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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
Comparative Performance of Information
Hiding in Vector Quantized Codebooks using
LBG, KPE, KMCG and KFCG
Dr. H. B. Kekre Archana Athawale Tanuja K. Sarode Kalpana Sagvekar
Senior Professor, Ph.D. Scholar, MPSTME, Ph.D. Scholar, MPSTME, Lecturer,
MPSTME, NMIMS University, NMIMS University, Fr. Conceicao Rodrigues
NMIMS University, Vileparle(W), Mumbai-56 Vileparle(W), Mumbai-56 COE, Bandra(W),
Vile-parle(W), Assistant Professor, TSEC, Assistant Professor, TSEC, Mumbai-50, India
Mumbai-56, India. Bandra(W), Mumbai-50, Bandra(W), Mumbai-50, kalpanasagvekar@gmail.c
hbkekre@yahoo.com India. India. om
Abstract - In traditional VQ - data hiding schemes secret data is appear on the picture to catch malicious attackers‟ attention.
hidden inside index based cover image resulting in limited embedding Thereupon, the security of the secret information is ensured
capacity. To improve the embedding capacity as well as to have against detection. As for the payload capacity limit, it
minimum distortion to carrier media, we have proposed one novel evaluates the power of a data-hiding scheme by checking
method of hiding secret data into the codebook. In this paper we have how big the maximum amount of the secret information is
used four different algorithms Linde Buzo and Gray (LBG), Kekre’s that can be hidden in the cover media. Generally speaking,
Proportionate Error (KPE), Kekre’s Median Codebook Generation
the larger the payload size is, the worse the stego-image
algorithm (KMCG) and Kekre’s Fast Codebook Generation Algorithm
(KFCG) to prepare codebooks. It is observed that KFCG gives visual quality will be. That is to say, in the world of data
minimum distortion. hiding, how to strike this balance and settle on an ideal
robustness-capacity tradeoff is maybe the core problem to
solve.
Keywords - Reversible (lossless) data hiding, VQ, LBG, KPE, KMCG, The existing schemes of data hiding can roughly be classified
KFCG. into the following three categories:
Spatial domain data hiding [2],[3],[4]: Data hiding of this
I. INTRODUCTION type directly adjust image pixels in the spatial domain for
data embedding. This technique is simple to implement,
Due to the digitalization of all kinds of data and the amazing offering a relatively high hiding capacity. The quality of the
development of network communication, information security stego image can be easily controlled. Therefore, data hiding
over the Internet has become more and more important. The of this type has become a well known method for image
Internet is basically a giant open channel with security steganography.
problems like modifications and interceptions occurring at any
time in any place. Under such circumstances, quite some Frequency domain data hiding [5],[6]: In this method images
different approaches have been proposed in an attempt to make are first transformed into frequency domain, and then data is
private communication secure. Researchers have developed embedded by modifying the transformed coefficients.
schemes where the secret message is protected by getting
transformed into the form of a stack of seemingly meaningless Compressed domain data hiding [7],[8]: Data hiding is
data, which only the authorized user can retransform back to its obtained by modifying the coefficients of the compressed
original form by way of some secret information. However, the code of a cover image. Since most images transmitted over
appearance of a stack of seemingly meaningless data could be Internet are in compressed format, embedding secret data into
an irresistible attraction to an attacker with a desire to recover the compressed domain would provoke little suspicion.
the original message. Another approach, called steganography,
hides the secret message in some cover material with a Due to the restricted bandwidth of networks, we cannot keep
common appearance to avoid suspicion. The data-hiding up with the growing sizes of various multimedia files. Many
efficacy can be judged according to two criteria: (1) visual popular image compression algorithms have been proposed
quality (2) payload capacity limit. The term “visual quality” to respond this problem, such as VQ [15], side match VQ
here refers to the quality of the stego-image. That is to say, only (SMVQ) [16], JPEG [17], JPEG2000 [18], and so on. One of
a limited number of distortions within limited areas are allowed the most commonly studied image compression techniques is
in the stego-image so that no obvious traces of modification Vector Quantization (VQ) [19], which is an attractive choice
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 8, No. 2, 2010
because of its simplicity and cost-effective implementation. decides the error ratio. Hereafter the procedure is same as
Indeed, a variety of VQ techniques have been successfully that of LBG. While adding proportionate error a safe guard is
applied in real applications such as speech and image coding also introduced so that neither v1 nor v2 go beyond the
[20], [22], VQ has faster encode/decode time along with training vector space. This removes the disadvantage of the
simpler framework compared to JPEG/JPEG2000. Vector LBG. Both LBG and KPE requires 2M number of Euclidean
Quantization requires limited information during decoding and distance computations and 2M number of comparisons where
works best in applications in which the decoder has only M is the total number of training vectors in every iteration to
limited information [21]. generate clusters.
c. Kekre’s Median Codebook Generation Algorithm
There are two approaches for hiding data into VQ compressed (KMCG) [13]
domain; either hides the covert data into index based cover
image or in codebook. In this paper we have proposed a method In this algorithm image is divided in to blocks and blocks are
of hiding data into codebook which is not been explored. In converted to the vectors of size k. The Fig. 2 below
section II we present codebook design algorithms. Section III represents matrix T of size M x k consisting of M number of
explains proposed search algorithm followed by Section IV in image training vectors of dimension k. Each row of the
which results and evaluation is given. Section V gives matrix is the image training vector of dimension k.
conclusion.
x1,1 x1,2 .... x1,k
II. VQ COMPRESSION TECHNIQUE x2,1 x2,2 .... x2,k
T . . . .
Vector Quantization (VQ) [9-14] is an efficient technique for . . . .
data compression [31-34] and is very popular in a variety of xM,1 xM,2 .... xM,k
research fields such as data hiding techniques [7,8], image
segmentation [23-26], speech data compression [27], content
based image retrieval CBIR [28, 29] and face recognition [30]. Fig. 2. Training Vectors
A. Codebook Generation Algorithms The training vectors are sorted with respect to the first
member of all the vectors i.e. with respect to the first column
a. Linde-Buzo-Gray (LBG) Algorithm [9], [10] of the matrix T and the entire matrix is considered as one
single cluster. The median of the matrix T is chosen
In this algorithm centroid is calculated as the first codevector (codevector) and is put into the codebook, and the size of the
for the training set. In Fig. 1 two vectors v1 & v2 are generated codebook is set to one. The matrix is then divided into two
by using constant error addition to the codevector. Euclidean equal parts and the each of the part is then again sorted with
distances of all the training vectors are computed with vectors respect to the second member of all the training vectors i.e.
v1 & v2 and two clusters are formed based on nearest of v1 or with respect to the second column of the matrix T and we
v2. This procedure is repeated for every cluster. The drawback obtain two clusters both consisting of equal number of
of this algorithm is that the cluster elongation is –45o to training vectors. The median of both the parts is the picked
horizontal axis in two dimensional cases. Resulting in up and written to the codebook, now the size of the codebook
inefficient clustering. is increased to two consisting of two codevectors and again
each part is further divided to half. Each of the above four
parts obtained are sorted with respect to the third column of
the matrix T and four clusters are obtained and accordingly
four codevectors are obtained. The above process is repeated
till we obtain the codebook of desired size. Here quick sort
algorithm is used and from the results it is observed that this
algorithm takes least time to generate codebook, since
Euclidean distance computation is not required.
d. Kekre’s Fast Codebook Generation (KFCG) Algorithm
In [14], KFCG algorithm for image data compression is
Fig.1 LBG for 2 dimensional case proposed. This algorithm reduces the time for codebook
generation. It does not use Euclidian distance for codebook
b. Proportionate Error Algorithm (KPE) [11], [12] generation. In this algorithm image is divided in to blocks
and blocks are converted to the vectors of size k. Initially we
Here proportionate error is added to the centroid to generate have one cluster with the entire training vectors and the
two vectors v1 & v2. Magnitude of elements of the centroid codevector C1 which is centroid.
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In the first iteration of the algorithm, the clusters are formed by A. Embedding Procedure
comparing first element of training vector with first element of
code vector C1. The vector Xi is grouped into the cluster 1 if
xi1< c11 otherwise vector Xi is grouped into cluster 2 as shown Divide the image into 2×2 block of pixels
in Figure. 3a. where codevector dimension space is 2. window
In second iteration, the cluster 1 is split into two by comparing Generate initial cluster of training set using the
second element xi2 of vector Xi belonging to cluster 1 with that rows of 12 values per pixel window
of the second element of the codevector which is centroid of
cluster 1. Cluster 2 is split into two by comparing the second
element xi2 of vector Xi belonging to cluster 2 with that of the
second element of the codevector which is centroid of cluster Apply codebook generation algorithm
2, as shown in Figure. 3b. LBG/KPE/KFCG/KMCG on initial cluster to
obtain codebook of size 2048 codevectors
This procedure is repeated till the codebook size is reached to
the size specified by user. It is observed that this algorithm
gives less error as compared to LBG and requires least time to
generate codebook as compared to other algorithms, as it does Embed every bit of each pixel in the LSB‟s of
not require computation of Euclidian distance. (i.e. 1, 2, 3, 4, variable bit method) each element
of codevector belonging to CB
Modified CB
Generate Index based cover image
3(a). First Iteration B. Extraction & Recovery Procedure
Modified CB
Index based cover image
Extract secret Reconstruct the original
data from image by replacing
LSB of every each index by
3(b) Second Iteration corresponding
element of CB
codevector
Fig. 3. KFCG algorithm for 2-D case
III. PROPOSED APPROACH C. Variable Bit Hiding Algorithm
In this approach, we are hiding the secret data into codebook
For variable bit hiding Kekre‟s algorithm [2] is used.
generated using various codebook generation algorithm such as
LBG[10][11], KPE[12][13], KMCG[14], KFCG[15]. There are 1. If the value of codebook vector element is in the range
various ways of hiding: 1bit, 2 bits, 3 bits, 4 bits & variable bits 240≤gi≤255 then we embed 4 bits of secret data into the
hiding. 4 LSB‟s codebook vector element. This can be done by
observing the 4 most significant bits (MSB‟s). If they are
all 1‟s then the remaining 4 LSB‟s can be used for
embedding data.
2. If the value of codebook vector element is in the range
224≤gi≤239 then we embed 3 bits of secret data. . This
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can be done by observing the 3 most significant bits
(MSB‟s). If they are all 1‟s then the remaining 3 LSB‟s can
be used for embedding data.
3. If the value of codebook vector element is in the range
192≤gi≤223 then we embed 2 bits of secret data. . This can
be done by observing the 2 most significant bits (MSB‟s).
If they are all 1‟s then the remaining 2 LSB‟s can be used 5 (a) 5 (b) 5 (c)
for embedding data. Original Secret Reconstructed image using
4. If the value of codebook vector element is in the range Cover image Message KFCG for Variable bits
Fern.bmp Method
0≤gi≤191 we embed 1 bit of secret data.
60
50
40
IV. RESULTS & EVALUATIONS
MSE
30
20
In our proposed approach, we have generated codebook using 10
0
LBG, KPE, KMCG and KFCG for 24 bit color image of size
KPE
KPE
KPE
KPE
KPE
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
KFCG
KFCG
KFCG
KFCG
KFCG
256×256 shown in Fig. 4 & 5. Codebook is of size 2048×12
(i.e. 2048 code vectors each contains 12 bytes - 4 pairs of 1 bit 2 bits 3 bits 4 bits variable
bits
RGB). We have hidden 32×32 gray image.
Hiding Capacity
Fig. 4. to Fig. 8. Shows the results of 1bit, 2bits 3bits 4bits and 5 (d) plot of Hiding Capacity versus MSE
Variable bits using codebook obtained from LBG, KPE, Fig. 5. Results of 1bit, 2bits 3bits 4bits and Variable bits on the cover image
KMCG and KFCG on the various cover images Bird, Fern, Fern shown in Fig.5(a) and secrete image shown in Fig. 5(b).
Puppy, Cat and Temple hiding same secrete image for fair
comparison respectively.
Fig. 9. Shows the plot of Hiding Capacity versus average MSE
for various hiding methods 1bit, 2bits 3bits 4bits and Variable
bits on LBG, KPE, KMCG and KFCG VQ Codebooks
respectively.
6 (a) 6 (b) 6 (c)
Original Secret Reconstructed image using
Cover image Message KFCG for Variable bits
Puppy.bmp Method
30
25
20
MSE
15
4 (a) 4 (b) 4 (c) 10
5
Original Secret Reconstructed image using
0
Cover image Message KFCG for Variable bits
KPE
KPE
KPE
KPE
KPE
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
KFCG
KFCG
KFCG
KFCG
KFCG
Birds.bmp Method
1 bit 2 bits 3 bits 4 bits variable
80 bits
70
60 Hiding Capacity
50
MSE
40 6 (d) plot of Hiding Capacity versus MSE
30 Fig. 6. Results of 1bit, 2bits 3bits 4bits and Variable bits on the cover image
20
10 Puppy shown in Fig.6(a) and secrete image shown in Fig. 6(b).
0
KPE
KPE
KPE
KPE
KPE
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
KFCG
KFCG
KFCG
KFCG
KFCG
1 bit 2 bits 3 bits 4 bits variable
bits
Hiding Capacity
4 (d) plot of Hiding Capacity versus MSE
Fig. 4. Results of 1bit, 2bits 3bits 4bits and Variable bits on the cover image
bird and secrete image shown in Fig. 4(b).
7 (a) 7 (b) 7 (c)
Original Secret Reconstructed image using
Cover image Message KFCG for Variable bits
Cat.bmp Method
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60 60
50 50
Avg. MSE
40 40
MSE
30 30
20 20
10 10
0 0
KPE
KPE
KPE
KPE
KPE
KPE
KPE
KPE
KPE
KPE
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
KFCG
KFCG
KFCG
KFCG
KFCG
KFCG
KFCG
KFCG
KFCG
KFCG
1 bit 2 bits 3 bits 4 bits variable 1 bit 2 bits 3 bits 4 bits variable
bits bits
Hiding Capacity Hiding Capacity
7 (d) plot of Hiding Capacity versus MSE Plot of Hiding Capacity versus Avg. MSE
Fig. 7. Results of 1bit, 2bits 3bits 4bits and Variable bits on the cover image
Cat shown in Fig.7(a) and secrete image shown in Fig. 7(b). Fig. 9. Plot of Hiding Capacity versus average MSE for various hiding
methods 1bit, 2bits 3bits 4bits and Variable bits on LBG, KPE, KMCG and
KFCG VQ Codebooks respectively.
It is observed from Fig. 4 to Fig. 9. that KFCG codebook
gives less MSE in all the data hiding methods 1bit, 2bits,
3bits, 4bits and varible bits as compared to LBG, KPE, and
KMCG codebook. Further it is observed that varible bit
8 (a) 8 (b) 8 (c) method using KFCG gives the best performance.
Original Secret Reconstructed image using
Cover image Message KFCG for Variable bits
Temple.bmp Method
Table 1. Shows the hiding Capacity in bits using 1 bit, 2 bits,
60 3 bits 4 bits, and variable bits method on LBG, KPE, KMCG
50
40
and KFCG codebook of size 2048.
MSE
30
20
10
0
KPE
KPE
KPE
KPE
KPE
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
LBG
KMCG
KFCG
KFCG
KFCG
KFCG
KFCG
1 bit 2 bits 3 bits 4 bits variable
bits
Hiding Capacity
8 (d) plot of Hiding Capacity versus MSE
Fig. 8. Results of 1bit, 2bits 3bits 4bits and Variable bits on the cover image
Temple shown in Fig.8(a) and secrete image shown in Fig. 8(b).
TABLE I. HIDING CAPACITY IN BITS USING 1 BIT, 2 BITS, 3 BITS, 4 BITS, AND VARIABLE BITS METHOD ON LBG, KPE,
KMCG AND KFCG CODEBOOK OF SIZE 2048
Hiding Capacity in bits
Cover
Variable bits
Images 1 bit 2 bits 3 bits 4 bits
LBG KPE KMCG KFCG
Birds 28488 27202 26881 27751
Fern 27561 23891 27646 27965
Puppy 24576 49152 73728 98304 39181 38899 39962 38362
Cat 38076 37891 36364 33940
Temple 26595 26207 25545 26034
From table I it is observed that variable bits give high hiding capacity as compared to 1 bit, 2 bits, 3 bits and 4 bits
embedding methods.
V. CONCLUSION using MSE as a parameter. It has been observed that
KFCG with variable bits for hiding information gives the
In this proposed approach the information is hidden in a best performance giving mse equivalent to 2.2 bits per
vector quantized codebook by using 1,2,3,4 LSBs of the byte of codevectors. In addition KMCG has very low
codevectors. Further a variable bit embedding is also computational complexity.
considered which gives better embedding capacity
coupled with low distortion. For preparing codebooks
four different algorithms namely LBG, KPE, KMCG,
KFCG are considered & their performance is considered
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G. H. Raisoni College of Engineering, Nagpur on 16-18 December of ISTE and also a member of International Association of Engineers
2009, this paper will be uploaded online at IEEE Xplore. (IAENG). Her area of interest is Image Processing, Signal Processing
and Computer Graphics. She has about 30 papers in National
/International Conferences/Journals to her credit.
AUTHORS PROFILE
Tanuja K. Sarode has Received Bsc.(Mathematics) from Mumbai
Dr. H. B. Kekre has received B.E. (Hons.) in Telecomm. Engineering. University in 1996, Bsc.Tech.(Computer
from Jabalpur University in 1958, M.Tech Technology) from Mumbai University in 1999,
(Industrial Electronics) from IIT Bombay in 1960, M.E. (Computer Engineering) from Mumbai
M.S.Engg. (Electrical Engg.) from University of University in 2004, currently Pursuing Ph.D. from
Ottawa in 1965 and Ph.D. (System Identification) Mukesh Patel School of Technology,
from IIT Bombay in 1970 He has worked as Management and Engineering, SVKM‟s NMIMS
Faculty of Electrical Engg. and then HOD University, Vile-Parle (W), Mumbai, INDIA. She
Computer Science and Engg. at IIT Bombay. For has more than 10 years of experience in teaching. Currently working as
13 years he was working as a professor and head in the Department of Assistant Professor in Dept. of Computer Engineering at Thadomal
Computer Engg. at Thadomal Shahani Engineering. College, Mumbai. Shahani Engineering College, Mumbai. She is life member of IETE,
Now he is Senior Professor at MPSTME, SVKM‟s NMIMS University. member International Association of Engineers (IAENG) and
He has guided 17 Ph.Ds, more than 100 M.E./M.Tech and several B.E./ International Association of Computer Science and Information
B.Tech projects. His areas of interest are Digital Signal processing, Technology (IACSIT), Singapore. Her areas of interest are Image
Image Processing and Computer Networking. He has more than 250 Processing, Signal Processing and Computer Graphics. She has 60
papers in National / International Conferences and Journals to his credit. papers in National /International Conferences/journal to her credit.
He was Senior Member of IEEE. Presently He is Fellow of IETE and
Life Member of ISTE Recently six students working under his guidance Kalpana R. Sagvekar has received B.E.(Computer) degree from
have received best paper awards. Currently 10 research scholars are Mumbai University with first class in 2001.
pursuing Ph.D. program under his guidance. Currently Perusing M.E. in Computer Engineering
from University of Mumbai. She has more than 08
Ms. Archana A. Athawale has Received B.E.(Computer Engineering) years of experience in teaching. Currently
degree from Walchand College of Engineering, working as Lecturer in Computer Engineering at
Sangli, Shivaji University in 1996, Fr. Conceicao Rodrigues College of Engineering,
M.E.(Computer Engineering) degree from Bandra(w), Mumbai. Her areas of interest are
V.J.T.I., Mumbai University in 1999, currently Image Processing, Data Structure, Analysis of
pursuing Ph.D. from NMIMS University, Algorithms, and Theoretical Computer Science. She has about 2 papers
Mumbai. She has more than 10 years of in National /International Conferences/Journals to her credit.
experience in teaching. Presently working as - an
Assistant Professor in Department of Computer Engineering at
Thadomal Shahani Engineering College, Mumbai. She is a Life member
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