Yanushkevich S.N., Wang P.S.P., Gavrilova M.L., Srihari S.N. (eds.) Image Pattern Recognition. Synthesis and Analysis in Biometrics

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April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

228 Synthesis and Analysis in Biometrics

suitable for criminal related applications since ridges, datum points

and minutiae points can be extracted and matched to the features in

latent prints. For civil and commercial applications that require real-

time identiﬁcation/veriﬁcation, low-resolution palmprints images are more

suitable than high-resolution images since low-resolution palmprints images

product small ﬁle size, which results in short computation time for

preprocessing and feature extraction and therefore, they are useful for real-

time applications.

The wavelet theory has become hot in the last few years. It has

important relative characters, such as sub-band coding, multi-resolution

analysis and ﬁlter banks. It has been widely used in signal and image

processing, and has better local performance in the time domain and the

frequency domain. We also ﬁnd that it has good quality for textural feature

extraction. Texture description using the wavelet transform provides sub-

bands (LL, HL, LH, HH), which have spatial and orientational selectivity

[

]

. The features of a palmprint image extracted by the wavelet transform

represent an approximation of the image energy distribution over diﬀerent

scales and orientations.

This chapter is organized as follows: the palmprint image collection

and preprocessing are described in Section 9.2. Section 9.3 presents a

brief introduction to wavelet-based palmprint feature extraction. Palmprint

matching and decision combination are given in Section 9.4. Experimental

results and some conclusions are given in Section 9.5 and Section 9.6,

respectively.

9.2. Palmprint Images Collection and Preprocessing

Palmprint images collection, especially online collection, is the fundamental

work for palmprint algorithm research and palmprint identiﬁcation system

development. During the passed several years, we have put great eﬀorts into

designing and implementing an online palmprint acquisition device. Such a

device must be able to online acquire a good quality palmprint image and

have good interface to users.

The architecture of the newest version of palmprint acquisition device

is shown in Fig. 9.2. There is a user interface for the input of a palm.

A set of optical components work together to obtain the data from the

palm. The analog signal is converted into digital signal by the video frame

grabber using an A/D converter, and the digitized signals are stored in the

system main memory

[

]

. Figure 9.3 shows some typical palmprint images

captured by our proposed device.

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

Palmprint Identiﬁcation by Fused Wavelet Characteristics 229

Fig. 9.2. The architecture of our palmprint capture device.

Fig. 9.3. Several typical palmprint images captured by our proposed device: (a) is the

images from the Right hand of two diﬀerent persons, and (b) is the corresponding Left

hand palmprints.

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

230 Synthesis and Analysis in Biometrics

When capturing a palmprint, the position, direction and stretching

degree may vary from time to time. As a result, even the palmprints

from the same palm could have a little rotation and translation.

Also the sizes of palms are diﬀerent from one another. It is necessary to

align all palmprints and normalize their sizes for further feature extraction

and matching

[

]

. In our palmprint acquisition device, a panel, which

can locate the palms by several pegs, is designed to constrain both the

rotation and translation of the palms. Then the preprocessing algorithm

can locate the coordination system of the palmprints quickly. Sub-images

with ﬁxed size (128×128) are extracted from the captured palmprint images

(384 ×284) based on the coordination system. So that diﬀerent palmprints

are converted into the same image size for further processing. The size and

location of the sub-image are determined through many observations. The

principle used to decide the size and location of the sub-image is simply

based on making sure that most palmprint features are retained within this

area, and that all palmprints contain that sub-image. The basic steps of

palmprint alignment are shown in Fig. 9.4, and described in detail as below.

Fig. 9.4. The major steps on palmprint preprocessing: H1andH2are boundary of the

holes between the two ﬁngers, where T 1andT 2 are the tangent point of H1andH2,

respectively.The central box is the sub-image of a palm.

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Palmprint Identiﬁcation by Fused Wavelet Characteristics 231

Step 1. Use a threshold to convert the original grayscale image

into a binary image, then using a low-pass filter to smooth

the binary image.

Step 2. Trace the boundary of the holes H1 and H2 between

those fingers.

Step 3. Compute the tangent of the holes H1 and H2. T 1 and

T 2 are the tangent points of H1 and H2, respectively.

Step 4. Align T 1 and T 2to determine the Y -axis of the

palmprint coordination system and making a line passing

through the midpoint of the two points (T 1 and T 2), which

is perpendicular to this Y-axis to determine the origin of

the system.

Step 5. Extract a sub-image of a fixed size based on the

coordinate system (see Fig. 9.4). The sub-image is located

at a certain area of the palmprint image for feature

extraction.

Some typical original palmprints and their corresponding sub palmprint

images are shown in Fig. 9.5.

9.3. Wavelet Based Feature Extraction

Feature extraction is to describe a palmprint in a concise feature set

other than the original image. How to deﬁne the feature is the key

point of palmprint identiﬁcation. A good feature must well distinguish

the palmprint from diﬀerent persons and at the same time, be similar to

each other from the same persons’ palmprints. The sub-images derived

from the palmprint preprocessing have a great deal of diﬀerent features,

such as principal lines, wrinkes, ridges, minutiae points, singular points

and texture, which constitute a set of multi-scale features. Then, it is

reasonable for us to take account of the multi-resoulution analysis based

method to represent the multi-scale features

[

]

. The wavelet transform

is implemented as ﬁlter banks, and is an eﬀective tool for multi-resolution

analysis. In this Chapter, we extend the use of the wavelet transform for

palmprint feature extraction and propose a 2-D wavelettransform scheme

for palmprint feature representation.

Generally, the one-dimensional (1-D) wavelet function and 1-D

wavelettransform can be deﬁned as follows:

If function ψ(x) ∈ L

(R), and ψ(ω) stands for the Fourier transform

of ψ(x), the square integrable functions ψ(ω) satisﬁes the admissibility

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

232 Synthesis and Analysis in Biometrics

Fig. 9.5. Some typical original palmprints and their corresponding sub palmprint

images.

condition



|ψ(ω)|

|ω|

dω ≺∞, (9.1)

we call ψ(ω) the mother wavelet. In the case of continuous wavelet

transform, the wavelet function can be expanded from the mother wavelet

by various translations and dilations. In other words, the transform makes

use of the functions

(x)=



|a|

x − a

,a,b∈ R, a =0. (9.2)

These functions are scaled so that their L

(R) norms are independent

of a. The continuous wavelet transform of a function f ∈ L

(R)isnow

deﬁned by

W (a, b)=f, ψ

 =



|a|



f(x)ψ

x − a

dx (9.3)

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Palmprint Identiﬁcation by Fused Wavelet Characteristics 233

Initially, wavelet transform just focused on the 1-D situation. However,

multidimensional wavelets are also available, especially the two dimensional

(2-D) wavelets. In the same way, the 2-D wavelet transform can be treated

as two 1-D wavelet transforms: one 1-D wavelet transforms along the row

direction and the other 1-D wavelet transforms along the column direction.

Thus, the 2-D wavelet transform can be computed in cascade by ﬁltering the

rows and columns of images with 1-D ﬁlters

[

]

. Figure 9.6 shows a one-

octave decomposition of an image into four components: low-pass rows,

low-pass columns (LL); low-pass rows, high-pass columns (LH); high-pass

rows, low-pass columns (HL); high-pass rows, high-pass columns (HH). The

coeﬃcients obtained by applying the 2-D wavelet transform on an image are

called the sub images of the wavelet transform

[

]

–

[

]

. Figure 9.7 shows

the original palmprint and its corresponding wavelet sub images after 4

octaves wavelet transform.

Fig. 9.6. Decomposition algorithm of 2-D wavelet transform.

As mentioned above, the 2-D wavelet decomposition of I octaves of a

sub palmprint image g(m, n) represents the image by 3I + 1 sub images



i=1···I



, (9.4)

where

is a low resolution of the original image;

are the wavelet sub images containing the image details at diﬀerent

scales (2

) and orientations (d)athighresolution;

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

234 Synthesis and Analysis in Biometrics

The wavelet decomposition coeﬃcient g

corresponds to the vertical

high frequencies, g

corresponds to the horizontal high frequencies, and g

corresponds to the high frequencies in both directions

[

]

Fig. 9.7. The sub-palmprint image, and the feature images obtained after 4 octaves

wavelet transform.

As features, four statistical features are extracted from each sub-band

at each octave by the wavelet transform. The four statistical features are

mean, energy, variance, and kurtosis. Their deﬁnitions are shown below:

Mean magnitude:

i,d

∗ n



j=1



k=1

(j, k)

, (9.5)

Energy:

i,d

∗ n



j=1



k=1

(j, k))

, (9.6)

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

Palmprint Identiﬁcation by Fused Wavelet Characteristics 235

Variance:

i,d

∗ n



j=1



k=1

(j, k) − M

i,d

)

, (9.7)

Kurtosis:

i,d

∗ n



j=1



k=1

(j, k) − M

i,d

)

i,d

(9.8)

where

d =0, 1, 2, 3 refers to four sub-bands;

=[f

i,1

i,2

i,3

i,4

](f refers to M,E, V ,orK, respectively) and is the

feature vector at the i

octave;

and n

denote the width and height of sub-bands at the i

octave in

pixels.

So we can get a set of features with length 4 ∗ i, for example, after the

4 octaves wavelet transform a feature vector of length 16 is created. In

order to get a longer feature set, a feasible way is to divide the original sub-

palmprint image into smaller blocks. We try to divide the sub-palmprint

into 16 blocks, and for each block four octaves wavelet transform is applied,

then a feature set of length 256 is obtained.

9.4. Palmprint Feature Matching and Decision Fusion

Palmprint feature matching is based on measuring the distance between

the corresponding feature vectors. In our work, the Euclidean distance is

used to cluster those features. Since four sets of texture feature vectors of

each sample have been extracted, four distance vectors can be acquired

by the Euclideandistance classiﬁer. In order to get better recognition

accuracy, a considerable scheme is to combine the multiple classiﬁers. The

multiple classiﬁer combination makes the decision of which class from a set

of candidate is to be the ﬁnal result in the most reliable sense. It can be

considered as a special classiﬁcation problem. In this chapter, ﬁve kinds

of combination methods are proposed, including the minimum distance

algorithm, the mean distance algorithm and the majority voting. Before

the decision fusion, it is essential to normalize all the distances for each

classiﬁer. The well-known formula is used here:

norm

d − d

min

max

− d

min

(9.9)

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

236 Synthesis and Analysis in Biometrics

where d is the distance vector from the candidate to the templates in the

database, the d

min

and d

max

are the minimum and maximum value of the

vector d, respectively.

Then, each output of all classiﬁers C

(i =1,...,m) is denoted as a

distance vector r

(i =1,...,m) associated with each class, where m denotes

the number of the classiﬁers. The discriminant function is deﬁned as:

S = f (R) R = {r

, (i =1,...,m)} (9.10)

Five forms of the discriminant function f(R) are proposed:

Sumrule : f(R)=sum(r

,...,r

);

Maxrule : f(R)=max(r

,...,r

);

Minrule : f(R)=min(r

,...,r

);

Medianrule : f(R)=med(r

,...,r

);

Majorityvoting : f(R)=maj(r

,...,r

In the case of Majority voting, each classiﬁer C

(i =1,...,m)is

associated with a single label. The majority voting method selects the

class that gets more votes than any other class. Each candidate has the

same vote and weight

[

]

–

[

]

9.5. Experimental Results

Palmprint images were collected in our laboratory from 191 people using

our self-designed capture device. Since the two palmprints (right-hand and

left-hand) of each person are diﬀerent, we captured both and treated them

as palmprints from diﬀerent people. Eight samples were captured for each

palm with diﬀerent rotation and translations. Thus, a palmprint database

of 382 classes was created, which includes a total of 3056 (=191×2×8)

images with size 384×284 pixels in 256 gray levels.

Identiﬁcation test is a one-against-many, N comparison process. In

this experiment, N is set to 382, which is the total number of diﬀerent

palms in our database. The palmprint database is divided into two sub

databases: registration and testing databases. The registration database

April 2, 2007 14:42 World Scientiﬁc Review Volume - 9in x 6in Main˙WorldSc˙IPR˙SAB

Palmprint Identiﬁcation by Fused Wavelet Characteristics 237

Table 9.1. The recognition rate of each classiﬁer.

Individual feature set Identiﬁcation rate (%)

Mean features (Eq. (5)) 95.75

Energy features (Eq. (6)) 95.81

Variance features (Eq. (7)) 95.35

Kurtosis features (Eq. (8)) 95.62

contains 1528 palmprint images. Four images per palm are used to calculate

the mean feature set for registration. The testing database includes the

remaining 1528 palmprint images. Each palmprint image in the testing

database is matched to all of the palmprint images in the registration

database. Therefore, each testing image generates one correct and 381

incorrect matchings. The minimum distances of correct matching and

incorrect matchings are regarded as the identiﬁcation distances of genuine

and impostor, respectively.

As to the wavelet bases, the Symmlet wavelet is used with 9 vanishing

moments. Based on these schemes, the imposter and genuine distributions

of diﬀerent statistical features are presented by means of Receiver Operating

Characteristic (ROC) curves (as Fig. 9.8), which are plotted by the genuine

acceptance rates against the false acceptance rates, and measure the overall

performance of the method. Generally, a biometric system operates at a

low false acceptance rate and therefore, we only plot the range of false

acceptance rate between 0 and 5%. In this range, the feature of mean and

the feature of kurtosis obtain similar performance. The feature of energy

is the best and the feature of variance is the worst for all operating points.

According to the ROC curves, the features of energy can operate at a point

with 94% genuine acceptance rate and 0.05% false acceptance rate and its

equal error rate is about 4.2%.

In the decision fusion experiment, ﬁve diﬀerent combination rules are

applied and their results are compared. Table 9.1 shows the results

of the classiﬁcation of individual classiﬁers while the results of diﬀerent

combination rules are shown in Table 9.2. From the outcome of our

experiments, we ﬁnd that a higher recognition accuracy can be obtained

when the proper combination strategy is used. Among the ﬁve diﬀerent

combination rules, the Median rule has the best results. The majority

voting rule is very close to the Median rule in the performance.

Compared with the approach in

[

]

, which used a set of feature points

along the prominent palm lines and the associated line orientation of

palmprint images to identify the individuals, and a matching rate about

95% was achieved. But only 30 palmprint samples from three persons were