( )[ ]1211 ,......, −= MIIIP , ( )[ ]1212 ,......, −= MIIIP ,…….. ( )[ ]121 ,......, −= MN IIIP (16)
G2 group
[ ]MIP =1 , [ ]MIP =2 ,……………. [ ]MN IP = (17)
where Pi denotes i
th
person in group G1, G2, Ij denotes the j
th
palm image in group G1,
G2.
i
j
1 2 3 M-1
1 X HD12 HD13 ……… HD1(M-1)
2 HD21 X HD23 ………. HD2(M-1)
: : : : : :
: : : : : :
M-1 HD(M-1)1 HD(M-1)2 HD(M-1)3 X
TABLE 3: Matching in group G1 among person P1
In group G1, each hand feature vector in P1 is matched with all other (m-1) hands feature vector
by Hamming Distance similarity measurement method. The matching values are approaching “0”
and are stored in threshold array.
( ) ( ) ( )( )






=
−−−−
−−
212111
122321111312
1
,..,...........
,......,...,,,..,
MMMM
MM
HDHDHD
HDHDHDHDHDHD
TA (18)
Similarly, all N hand image samples matching results are stored in Threshold array (TA).
NA TATATAT +++= ........21 (19)
The minimum and maximum of matching values are found out from the threshold array (TA1,
TA2,……..TAN) for each individual as shown in equation (20).

( )
( ) NiAiAiMAX
AiAiMIN
TT
TT
,....1
max
min
=


=
=
(20)
The accuracy of the system is identified by matching group G2 samples with group G1 samples
using threshold values stored in threshold array. Finally, a threshold value is chosen where FAR
and FRR is minimum, this value is called Reference threshold.
6. EXPERIMENTAL RESULTS
The effectiveness of the proposed Complex Gabor Wavelet method for feature extraction
technique was assessed on the PolyU database [16]. The database consists of 600 palmprint
images from 100 palms with 6 samples for each palm.
6.1 Palmprint Authentication System
For the verification experiments the database has to be partitioned into two non-overlapping
groups. The first group (G1) represents the training group, consisting of 100 persons with each
person having 5 palm sample images whereas the second group (G2) represents the testing
group containing 100 persons with each person having one palm image different from the first
group images. The image size is 284×384 pixels.
G1 group
[ ]543211 ,,,, IIIIIP = , [ ]543212 ,,,, IIIIIP = ,….. [ ]54321100 ,,,, IIIIIP =
In G1 group each hand Pi contains 5 sample image I1-5.
G2 group
[ ]61 IP = , [ ]62 IP = ……………. [ ]6100 IP =
In G2 group each hand Pi contains only sample image I6.
Image is pre-processed to get the region of interest. Pre-processing includes image
enhancement, image binarization, boundary extraction, cropping of palmprint/ROI. The ROI size
is 60×60 pixels. Feature extraction is done by Complex Gabor Wavelet Transform to get the
imaginary wavelet coefficients. The Complex Gabor coefficients are calculated at seven different
orientations respectively. The feature vector contains features extracted by Complex Gabor
wavelet at different orientations. Feature vector of all hand images samples is calculated and
stored in database. Feature vector matrix
is [ ]6543210 ,,,,,, CGWFCGWFCGWFCGWFCGWFCGWFCGWFCGWF = . Sample of ROI
is shown in Fig.10.
Palm Image Palmprint
FIGURE 10: Sample of ROI.
Hamming distance is used as a similarity measurement method for feature matching.
6.2 Reference Threshold Calculation
In group G1, each hand feature vector in P1 is matched with all other 4 hands feature vector by
Hamming Distance similarity measurement method. Similarly, all 100 hand image samples 2000
matching values are stored in Threshold array (TA).
Image Pre-
Processing

10021 ........ TATATATA +++=
( )
( ) 100,....1
max
min
=


=
=
iAiAiMAX
AiAiMIN
TT
TT
The maximum and minimum values are found out from threshold array.
These 25 threshold values are tested with group G2 and group G1 images. The 25
threshold values, the respective FAR and FRR values and accuracy at frequency sixteen and
theta zero are shown in table 4.
Reference
Threshold
FAR FRR Accuracy
5.46E-01 1.23E-01 6.69E-03 9.35E+01
5.52E-01 1.27E-01 4.91E-03 9.34E+01
5.58E-01 1.16E-01 2.67E-03 9.40E+01
5.65E-01 9.25E-02 1.33E-03 9.53E+01
5.71E-01 6.95E-02 6.94E-03 9.62E+01
5.77E-01 4.92E-02 3.74E-04 9.75E+01
5.84E-01 3.59E-02 2.75E-04 9.82E+01
5.90E-01 2.71E-02 3.13E-04 9.86E+01
5.96E-01 2.16E-02 1.85E-04 9.89E+01
TABLE 4: Threshold Values, FAR, FRR, Accuracy Values for SWM.
Method FAR FRR Accuracy
SWM 6.95E-02 6.94E-03 9.62E+01
SWM1 6.94E-02 7.13E-03 9.62E+01
SWM2 7.07E-02 6.93E-03 9.61E+01
TABLE 5: FAR, FRR, Accuracy values for sliding window size 2
From the table 5 it can be concluded that by using SWM1 and SWM2 techniques the accuracy of
the system is not affected.
The FAR and FRR are values are plotted with respect to 25 threshold range values. From the
graph the value of reference threshold is chosen where FAR and FRR are minimum. Plot of FAR
and FRR is shown in figure 11. The plot between accuracy and threshold is shown in figure 11.

FIGURE 11: FAR Vs FRR
Accuracy values with respect to threshold values are plotted in Fig. 12.
FIGURE 12: Accuracy Vs Threshold
6.3 Speed Performance
Table 1 shows the reduction in comparison time by sliding window method 1 (SWM1) and sliding
window method 2 (SWM2). It can be observed that with palmprint segments, the comparison time
reduces and speed to verify the person is improved.

7. CONCLUSION
The Complex Gabor Wavelet transform is applied to each palmprint image in the database to get
imaginary wavelet coefficients. The features are computed at different orientations. The feature
vector generated from complex gabor features are matched by hamming distance using sliding
window method. Modified sliding window methods SWM1 and SWM2 are also used to make the
matching system fast. Experimental results clearly show that our proposed Complex Gabor
Wavelet method can discriminate palmprints and is fast authentication system.
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[16] The PolyU Palmprint Database: http://www4.comp. polyu.edu.hk/biometrics/

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