Steganography Using Adaptive Pixel Value Differencing(APVD) of Gray Images Through Exclusion of Overflow/Underflow

David C. Wyld, et al. (Eds): CCSEA, SEA, CLOUD, DKMP, CS & IT 05, pp. 93–102, 2012.
© CS & IT-CSCP 2012 DOI : 10.5121/csit.2012.2211
Steganography Using Adaptive Pixel Value
Differencing(APVD) of Gray Images Through
Exclusion of Overflow/Underflow
J. K. Mandal1
and Debashis Das 2
1
Department of Computer Science and Engineering,
University of Kalyani, Kalyani,
West Bengal, India
jkm.cse@gmail.com
2
Department of Computer Science and Engineering,
University of Kalyani, Kalyani,
West Bengal, India
debashisitnsec@gmail.com
ABSTRACT
In a gray scale image the pixel value ranges from 0 to 255. But when we use pixel-value
differencing (pvd) method as image steganographic scheme, the pixel values in the stego-image
may exceed gray scale range. An adaptive steganography based on modified pixel-value
differencing through management of pixel values within the range of gray scale has been
proposed in this paper. PVD method is used and check whether the pixel value exceeds the
range on embedding. Positions where the pixel exceeds boundary has been marked and a
delicate handle is used to keep the value within the range. From the experimental it is seen that
the results obtained in proposed method provides with identical payload and visual fidelity of
stego-image compared to the pvd method.
Keywords
Steganography, Pixel-value differencing, Adaptive Pixel-value differencing, Stego-image
1. INTRODUCTION
Now-a-days Internet has become the most popular communication media for message
transmission in different places of the world. Two schemes are used to protect secret messages
from being captured during transmission. One is encryption where the secret information is
encoded in another form by using a secret key before sending, which can only be decoded with
secret keys. The most popular encryption techniques are DES, RSA etc. Other way is
steganography which is a technique of hiding secret information into a cover media or carrier. If
the cover media is a digital image, it is called cover image and the cover image with hidden data
is called stego-image. Steganographic technique can be used in military, commercial, anti-
criminal and so on. There are various steganographic techniques available where a digital image
is used as a carrier. The most common and simplest method is least-significant-bit (LSB)
substitution, where the LSB position of each pixel of the cover image is replaced by one bit
of secret data. Wang et al.[6] proposed a method to embed data by using genetic algorithm to

94 Computer Science & Information Technology (CS & IT)
improve the quality of the stego-image. However, genetic algorithm takes more computational
time. Chang et al. Proposed[8] an efficient dynamic programming strategy to reduce the
computational time. Chan and Cheng [10] proposed to embed data by simple LSB substitution
with an optimal pixel adjustment process. Wu and Tsai[1] proposed a new scheme to hide more
data with outstanding quality of stego-image pixel-value-differencing (PVD) method. Thereafter,
based on PVD method various approaches have been proposed [2,3,4,7,9]. In PVD the range may
exceed -64 to 319 in embedding. In this paper, a range managed steganographic approach, using
PVD has been proposed. In APVD method a gray scale digital image has been used as a cover
image where pixel values ranged between 0 and 255 and the pixel values of stego-image will not
exceed the gray scale range. The proposed method will provide the same hiding capacity as of
the original PVD method with acceptable stego image quality .
2. REVIEW OF PVD METHOD
In PVD method[1], gray scale image is used as a cover image with a long bit-stream as the secret
data. At first the cover image is partitioned into non-overlapping blocks of two consecutive
pixels, pi and pi+1. From each block the difference value di is calculated by subtracting pi from
pi+1. The set of all difference values may range from -255 to 255. Therefore, |di| ranges from 0 to
255. The blocks with small difference value locates in smooth area where block with large
difference values are the sharp edged area. According to the properties of human vision, eyes can
tolerate more changes in sharp-edge area than smooth area. So, more data can be embedded into
edge area than smooth areas. Therefore, in PVD method a range table has been designed with n
contiguous ranges Rk (where k=1,2,…,n) where the range is 0 to 255. The lower and the upper
bound are denoted as lk and uk respectively, then Rk ∈[lk,uk]. The width of Rk is calculated as
wk=uk-lk+1.wk decides how many bits can be hidden in a pixel block. For security purpose Rk is
kept as a variable, as a result, original range table is required to extract the embedded data.The
embedding algorithm is given as algorithm 1
Algorithm 1:
1. Calculate the difference value di of two consecutive pixels pi and pi+1 for each block in
the cover image. This is given by di=|pi+1-pi |.
2. Compute the optimal range where the difference lies in the range table by using di. This
is calculated as Ri =min(uk- di ), where uk ≥di for all 1≤ k ≤ n
3. Compute the number of bits ‘t’ to be hidden in a pixel block can be defined as t=⎿log2
wi⏌. where wi is the width of the range in which the pixel difference di is belonging
4. Read t bits from binary secret data and convert it into its corresponding decimal value b.
For instance if t=010, then b=2
5. Calculate the new difference value diʹ which is given by diʹ=l i +b
6. Modify the values of pi and p i+1 by the following formula:
(piʹ, p i+1ʹ) = (pi+⎾m/2⏋,pi+1-⎿m/2⏌), if pi≥p i+1 and di'>di
(pi-⎿m/2⏌,pi+1+⎾m/2⏋), if pi<pi+1 and diʹ>di
(pi-⎾m/2⏋),p i+1+⎿m/2⏌), if pi≥p i+1 and d'i≤di
(pi+⎾m/2⏋,p i+1-⎿m/2⏌), if pi<p i+1 and di'≤di
where m=|di'-di|. Now we obtain the pixel pair (pi',pi+1') after embedding the secret data into pixel
pair (pi,pi+1). Repeat step 1-6 until all secret data are embedded into the cover image. Hence we
get the stego-image.

Computer Science & Information Technology (CS & IT) 95
When extracting the hidden information from the stego-image, original range table is required. At
first partition the stego-image into pixel blocks , containing two consecutive non-overlapping
pixels each. Calculate the difference value for each block as di'=|pi'-p i+1'|.Then find the optimum
range Ri of d'i . Then b' is obtained by subtracting li from di'. Convert b' into its corresponding
binary of ‘t’ bits, where t=⎿log2 wi ⏌. These t bits are the hidden secret data obtained from the
pixel block(pi',pi+1').
3. PROPOSED METHOD
In PVD method pixel values in the stego image may exceed the gray scale range which is not
desirable as it may leads to improper visualisation of the stego image. In this section we introduce
a method to overcome this problem. In the proposed method we have used the original PVD
method to embed secret data. If any pixel value exceeds the range (0 to 255), then check the bit-
stream ‘t’ to be hidden. If MSB(most significant bit) of the selected bit stream ’t’ is 1 then we
embed one less number of bits, where MSB position is discarded from t; otherwise the bit number
of hidden data depends on wi . For instance, if pixel value exceeds the range and selected bit-
stream t=101, then set t=01 and embed it. If it is seen that the pixel value again exceeding range,
then embed the value at one pixel, rather than both pixels(of the pixel block), which will not
exceed the range after embedding; where the other pixel is kept unchanged. It will keep the pixel
values within the range because both pixels of a block cannot exceed at the same time as per the
PVD method by Wu and Tsai. Keep the information within each block, whether one less bit is
embedded or not, as overhead. The embedding algorithm is presented in section 3.1. Figure 1
shows the block diagram of the embedding algorithm.
3.1. Embedding Algorithm
Step 1: Calculate the difference value di for each block of two consecutive non-overlapping
pixels pi and pi+1 , is given by di=|pi-pi+1|.
Step 2: Find optimal range Ri for the di such that Ri =min(ui-di) , where ui≥di .Then Ri ∈[li , ui] is
the optimum range where the difference lies.
Step 3: Compute the amount of secret data bits t from the width wi of the optimum range, can be
defined as t=⎿log2 wi⏌.
Step 4: Read t bits and convert it into a decimal value b. Then calculate the new difference value
by the formula di'=li+b .
Step 5: Now, calculate the pixel values after embedding t bits (pi' , pi+1')by original PVD method.
Step 6: Check the embedded pixel values whether it exceed the gray-level range or not . If it
exceeds then check the embedded bit-stream t . Otherwise go to step 7.
Step 6.1: If the left most position of the bit-stream is 1 then select ‘t’ by discarding one bit from
its left most position. Convert ‘t’ bits into its corresponding decimal value b and find
new difference value as di'=li+b . Otherwise do not discard any bit from ‘t’ and calculate
di' .
Step 6.2: Calculate new pixel values (pi' , pi+1') using original PVD method and check again if it
is in the gray range. If it is in the range then go to step 7.Otherwise do the following :
(pi' , pi+1')=(pi-m , pi+1), if pi+1 ≥ pi and pi+1 crossing the upper range(i.e 255) ;

(pi ', pi+1')=(pi , pi+1-m), if pi+1<pi and pi crossing the upper range(i.e 255) ;
(pi' , pi+1')=(pi , pi+1+m), if pi+1≥pi and pi crossing the lower range(i.e 0);
(pi ', pi+1')=(pi+m , pi+1), if pi+1<pi and pi+1 crossing the lower range(i.e 0) .
where m=|di'-di| .
Step 7: Now, the pixel block (pi , pi+1) is replaced by (pi' , pi+1').
Step 8: To keep the information whether ‘t’ bits or ‘t-1’ bits has been embedded, do the
following for each modified block :
Step 8.1:
If no bit has been discarded then do the following:
LSB of P'i LSB of P'i+1 then do
i) 0 0 P'i+1 +1
ii) 0 1
a) P'i+1 <255 and P'I ≥ 0 P'i+1 +1
b) P'i >0 and P'i+1 =255 P'i-2 and P'i+1 -1
c) P'i=0 , P'i+1=255 P'i +1
iii) 1 0 P'i -1
iv) 1 1 P'i -1
Step 8.2:
One bit has been discarded
LSB of P'i LSB of P'i+1 then do
i) 0 0 P'i +1
ii) 0 1 P'i +1
iii) 1 0
a) P'i+1 >0 and P'i ≤ 255 P'i+1 -1
b) P'i <255 and P'i+1 =0 P'i+2 and P'i+1+1
iv) 1 1 P'i+1 -1
Step 9: Now we get the stego blocks and hence the stego image.
3.2. Extraction Algorithm
Figure 1 shows the block diagram of the extraction algorithm. The steps used for extracting the
hidden data are as follows :

Step 1: Partition the stego-image into pixel blocks consist of two consecutive non-overlapping
pixels.
Step 2: Check the LSB positions of Pi for each block and do the following :
LSB of Pi Convert it as
0 Pi +1
1 Pi -1
Step 3: Now calculate the difference value di of two consecutive pixels of each block by using the
formula di=|pi-pi+1| .
Step 4: Find the appropriate range Ri for the difference di.
Step 5: Extract ‘t’ bits, by the extracting method of original PVD. where t=⎿log2 wi⏌, wi is
the width of the optimal range Ri .
Step 6: Check the LSB of Pi . If it is 1, replace the MSB position of extracted ‘t’ bits with ‘1’.
Otherwise do nothing.

Fig. 1 Block diagram of embedding and extraction algorithm
Cover
Image C
Partition C into
blocks of two
consecutive pixels
Calculate
difference value di
for each block
Find optimal Ri
for the di
Check whether pixel
value exceed gray
scale range after hiding
secret data by original
PVD
Use original PVD for
data embedding and
modify pixel value
Discard one bit from
MSB and new bit-
stream is used for
embedding
Embed
selected bits
by our method
Keep overhead
information in
each block
Stego
Image
S
Range
table
Check the MSB
of the selected
bit-stream to be
hidden
0
1
No Yes
Partition S into
blocks of two
consecutive pixels
Extract bits as per
original PVD
Replace the MSB
of extracted bit-
stream with 1
Secret
data
Extract bits as per
original PVD
Pi = Pi -1
0
1
Network
Check LSB of 1st
pixel (Pi) for
each pixel bock
Pi = Pi +1

4. EXPERIMENTAL RESULTS
The problem of overshooting gray-level range in PVD has been removed which results no effect
on hiding capacity. we have used C programming language to implement our scheme and Wu-
Tsai’s PVD scheme. The range table width used here are wi ={ 8, 8, 16, 32, 64, 128 }.We have
used cover images of size 512*512 and hide a digital image as the secret information. We have
used the Peak-Signal-to-Noise ratio (PSNR) to evaluate the quality of stego-image. The
experimental results are shown in Fig. 3 and Fig. 4. The comparison, of message capacity and
PSNR value, between proposed method and original PVD method is shown in Table 2. The
PSNR value and capacity of each stego-image is given as average value by executing 10 rounds
using standard digital images where the hidden information are different.
5. Analyses and Discussion
From the experimental results we can see that PSNR values are changing between -0.62 to +0.32
dB and capacity remains same compared to original PVD method. According to the proposed
method, if pixel value exceeds gray scale range, one bit is discarded from the selected bit-stream
to be hidden. So, decimal value of the reduced bits will be half or less than half. As a result the
distortion of the pixel value in the stego-image will be less. On the other hand, for keeping the
overhead information we are adding or subtracting some values with the pixel values. This can
increase the distortion of the image. It should be noted that whether the pixel exceeds range or
not, a track is kept as information in every pixel block. So, for the combined effect PSNR value
somewhere increases and also decreases in some cases but of a little bit.
Steganographic technique of C.M. Wang et al. [11] devised for increased PSNR of the stego
image with pixel value differencing and modulus function. They have also removed the problem
of range overflow in their paper. But the data embedding procedure was completely different
from original PVD devised by Wu and Tsai. So, it can be said that the original PVD was still
carrying the range overflow problem. Therefore we eliminate the problem of original PVD in our
proposed method where as, a completely different technique has been used from the method
proposed by C.M. Wang et al.
In the method of C.M. Wang et al. [11], they have used the pixel value differences to find the
number of embedding bits for each pixel block. Then a modulus function has been applied to
calculate the remainder values as follows;
Prem(i,x)= P(i,x) mod ti'
Prem(i,y)= P(i,y) mod ti [where ti' is the decimal value of secret bits ti ]
Frem(i) = (P(i,x) + P(i,y) ) mod ti'
Secret bit stream is embedded by altering two pixels such that Frem(i)= ti'. There may be eight
different cases for embedding bits to achieve minimum distortion [11].
After the embedding process is over, handling the falling-off boundary problem is done as
follows:
(P''(i,x) , P''(i,y)) = ( P'(i,x) – (2ti
)/2, P'(i,y) – (2ti
)/2 ) ; if P'(i,x)>255 or P'(i,y)>255 and di<128
(P''(i,x) , P''(i,y)) = ( P'(i,x) + (2ti
)/2, P'(i,y) + (2ti
)/2 ) ; if P'(i,x)<0 or P'(i,y)<0 and di<128
(P''(i,x) , P''(i,y)) = ( 0, P'(i,y) + P'(i,x) ) ; if P'(i,x)<0 and P'(i,y)≥ 0 and di>128
(P''(i,x) , P''(i,y)) = ( P'(i,x) + P'(i,y), 0 ) ; if P'(i,x) ≥ 0 and P'(i,y) <0 and di>128
(P''(i,x) , P''(i,y)) = ( 255, P'(i,y) +(P'(i,x)-255)) ; if P'(i,x) >255 and P'(i,y)≥0 and di>128

(P''(i,x) , P''(i,y)) = ( P'(i,x) +(P'(i,y)-255), 255) ; if P'(i,x) ≥0 and P'(i,y) >255 and di>128
In contrast, we have used original PVD method for data embedding and problem of boundary
overshooting has been managed during embedding process. If pixel value overflow, one bit is
discarded from MSB position and rest of the bit-stream is embedded, as shown in embedding
algorithm (section 3.1), if the problem still remains, then it has been handled using the formula
given in step 6.2 of embedding algorithm. Furthermore, we have used the same method, for every
difference value (di), to manage the range of pixel where C.M. Wang et al. used different
techniques for di>128 and di<128. Table 1 gives a comparative statement between C.M. Wang et
al. [11] and proposed methods where less distortions of pixels are occurred.
Table1:Comparison of proposed method with C.M. Wang et al. [11]
Method Input pixel
block
After embedding
‘111’
After managing
overflow
Pixel
distortion
C.M. Wang et
al.[11]
[254 , 255] [255 , 256] [251 , 252] [3 , 3]
Proposed method [254 , 255] [251 , 258] [252 , 255] [2 , 0]
a b
Fig. 3 Cover image and stego-image
a. cover image Lena b. stego-image on embedding 51370 bytes; PSNR is 40.61 dB.
c d
Fig. 4 Cover image and stego-image
c. cover image Elaine d. stego-image on embedding 51070 bytes; PSNR is 41.61 dB
.

Table 2: Comparison of results of the proposed and Wu and Tsai’s method
Cover image (512× 512) Wu and Tsai’s method
Capacity PSNR
Our method
Capacity PSNR
Lena 51370 41.70 51370 40.61
Baboon 57583 36.86 57583 36.67
Tank 50495 42.54 50495 42.05
Airplane 49735 42.31 49735 42.63
Truck 50061 43.05 50061 42.56
Elaine 51070 42.09 51070 41.47
Couple 51600 40.33 51600 40.07
Boat 52631 39.06 52631 39.04
Jet 51020 41.31 51020 40.94
Pepper 51107 40.55 51107 40.61
Capacity in bytes and PSNR in dB and Cover images of size 512*512 .
6. CONCLUSIONS
In this paper, we have discussed a steganographic method for data hiding by using pixel value
differencing which also guarantees that no pixel value will exceed the range 0 to 255 in stego-
image. We have used original PVD method where pixel value does not cross the range, elsewhere
proposed method has been used for embedding data. It gives same hiding capacity as the original
PVD with acceptable stego-image quality.
ACKNOWLEDGEMENTS
The authors express gratitude to the Department of Computer Science and Engineering,
University of Kalyani and the PURSE scheme of DST, Govt. of India, under which the research
has been carried out.
REFERENCES
[1] H.C. Wu, N.I. Wu, C.S. Tsai and M.S. Hwang, “Image steganographic scheme based on pixel value
differencing and LSB replacement method”, IEEE Proceedings on Vision, Image and Signal
processing, Vol. 152, No. 5,pp. 611-615, 2005.
[2] Schneier B.:'Applied cryptography'(John Wiley & Sons, New York, 1996, 2nd
Edn.)
[3] W. bender, D. gruhl, N. Morimoto, A.Lu, “Techniques for data hiding”, IBM Systems Journal Vol.
35(3-4),pp. 313-336, 1996.
[4] F.A.P peticolas, R.J Anderson and M.G. Kuhn, “Information Hiding – a Survey” proceedings of the
IEEE,VOL. 87,PP. 1062-1078, 1999.
[5] Y.K. Lee, L.H. Chen, “High capacity image steganographic model”, IEEE Proceedings on Vision,
Image and Signal processing, Vol. 147, No.3,pp. 288-294, 2000.
[6] R.Z. Wang, C.F. Lin, J.C. Lin, “Image hiding by optimal LSB substitution and genetic algorithm”,
Pattern Recognition Vol. 34, pp. 671-683, 2001.
[7] Tseng, Y.C. , Chen Y.Y. Pan H.K.:'A secure data hiding scheme for binary images', IEEE Trans.
Commun. , 2002, 50,pp. 1227-1231

[8] C.C. Chang, J.Y. Hsiao, C.S. Chan, “Finding optimal least-significant -bit substitution in image
hiding by dynamic programming strategy”, Pattern Recognition Vol. 36, Issue 7,pp. 1583-1595, 2003.
[9] D.C. Wu, and W.H. Tsai, “A Steganographic method for images by pixel-value differencing”, Pattern
Recognition Letters, Vol. 24, pp. 1613-1626, 2003.
[10] C.K. Chan, L.M. Cheng,” Hiding data in images by simple LSB substitution” ,pattern recognition vol.
37, Issue 3,pp. 469-474, 2004.
[11] C.M. Wang, Nan-I Wu, C.S. Tsai, M.S. Hwang, “A high quality Steganographic method with pixel
value differencing and modulus function”, The journal of Systems and software, 2007.
Authors
Dr. Jyotsna Kumar Mandal, M.Tech(Computer Science, University of Calcutta), Ph.
D.(Engg. , Jadavpur University) in the field of Data Compression and Error
Correction Techniques, Professor in Computer Science and Engineering, University
of Kalyani, India. Life member of Computer Society of India since 1992 amd life
member of Cryptology Research Society of India. Dean Faculty of Engineering,
Technology and Management, working in the field of Network Security,
Steganography, Remote Sensing & GIS Application, Image Processing. 25 years of
teaching and research experiences. Eight scholars awarded Ph.D., one submitted and
8 scholars are pursuing. Total number of publications more than 228.
Debashis Das pursuing his M. Tech. in Computer Science and Engineering from
University of Kalyani, under the Department of Computer Science and Engineering.

Steganography Using Adaptive Pixel Value Differencing(APVD) of Gray Images Through Exclusion of Overflow/Underflow

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