Effect of Fuzzy and Crisp Clustering Algorithms to Design Code Book

for Vector Quantization in Applications

Yukinori Suzuki, Hiromu Sakakita and Junji Maeda

Department of Information and Electronic Engineering, Muroran Institute of Technology,

27-1 Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan

Keywords:

Fuzzy and Crisp Clustering Algorithms, Vector Quantization, Code Book Design.

Abstract:

Image coding technologies are widely studies not only to economize storage device but also to use commu-

nication channel effectively. In various image coding technologies, we have been studied vector quantiza-

tion. Vector quantization technology does not cause deterioration image quality in a high compression region

and also has a negligible computational cost for image decoding. It is therefore useful technology for com-

munication terminals with small payloads and small computational costs. Furthermore, it is also useful for

biomedical signal processing: medical imaging and medical ultrasound image compression. Encoded and/or

decoded image quality depends on a code book that is constructed in advance. In vector quantization, a code

book determines the performance. Various clustering algorithms were proposed to design a code book. In this

paper, we examined effect of typical clustering (crisp clustering and fuzzy clustering) algorithms in terms of

applications of vector quantization. Two sets of experiments were carried out for examination. In the ﬁrst set

of experiments, the learning image to construct a code book was the same as the test image. In practical vector

quantization, learning images are different from test images. Therefore, learning images that were different

from test images were used in the second set of experiments. The ﬁrst set of experiments showed that selection

of a clustering algorithm is important for vector quantization. However, the second set of experiments showed

that there is no notable difference in performance of the clustering algorithms. For practical applications of

vector quantization, the choice of clustering algorithms to design a code book is not important.

1 INTRODUCTION

Transmission bandwidths of the Internet have in-

creased remarkably, and images, videos, voices, mu-

sics and texts can now be transmitted instantly to

every corner of the world. Immeasurable quantities

of data are being transmitted around the world. Al-

though new technologies have provided larger trans-

mission bandwidths, the demand for transmission ca-

pacity continues to outstrip the capacity implemented

with current technologies. The demand for communi-

cation capacity shows no sign of slowing down. Data

compression technology is therefore important for ef-

fective use of communication channels. Since image

and video data transmitted through the Internet oc-

cupy a large communication bandwidth, various cod-

ing methods have been proposed. There are two cat-

egories of coding methods: lossless coding and lossy

coding. In lossless coding, the original image and

video can be recovered from the compressed image

and video completely. Huffman coding is the most

widely used type of lossless coding. In lossy coding,

on the other hand, the original image and video cannot

be recovered from the compressed image and video.

In lossy coding, JPEG (Joint Photographic Experts

Group) is used as a defect standard for still image

coding and MPEG (Moving Picture Experts Group) is

used as a defect standard for video coding. The com-

pression ratio of lossless coding is much smaller than

that of lossy compression (Sayood, 2000; Gonzalez,

2008).

We have been studying vector quantization for im-

age coding (Miyamoto, 2005; Sasazaki, 2008; Mat-

sumoto, 2010; Sakakita, 2014). For vector quanti-

zation, we have to design a code book in advance.

It needs much computational cost to design a code

book. However, once we obtained the code book, en-

coding an image is to look for the nearest code vec-

tor in the code book. For decoding, it is only sim-

ple table look-up of the code vectors from the code

book and therefore computational cost is negligible.

Fujibayashi and Amerijckx showed that PSNR (peak-

signal-to-noise ratio) gradually decreases as compres-

sion ratio increases in the case of vector quantiza-

198

Suzuki Y., Sakakita H. and Maeda J..

Effect of Fuzzy and Crisp Clustering Algorithms to Design Code Book for Vector Quantization in Applications.

DOI: 10.5220/0005207501980205

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2015), pages 198-205

ISBN: 978-989-758-069-7

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

tion while PSNR rapidly decreases as compression ra-

tio increases in the case of JPEG (Fujibayashi, 2003;

Amerijcks, 1998). In (Fujibayashi, 2003; Amerijcks,

1998), it was shown that an PSNR of the image com-

pressed with JPEG rapidly decreases compared with

that in the case of vector quantization when the com-

pression ratio is larger than approximately 28. These

results were supported by results reported by Laha et

al. (Laha, 2004). Vector quantization is therefore con-

sidered to be appropriate for image coding to achieve

a high compression ratio. A high compression ra-

tio of an image decreases the payloads of commu-

nication terminals. Furthermore, decoding by table

look-up of the code vectors decreases computational

costs of the terminals. In this sense, vector quan-

tization is useful technology for communication ter-

minals with small payloads and small computational

costs. We call these conditions SPSC (small payload

and small compression cost). Furthermore, vector

quantization is useful technology for medical image

processing and medical ultrasound image compres-

sion (Hosseini, 2012; Hung, 2011; Nguyen, 2011).

Small computational cost was allowed using vector

quantization for medical image processing.

For vector quantization, we have to initially con-

struct a code book. Fig. 1 shows a conceptual dia-

gram of the vector quantization. At the source side,

an image is divided into square blocks of τ × τ such

as 4 × 4 or 8 × 8 pixels. Each block is treated as a

vector in a 16- or 64-dimensional space. For encod-

ing an image, each vector made by a block of pix-

els is compared with a code vector in a code book.

The nearest code vector is chosen for the vector and

the index of the code vector is assigned to the vector.

Selection of a code vector is carried out for all vec-

tors. This encoding process generates an index map

as shown in Fig. 1. The index map consists of integer

numbers. For the code book consisting of 256 code

vectors, indexes take values from 1 to 256. These in-

dexes are compressed using entropy coding and sent

to a destination via a communication channel. At the

destination, the compressed integer numbers are de-

coded to obtain the index map. We look for the code

vector corresponding to the indexes in the index map

using a code book and decode the image sent from the

source side. As stated before, this is a table look-up

process and consequently computational cost is neg-

ligible. Since the quality of a decoded image depends

on the code vectors in a code book, code book design

is important for vector quantization. A code book is

constructed by the following procedure. First, the size

of a code book, which is the number of code vectors

is determined. The learning images are prepared to

compute code vectors. Each of the images is divided

Figure 1: A conceptual diagram encoding/decoding with

VQ.

into rectangular blocks such as 4 × 4 or 8× 8. Each

block is treated as a vector and it is called a learning

vector. All learning vectors are classiﬁed into classes.

Prototype vectors generated through classiﬁcation are

code vectors.

Clustering, self-organizing feature map (SOFM)

and evolutionary computing were used to design a

code book. In these methods, clustering algorithms

were widely used, because they were easy to im-

plement. In hard clustering, since each learning

vector belongs to only one cluster, the membership

value is unitary. On the other hand, each vector

belongs to several clusters with different degrees of

membership in fuzzy clustering (Patane, 2001). The

k means algorithm, also called LBG (Linde-Buzo-

Gray) algorithm (Linde, 1980) is the most popular al-

gorithm. The main problem in clustering algorithms

is that the performance is strongly dependent on the

choice of initial conditions and conﬁguration param-

eters. Patane and Russo (Patane, 2001) improved the

LBG algorithm and named it the enhanced LBG al-

gorithm. The fuzzy k means algorithm is the most

popular fuzzy clustering algorithm (Bezdek, 1987).

There are fuzzy clustering algorithms to implement

transition from fuzzy to crisp. The typical algorithm

is fuzzy learning vector quantization (FLVQ) (Tsao,

1994; Tsekouras, 2008). In the FLVQ algorithm, a

smooth transition from fuzzy to crisp mode is accom-

plished to manipulate the fuzziness parameter.

A self-organizing feature map (SOFM) shows in-

teresting properties to design a code book (Amerijcks,

1998; Laha, 2004; Tsao, 1994). Those are topol-

ogy preservation and density mapping. Vectors near

the input space are mapped to the same node or a

nearby node in the output space by the property of

topology preservation. After training the input vec-

tors, the distribution of weight vectors of the nodes

reﬂects the distribution of training vectors in the in-

put space by the property of density mapping. By

these two properties, there are more code vectors in

a region with a high density of training vectors. For

EffectofFuzzyandCrispClusteringAlgorithmstoDesignCodeBookforVectorQuantizationinApplications

199

a code book design using evolutionary algorithms,

fuzzy particle swarm optimization (FPSO), quantum

particle swarm optimization (QPSO), and ﬁreﬂy (FF)

algorithms have been recently been reported as suc-

cessful algorithms (Feng, 2007; Wang, 2007; Horn,

2012). These algorithms are all swarm optimization

algorithms. PSO is an evolutionary computation tech-

nique in which each particle represents a potential so-

lution to a problem in multi-dimensional space. A

ﬁtness evaluation function was deﬁned for designing

a code book. The population of particles is moving

in the search space and every particle changes its po-

sition according to the best global position and best

personal position. These algorithms were developed

to construct a near-optimal code book for vector quan-

tization to avoid getting stuck at local minima in the

ﬁnally selected code book. The FF algorithm was

inspired by social behavior of ﬁreﬂies and showed

the best performance among swarm optimization al-

gorithms (Horn, 2012). Another successful swarm-

based algorithm is the honey bee mating optimization

(HBMO) algorithm, which was inspired by the intelli-

gent behavior of bees in a honey bee colony (Abbass,

2001). The algorithm is based on a model that simu-

lates the evolution of honey bees starting with a soli-

tary colony to the emergence of an eusocial colony.

To design a code book for vector quantization,

clustering algorithms (crisp and fuzzy) are simple to

reduce computational costs and they therefore were

widely used. However, previous studies focused on

reduction of the average distortion error of coding im-

ages (Patane, 2001; Tsekouras, 2008; Kayayiannis,

1995; Tsekouras, 2005; Tsolakis, 2012). Those were

basically studies on clustering algorithms, not on im-

age coding, and the results of those studies were not

sufﬁcient to consider practical applications of cluster-

ing algorithms for image coding. In this study, we

examined the effect of clustering algorithms for de-

signing a code book in terms of practical applications.

For examination, we prepared two types of images:

learning images and test images. A code book was

constructed using the learning images and test im-

ages were used to examine the performance of the

code book for vector quantization. In most previous

studies, the learning images were the same as the test

images (Amerijcks, 1998; Patane, 2001; Tsekouras,

2008; Feng, 2007; Horn, 2012; Kayayiannis, 1995;

Tsekouras, 2005; Tsolakis, 2012). For example, a

code book was constructed with the Lenna image as

a learning image, and the same Lenna image was also

used as the test image. However, as shown in Fig.

1, an image is encoded using a code book that has

to be prepared in advance for practical usage of vec-

tor quantization. The learning images to construct a

code book are different from images to be encoded.

For that reason, we examined clustering algorithms

under the condition of learning images being differ-

ent from test images. There are many clustering al-

gorithms (Jain, 1999). We chose two crisp cluster-

ing algorithms: k means algorithm and ELBG algo-

rithm (Patane, 2001). They are simple algorithms and

widely used to design a code book (Tsekouras, 2008;

Tsekouras, 2005; Tsolakis, 2012). For fuzzy cluster-

ing algorithms, we chose fuzzy k means and fuzzy

learning vector quantization (Bezdek, 1987; Tsao,

1994). They are also frequently employed to design

code book for vector quantization (Tsekouras, 2008;

Tsolakis, 2012). We carried out two sets of exper-

iments. In the ﬁrst sets of experiments, we exam-

ined four clustering algorithms using Lenna image.

The Lenna image was used both learning and test

images. In the second sets of experiments, we ex-

amined the clustering algorithms under the condition

that learning images were different from test images.

We have carried out these experiments in (Sakakita,

2014). However, test images used in the experi-

ments were different from test images employed in

(Sakakita, 2014) to conﬁrm the performance of clus-

tering algorithms.

The paper is organized as follows. Four represen-

tative clustering algorithms used in image coding are

brieﬂy described in section 2. Results of examina-

tion for vector quantization by the four clustering al-

gorithms are presented in section 3, and conclusions

are given in section 4.

2 CLUSTERING ALGORITHMS

AND CODE BOOK DESIGN

A learning image X is divided into square blocks of

τ × τ pixels, and each block is treated as a learn-

ing vector that is represented as X = {x

,··· ,x

where x

∈ R

τ×τ

. We design a code book from these

learning vectors, which consists of code vectors such

as C = {c

,··· ,c

}, where c

∈ R

τ×τ

. To de-

sign a code book, we organize these learning vec-

tors into clusters using a clustering algorithm. Code

vectors are computed so as to minimize discrepancy

between learning vectors and code vectors by clus-

tering algorithms. The following average distortion

measure is frequently employed for clustering algo-

rithms (Patane, 2001).

ave

∑

i=1

min

∈C

d(x

), (1)

where d(x

) is the distance between x

and c

. We

used the squared Euclidean norm for the distance.

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ave

is also called MQE (mean quantization error).

2.1 k-Means Clustering Algorithm

In the k-mean clustering (KMC) algorithm, each

learning vector is assigned to a certain cluster by the

nearest neighbor condition (Kayayiannis, 1995; Jain,

1999). The learning vector x

is assigned to the jth

cluster when d(x

) = min

∈C

d(x

) is true. The

following membership function is derived from the

nearest neighbor condition (Kayayiannis, 1995)

) =



1 if d(x

) = min

∈C

d(x

)

0 otherwise.

(2)

is updated so as to minimize a distortion function

J =

∑

j=1

∑

i=1

)



− c



, (3)

where



− c



is Euclidean norm. The minimiza-

tion of (3) is achieved by updating c

according to the

the equation

∑

i=1

∑

i=1

)

. (4)

where j = 1,2, · · · ,k. For experiments using KMC,

we set a convergencecondition to terminate repetition

ave

(ν− 1) − D

ave

(ν)|

ave

(ν)

< ε, (5)

where ν is the number of iterations and ε = 10

−4

2.2 LBG and Enhanced LBG

Algorithms

In the LBG (Linde-Buzo-Gray) algorithm, there are

two methods of initialization: random initialization

and initialization by splitting (Patane, 2001; Linde,

1980). In random initialization, the initial code vec-

tors are randomly chosen from X . This algorithm is

KMC algorithm. On the other hand, initialization by

splitting requires the number of code vectors to be

a power of 2. The clustering procedure starts with

only one cluster. The cluster is recursively split into

two distinct clusters. After splitting the clusters up to

predetermined number, the code vectors of respective

clusters are computed. We obtain the code book of

, where ν stands for the number of times the clus-

ters were split. The learning vector x

(i = 1, 2,··· ,n)

is assigned to the jth cluster according to the near-

est neighbor condition, d(x

) = min

∈C

d(x

The membership function is also deﬁned as

) =



1 if d(x

) = min

∈C

d(x

)

0 otherwise.

(6)

The code vector c

∈ C

is updated by formula (4)

using the above membership function.

The enhanced LBG (ELBG) algorithm was pro-

posed by Patane and Russo (Patane, 2001). Patane

and Russo revealeda drawbackof the LBG algorithm.

The LBG algorithm ﬁnds local optimal code vectors

that are often far from an acceptable solution. In the

LBG algorithm, a code vector moves through a con-

tiguous region at each iteration. Thus, a bad initializa-

tion could lead to the impossibility of ﬁnding a good

solution. To overcome this drawback of the LBG

algorithm, they proposed a code vector shift from a

small cluster to a larger one. They introduced the idea

of utility index of a code vector. After the LBG al-

gorithm, the ELBG algorithm identiﬁes clusters with

low utility and attempts to shift a code vector with low

utility close to a code vector with high utility. The

clusters with low utility are merged to the adjacent

clusters. For our computational experiments, distor-

tion to terminate the repetition was computed by (5)

and ε was set to 10

−4

2.3 Fuzzy k-Means Clustering

Algorithm

The k-means clustering algorithm assigns each learn-

ing vector to a single cluster based on a hard deci-

sion. On the other hand, the fuzzy k-means clus-

tering (FKM) algorithm assigns each learning vec-

tor to multiple clusters with membership values be-

ing between zero and one (Bezdek, 1987; Kayayian-

nis, 1995; Tsekouras, 2005). The learning vectors are

assigned to clusters so as to minimize the objective

function

∑

j=1

∑

i=1

)



− c



(7)

under the following constraints:

0 <

∑

i=1

) < n (8)

∑

j=1

) = 1. (9)

1 < m < ∞ controls the fuzziness of the clustering and

it is given in advance. If m is equal to 1, it is crisp

clustering. Minimization of (7) results in membership

function update such that

) =

∑

l=1



d(x

)

d(x

)



m−1

, (10)

where d(x

) =



− c



. The distance becomes

zero, it is replaced by one to avoid zero division in our

EffectofFuzzyandCrispClusteringAlgorithmstoDesignCodeBookforVectorQuantizationinApplications

201

experiments. For update of the membership function

by (10), the code vectors were renewed as

∑

i=1

)

∑

i=1

)

( j = 1, 2,··· , k). (11)

For our computational experiments, m was set to 1.2.

The repetition of the FKM algorithm terminates when

ε of (5) is less than 10

−4

2.4 Fuzzy Learning Vector

Quantization

Transition from a fuzzy condition to a crisp condi-

tion is achieved by gradually decreasing the fuzzi-

ness parameter m in fuzzy learning vector quantiza-

tion (FLVQ) (Tsao, 1994; Tsekouras, 2008). The ob-

jective function and the constraints are the same as

those of the FKM algorithm. A fuzziness parameter

is decreased from the initial value m

to m

according

m(t) = m

− [t(m

− m

)]/t

max

, (12)

for t = 0,1, 2,··· ,t

max

. m

and m

are the initial and

ﬁnal values, respectively and t

max

is the maximum

number of iterations. The membership function is up-

dated for t = 1,2,··· ,t

max

) =

∑

l=1



d(x

)

d(x

)



(m(t)−1)

−m(t)

, (13)

where d(x

) =



− c



. The distance becomes

zero, it is replaced by one to avoid zero division in our

experiments. The code vectors were also evaluated by

the equation

∑

i=1

∑

i=1

)

(14)

We set a convergence conditionto terminate repetition

∑

j=1



t−1

− c



< ε (15)

where ε = 10

−4

. For our computational experiments,

we used the following parameters: m

= 1.5,m

1.001, and t

max

= 100.

3 EFFECT OF CLUSTERING

ALGORITHMS FOR VECTOR

QUANTIZATION

To examine clustering algorithms, we carried out two

sets of experiments.

In the ﬁrst set of experiments,

we examined four clustering algorithms using the

Lenna image, which is 256 × 256 in size and an 8-

bit grayscale image. This image was used as both the

learning image and the test image. The Lenna im-

age was segmented into 4 × 4 blocks in size. Each

block was treated as a learning vector with 16 dimen-

sions. There were 4096 learning vectors to construct

a code book. We designed a code book consisting

of 256 code vectors. It must be the minimum num-

ber of code vectors for us to keep acceptable image

quality. In this sense, the number of 256 code vectors

is suitable for comparative studies of clustering algo-

rithms. 4 × 4 blocks in size means that each block

containing 4 × 4 = 16 pixels is represented by 8 bits

(256 code vectors). The compression rate is therefore

8/16 = 0.5 bits per pixel (bpp). The four clustering

algorithms tested were the KMC algorithm, ELBG al-

gorithm, FKM algorithm and FLVQ algorithm. The

performance of each of the four clustering algorithms

was examined in terms of PSNR. The PSNR is com-

puted as

PSNR = 10log



MSE



(dB), (16)

where PS = 255. MSE is the mean square error

between the original image and the decoded image.

Since we carried out ﬁve trials for each clustering al-

gorithm to design code books, ﬁve code books were

constructed for one clustering algorithm. Thus, a to-

tal of 20 code books were constructed. PSNR was

computed to examine the performance of each al-

gorithm. Table 1 shows the results of these experi-

ments. Among the four clustering algorithms, KMC

showed the smallest average PSNR (29.42 dB) and

ELBG showed the largest average PSNR (30.40 dB).

The difference between those two values is 0.98 dB,

which is a large difference for image quality. The re-

sults indicate that selection of a clustering algorithm

is important for designing a code book. Tsekouras

et al. (Tsekouras, 2008) reported results of an exper-

iment in which they used the Lenna image with a

size of 512 × 512 pixels and 8-bit gray scale. When

the number of code vectors was 256, the difference

in PSNR between KMC and their proposed cluster-

ing algorithm was 2.653 dB. Tsolakis et al. (Tsolakis,

Images used in the experiments were images from

CVG-UGR-Image database (http://decsai.ugr.es/cvg/

dbimagenes/index.php)

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Table 1: The PSNRs (dB) for four clustering algorithms

(Lenna). PSNRs were rounded at the second decimal

places.

KMC ELBG

trial PSNR PSNR

1 29.47 30.37

2 29.47 30.37

3 29.52 30.42

4 29.35 30.39

5 29.30 30.42

average 29.42 30.40

FKM FLVQ

trial PSNR PSNR

1 30.07 30.24

2 29.99 30.15

3 29.99 30.07

4 30.07 30.06

5 29.88 30.01

average 30.00 30.10

2012) carried out experiments using the same Lenna

image as that above, and the difference in PSNR be-

tween the LBG algorithm and their proposed algo-

rithm (θ = 0.5) was 2.5429 dB. Their experiments

also demonstrated that selection of a clustering algo-

rithm was important for designing a code book of high

quality.

A code book must be prepared in advance for

practical application of image coding using vector

quantization. This means that the learning images to

construct a code book are different from images to

be coded. It is therefore necessary to examine clus-

tering algorithms under the condition of learning im-

ages to construct a code book being different from test

images. In other words, the performance of vector

quantization must be examined not only for speciﬁc

learning images but also for previously unseen test

images (Lazebnik, 2009). In the second set of ex-

periments, we therefore prepared 20 learning images

that were consisted of some images as shown in Fig.

2. Each image is 256 × 256 in size and 8-bit gray

scale. The smallest image consisted of one image of

256 × 256 in size. The second images consisted of

two images of 256× 256 in size. The largest learning

image consisted of 20 images of 256 × 256 in size.

In this manner, we made 20 learning images and also

constructed 20 code books using these learning im-

ages. Four clustering algorithms were used to con-

struct the code books. A total of 80 code books were

constructed. We selected four test images that did not

include learning images (Cat512, City512, Crows512,

Girlface512). These images were 512× 512 pixels in

size and 8-bit gray scale. Each learning image was

segmented 4× 4 pixels and the number of code vec-

tors was 256 for each code book.

Fig. 3 shows changes in PSNR with increases in

the number of learning images for the test images. In

the Cat512 image, it seems that PSNR increases grad-

ually as the number of learning images increases for

all clustering algorithms as shown in Fig. 3. How-

ever, when the number of learning images are more

than 10, PSNR curve becomes ﬂat. The PSNR dif-

ferences among clustering algorithms are small. For

other curves of PSNR, the curves become ﬂat when

the number of learning images are more than 10. Fur-

thermore, the PSNR difference among four clustering

algorithms are small as well as Cat512 image.

We constructed ﬁve learning images using images

shown in Fig. 2. For learning image 1, we picked up

11 images from the set of images. The images were

picked up in raster scan order. In the same manner,

learning image 2 consisted of 12 images and learn-

ing images 3 consisted of 13 images. Learning im-

ages 4 and 5 consisted of 14 and 15 images, respec-

tively. Five code books were constructed using these

learning images. Since there are four clustering al-

gorithms, total 20 code books were constructed. The

number of code vectors was 256 and the learning im-

ages were segmented 4× 4 pixels. The same four test

images were employed to examined the performance

of each clustering algorithm. Table II shows the re-

sults. The minimum PSNR value was 28.36 in the

case of the learning image 5, Crowd512 and ELBG al-

gorithm. The maximum PSNR value was 30.87 in the

case of the learning image 1, Girlface512, and KMC

algorithm. The difference is 2.51 and this value is sig-

niﬁcant for us to perceive image quality.

However, we computed the average PSNR of four

test images in each clustering algorithm. The average

values are 29.48 for KMC, 29.37 for ELBG, 29.51 for

FKM and 29.44 for FLVQ. The difference among the

average values were too small (0.14) for us to perceive

image between compressed image. In the end, these

results indicate that selection of clustering algorithm

is not important to design a code book when the learn-

ing images are different from test images. This re-

sult is the same as the result we obtained in (Sakakita,

2014).

4 CONCLUSIONS

We examined effect of clustering algorithms to design

a code book for vector quantization. Four widely used

clustering algorithms were selected for examination.

Two sets of experiments were carried out for examina-

tion. In the ﬁrst set of experiments, we examined the

EffectofFuzzyandCrispClusteringAlgorithmstoDesignCodeBookforVectorQuantizationinApplications

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Table 2: The PSNRs(dB) of four clustering algorithms.

PSNRs were rounded at the second decimal places.

learning images 1

test image KMC ELBG FKM FLVQ

Cat512 29.16 29.01 28.94 28.90

City512 29.65 29.53 29.62 29.50

Crowd512 28.60 28.56 28.64 28.60

Girlface512 30.87 30.56 30.82 30.80

learning images 2

test image KMC ELBG FKM FLVQ

Cat512 29.07 29.06 29.05 28.98

City512 29.64 29.50 29.70 29.58

Crowd512 28.61 28.54 28.66 28.60

Girlface512 30.76 30.44 30.85 30.71

learning images 3

test image KMC ELBG FKM FLVQ

Cat512 29.07 29.04 29.00 29.10

City512 29.62 29.51 29.74 29.60

Crowd512 28.55 28.58 28.63 28.60

Girlface512 30.68 30.47 30.87 30.64

learning images 4

test image KMC ELBG FKM FLVQ

Cat512 29.07 29.03 29.06 29.00

City512 29.57 29.47 29.67 29.59

Crowd512 28.57 28.52 28.63 28.55

Girlface512 30.68 30.47 30.80 30.65

learning images 5

test image KMC ELBG FKM FLVQ

Cat512 28.95 28.81 28.82 28.87

City512 29.46 29.45 29.53 29.48

Crowd512 28.37 28.36 28.47 28.42

Girlface512 30.65 30.52 30.69 30.59

performance of the four clustering algorithms using

the Lenna image. The Lenna image was used to con-

struct a code book and also used as a test image. The

results indicated that selection of a clustering algo-

rithm is important. In the second set of experiments,

code books using ﬁve learning images in which were

different from test images. There were small perfor-

mance differences among clustering algorithms. The

differences were too small for us to perceive them.

The results indicated that selection of a clustering al-

gorithm is not important for constructing a code book

when the learning images are different from test im-

ages.

ACKNOWLEDGEMENT

This research project is partially supported by

granting-in-aid for scientiﬁc research of Japan Soci-

ety for Promotion of Science (24500270).

Figure 2: 20 images to construct learning images.

0 5 10 15 20

Cat512

the number of images

PSNR

KMC

ELBG

FKM

FLVQ

0 5 10 15 20

City512

the number of images

PSNR

KMC

ELBG

FKM

FLVQ

0 5 10 15 20

Crowd512

the number of images

PSNR

KMC

ELBG

FKM

FLVQ

0 5 10 15 20

Girlface512

the number of images

PSNR

KMC

ELBG

FKM

FLVQ

Figure 3: Changes in PSNR(dB) with increasing the number

of learning images for the test images of Cat512, City512,

Crowd512, and Girlface512.

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