Adaptive data hiding in edge areas of images with spatial lsb domain systems

488 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 3, NO. 3, SEPTEMBER 2008
Adaptive Data Hiding in Edge Areas of Images
With Spatial LSB Domain Systems
Cheng-Hsing Yang, Chi-Yao Weng, Shiuh-Jeng Wang, Member, IEEE, and Hung-Min Sun
Abstract—This paper proposes a new adaptive least-significant-
bit (LSB) steganographic method using pixel-value differencing
(PVD) that provides a larger embedding capacity and impercep-
tible stegoimages. The method exploits the difference value of two
consecutive pixels to estimate how many secret bits will be em-
bedded into the two pixels. Pixels located in the edge areas are em-
bedded by a -bit LSB substitution method with a larger value of
than that of the pixels located in smooth areas. The range of differ-
ence values is adaptively divided into lower level, middle level, and
higher level. For any pair of consecutive pixels, both pixels are em-
bedded by the -bit LSB substitution method. However, the value
is adaptive and is decided by the level which the difference value
belongs to. In order to remain at the same level where the differ-
ence value of two consecutive pixels belongs, before and after em-
bedding, a delicate readjusting phase is used. When compared to
the past study of Wu et al.’s PVD and LSB replacement method,
our experimental results show that our proposed approach pro-
vides both larger embedding capacity and higher image quality.
Index Terms—Adaptive least-significant-bit (LSB) substitution,
pixel-value differencing (PVD), steganography.
I. INTRODUCTION
THE Internet is becoming increasingly popular as a com-
munication channel. However, message transmissions via
the Internet have some problems, such as information security,
copyright protection [1], [2], etc. Therefore, we need a secure
communication method to transmit messages via the Internet.
Encryption is one way. However, encryptions result in a disor-
dered and confusing message and make it suspicious enough
to attract eavesdroppers. Steganographic methods [3]–[8] over-
come this problem by hiding the secret information behind a
cover, and the result does not attract any special attention.
A well-known steganographic method is the least-signif-
icant-bit (LSB) substitution [9]–[11]. This method embeds
secret data by replacing LSBs of a pixel with secret bits
Manuscript received November 1, 2007; revised March 12, 2008. Pub-
lished August 13, 2008 (projected). This research was supported in part by
the National Science Council of the Republic of China under Grants NCS
96-2221-E-153-001 and in part by the TWISC@NCKU, National Science
Council under Grants NSC 96-2219-E-006-009, NSC 96-3114-P-001-002-Y,
and NSC 95-2221-E-015-002-MY2.The associate editor coordinating the
review of this manuscript and approving it for publication was Dr. Hany Farid.
C.-H. Yang is with the Department of Computer Science, National Pingtung
University of Education, Pingtung, 900, Taiwan (e-mail: chyang@mail.npue.
edu.tw).
C.-Y. Weng and H. M. Sun are with the Department of Computer Science,
National Tsing-Hua University, Hsinchu, 300, Taiwan, R.O.C. (e-mail: cy-
weng@is.cs.nthu.edu.tw; hmsun@cs.nthu.edu.tw).
S.-J. Wang, corresponding author, is with the Department of Information
Management, Central Police University, Taoyuan, 333, Taiwan, R.O.C. (e-mail:
sjwang@mail.cpu.edu.tw).
Digital Object Identifier 10.1109/TIFS.2008.926097
directly. However, not all pixels can tolerate an equal amount of
change. As a result, many new sophisticated LSB approaches
have been proposed to improve this drawback [12], [13]. Some
of these methods use the concept of human vision to increase
the quality of the stegoimages [14]–[16].
In 2003, Wu and Tsai proposed a “pixel-value differencing”
steganographic method that uses the difference value between
two neighbor pixels to determine how many secret bits should
be embedded [17]. In 2005, Wu et al. proposed the pixel-value
differencing (PVD) and LSB replacement method [18]. In their
approach, two pixels are embedded by the LSB replacement
method if their difference value falls into a lower level. Simi-
larly, the PVD method is used if the difference value falls into
a higher level. If the embedding result causes the difference
value to change from the lower level to the higher level, the
two pixels values need to be readjusted such that their differ-
ence value comes back to the lower level. Usually, the edge areas
can tolerate more changes than the smooth areas. Consider the
past studies, such as Wu et al.’s scheme [18], that would cause
pixels located in the lower level to embed more data than that in
the higher level. Next, the scheme in [19] provided the analyses
of the PVD and LSB replacement to significantly improve the
works in [18].
In 2005, Park et al. proposed a steganographic scheme based
on the information of neighboring pixels [20]. In their approach,
the number of bits embedded into a target pixel is deter-
mined by the difference value of its neighboring pixels and
, where is the upper pixel of and is the left pixel of
. Their approach is similar to Chang and Tseng’s side-match
method [14]. However, their is embedded by LSB methods
and Chang and Tseng’s is embedded by PVD methods. The
embedding capacity of Park et al.’s method is far less than that
of Wu et al.’s PVD and LSB replacement method [18], [20].
It is an important topic to find an adaptive steganographic
method, which embeds data adaptively by considering the con-
cept of human vision, with the features of high capacity and low
distortion. A lot of approaches, including LSB techniques, PVD
techniques, and side-match techniques have been proposed to
this topic [14]–[20]. Nevertheless, some of them seemed not to
provide efficient capacities [14], [20], and not completely obey
the principle that the edge areas can tolerate more changes than
smooth areas [18], [19]. The fundamental analyses were also
not discussed in past studies. In this paper, a novel adaptive
steganographic method for hiding data in gray images is pro-
posed. Our method obeys the basic concept that edge areas can
tolerate more changes than smooth areas, and our method can
embed a large number of secret data and maintain high qualities
of the stegoimages. First, some ranges are predefined by users.
1556-6013/$25.00 © 2008 IEEE

YANG et al.: ADAPTIVE DATA HIDING IN EDGE AREAS OF IMAGES WITH SPATIAL LSB DOMAIN SYSTEMS 489
Fig. 1. Wu et al.’s division of “lower level” and “higher level” (Div = 15).
Then, all pixels are embedded by the LSB replacement method
with different numbers of secret bits. Given two neighbor pixels,
the number of embedding bits is evaluated by the range which
their difference value falls into. In addition, in order to increase
the quality of stegoimages, a more skilful method is proposed to
readjust the pixel values when embedding results cause the dif-
ference values to fall into another range. Besides, perspective
views to usher in our contributions are presented in a series of
proof-based discussions in this paper.
The remainder of this paper is organized as follows.
Wu et al.’s pixel-value differencing and LSB replacement
method is introduced in Section II. Our proposed method is
presented in Section III, and the experimental results are shown
in Section IV. The key fundamentals related to our ideas are
discussed in lemmas and theorems, shown in Section V. Finally,
conclusions are given in Section VI.
II. LITERATURE REVIEW
In this section, Wu et al.’s PVD and LSB replacement method
[18] is followed first. Their approach uses gray-level images as
cover images. First, the cover image is partitioned into nonover-
lapping blocks with two consecutive pixels, and a division (Div)
is used to partition the range [0, 255] into a “lower level” and
a “higher level.” For example, as shown in Fig. 1, Div is 15;
therefore, the lower level includes range , and the higher
level includes ranges , and . Then, for the block
with pixels and , the difference value is calculated by
, and the range which falls into is determined. If
the difference value belongs to the higher level, the embed-
ding method is the same as the pixel-value differencing. Oth-
erwise, the difference value belongs to the lower level, and
and are embedded by the 3-b LSB substitution method.
Let and be the embedded results of and , re-
spectively. Note that the LSB substitution method may cause
the new difference value to fall into the higher level. There-
fore, if the new difference value (i.e., higher
level), (1) is used to readjust and . After the readjusting
operation, the new difference then belongs to the lower level
if
if
(1)
For example, assume that , and
secret data . The difference value is calculated
by , which belongs to the lower level. Therefore,
the 3-bit LSB substitution method is used to embed
into pixels and . After being embedded, and
. Thus, . After being readjusted,
and . Hence, the new difference value is
, which belongs to the lower level.
III. OUR PROPOSED APPROACH
The embedding strategy of our adaptive LSB substitution ap-
proach is based on the concept that edge areas can tolerate a
larger number of changes than smooth areas. Similar to Wu and
Tsai’s scheme [17], pixel-value differencing is used to distin-
guish between edge areas and smooth areas. The range [0, 255]
of difference values is divided into different levels, for instance,
lower level, middle level, and higher level. For any two consec-
utive pixels, both pixels are embedded by the -bit LSB substi-
tution, but the value is decided by the level which their differ-
ence value belongs to. A higher level will use a larger value of .
In order to improve the quality of the stegoimages, we apply the
well-known LSB substitution method, called the modified LSB
substitution method [8], [11]. The concept of the modified LSB
substitution is to increase or decrease the most-significant-bit
(MSB) part by 1 for reducing the square error between the orig-
inal pixel and the embedded pixel. In order to extract data ex-
actly, the difference values before and after embedding must
belong to the same level. If the difference value changes into an-
other level after embedding, a readjusting phase is used to read-
just the pixel values. The embedding and extracting procedures
of our approach are described in the following subsections.
A. Embedding Procedure
The cover images used in our method are 256 gray values.
The difference value is computed for every nonoverlapping
block with two consecutive pixels. The way of partitioning the
cover image into two-pixel blocks runs through all of the rows
in a raster scan. Prior to the embedding procedure, the range [0,
255] must be divided into different levels. Fig. 2 shows two di-
viding cases: an - division and an - - division. In Fig. 2(a),
the first case has one dividing line , which divides the
range [0, 255] into ranges and ,
where the lower level contains and the higher level contains
. Similarly, in Fig. 2(b), the second case has two dividing
lines; and , which divide range [0, 255]
into ranges , and ,
where , and belong to the lower level, middle level,
and higher lever, respectively. The width of range is denoted
as . For example, , and
are shown in Fig. 2(b). The - - division means that two-pixel
blocks with difference values falling into the lower level, middle
level, and higher level, will be embedded by the -bit, -bit and
-bit LSB substitution approaches, respectively. Since the edge

Fig. 2. Two dividing cases: (a) “lower level” and “higher level” and (b) “lower
level,” “middle level,” and “higher level.”
areas can tolerate a larger number of changes, the proper rela-
tions of values , and in Fig. 2(a) and (b) are and
, respectively. In addition, to succeed in the read-
justing phase, we apply the restrictions and
to the - division, and restrictions
and to the - - division. Examples in
Fig. 2(a) and (b) show a 2–3 division and a 3-4-5 division, re-
spectively. For each block, the detailed embedding steps for an
- - division are as follows.
Step 1) Calculate the difference value for each block with
two consecutive pixels, say and , using
.
Step 2) From the - - division, find out the level to which
belongs to. Let , and , if belongs
to the lower level, middle level, and higher level,
respectively.
Step 3) By the -bit LSB substitution method, embed se-
cret bits into and secret bits into , respec-
tively. Let and be the embedded results of
and , respectively.
Step 4) Apply the modified LSB substitution method to
and .
Step 5) Calculate the new difference value by
.
Step 6) If and belong to different levels, execute the
readjusting phases as follows.
Case 6.1 lower-level, lower level.
If , readjust to being the
better choice between and
; otherwise, readjust to be
the better choice between and
.
Case 6.2 middle level, lower level.
If , readjust to be the
; otherwise, readjust
to be the better choice between
and .
Case 6.3 middle level, higher level.
and .
Case 6.4 higher level, higher level.
and .
In Step 6), the better choice, say , means that it
satisfies the conditions that and belong to the
same level and , also the value of
is smaller.
For instance, consider the 3-4-5 division shown in Fig. 2(b)
with , and secret data .
First, the difference value is calculated by .
Since is the middle level, pixels and are em-
bedded by the 4-bit LSB substitution and have results
and . After the modified LSB substitution is ap-
plied, and . Now,
belongs to the lower level. In the readjusting phase, Case
6.2 is executed. There are two readjusting results to be chosen
and . The first result is the better
choice, that is, . Hence,
belongs to the middle level.
B. Data Extraction
The stegoimage is partitioned into nonoverlapping blocks
with two consecutive pixels, and the process of extracting the
embedded message is the same as the embedding process with
the same traversing order of blocks. Also, the same - -
division, which is used in the embedding procedure, is used
here. For each block, the detailed steps of data extracting are as
follows.
Step 1) Calculate the difference value for each block with
two consecutive pixels, say and , using
.
Step 2) From the - - division, find out the level to which
belongs to. Let , and if belongs
to the lower level, middle level, and higher level,
respectively.
Step 3) From the -bit LSB of a pixel, extract secret bits
from and secret bits from .
The embedding example shown in the previous subsection is
extracted here, where a 3-4-5 division is used and there is a block
with . For this block,
belongs to the middle level. Therefore, . There are 4 bits
embedded in and 4 bits embedded in . Thus, secret bits
1010 can be extracted from and secret bits can be
extracted from .
IV. EXPERIMENTAL RESULTS
In this section, we present some experiments to demonstrate
that our adaptive LSB substitution approach is better than Wu et
al.’s approach. Ten cover images with size 512 512 are used
in the experiments, and two of them are shown in Fig. 3. A series
of - divisions and - - divisions with various dividing lines
are used in the experiments. We use the peak signal-to-noise
ratio (PSNR) to evaluate qualities of the stegoimages. Experi-
mental results of two stegoimages are shown in Fig. 4, where
a 3-4 division with is used. Also, two stegoimages

Fig. 3. Two cover images. (a) Elaine. (b) Baboon.
Fig. 4. Two stegoimages created by our approach with 3-4 division and D =
7. (a) Elaine (embedded data are 883 196 bits, PSNR is 33.52 dB). (b) Baboon
(embedded data are 916 010 bits, PSNR is 33.01 dB).
Fig. 5. Two stegoimages created by our approach with 3-4-5 division D =
15 and D = 31. (a) Elaine (embedded data are 816 956 bits, PSNR is 37.82
dB). (b) Baboon (embedded data are 874 642 bits, PSNR is 34.84 dB).
TABLE I
RESULTS OF CAPACITIES AND PSNRS USING VARIOUS l-h
DIVISIONS WITH DIVIDING LINE D = 7
are shown in Fig. 5, where a 3-4-5 division with and
are used. More experimental results using various -
divisions with dividing line are shown in Table I. Also,
experimental results using various - divisions with dividing
line are shown in Table II. All results of capacities
and PSNRs are the averages of results created by executing dif-
ferent random bit streams 100 times. Table III shows the com-
parisons between the results of our proposed approach and that
of Wu et al.’s, in which our approach uses a 3–4 division with
and a 3-4-5 division with and .
From Table III, we can see that our approach results in not only
more capacity but also better quality. On average, our approach
with 3–4 division obtains 49 997 more bits than Wu et al.’s;
moreover, the PSNR value increases by 4.15 dB. For the case of
the 3-4-5 division, our approach results in 58 441 more bits, and
the PSNR value increases by 0.36 dB, on average. In addition,
other noticeable image quality measures, such as mean square
error (MSE) and image fidelity (IF) [21] are also applied to our
method indicating the significance we contribute in this paper.
As shown in Table IV, it demonstrates that our approach has a
characteristic of imperceptibility. Since IF values are close to 1,
it shows that our stegoimages remain as high fidelity. Besides,
from MSE values, it shows that the changed value of each pixel
is between 3 and 6 on average.
V. FUNDAMENTALS AND DISCUSSIONS
In this section, we show that our approach can embed data
and extract data correctly, and give some discussions. First of
all, the restrictions of our approach are shown here. For an - -
division, let ranges , and be the ranges of lower level,
middle level, and higher level, respectively. In order to apply the
- - division at our approach reasonably and correctly, some
restrictions are given to our approach and all theorems in this
section. The restrictions are
,
and . The restriction means
that the -bit modified LSB substitution used in our approach
must have .
In the following theorems, we show that our approach suc-
ceeded in embedding and extracting by proving that the read-
justing phase works.
Definition 1: For the -bit modified LSB substitution, the
range is called the Bottom extreme range and the range
is called the Top extreme range. Both of the
aforementioned ranges are called extreme ranges.
For the example of the 5-bit modified LSB substitution, range
is the Bottom extreme range and range is the
Top extreme range.
Definition 2: For the -bit modified LSB substitution, pixel
is modifiable if does not belong to the extreme ranges.
Note that if is modifiable, the MSB part of can be used
to reduce the difference between original and embedded
whenever it is needed. For instance, and secret
data , then is the embedded result
using the 4-bit simple LSB substitution. Now, the MSB part of
is decreased by 1, which causes to reduce
the difference between and . Therefore, is modifiable. In
another example, assume and secret data
, then is the embedded result using the
4-bit simple LSB substitution. Now, the MSB part of cannot
be used to reduce the difference between and . Therefore,
is not modifiable.
Lemma 1: For the -bit modified LSB substitution, if pixel
is modifiable, then .
Proof: After the -bit simple LSB substitution, the em-
bedded result has . The range
is divided into three ranges,

TABLE II
RESULTS OF CAPACITIES AND PSNRS USING VARIOUS l-h DIVISIONS WITH DIVIDING LINE D = 15
TABLE III
COMPARISONS OF THE RESULTS BETWEEN WU ET AL.’S METHOD AND OURS,
WHICH USE A 3–4 DIVISION WITH D = 15 AND A 3–4–5 DIVISION
WITH D = 15 AND D = 31
TABLE IV
RESULTS OF MEAN SQUARE ERROR (MSE) AND IMAGE FIDELITY (IF)
USING A 3–4 DIVISION WITH D = 15 AND A 3–4–5 DIVISION
WITH D = 15 AND D = 31
, and ,
to be considered.
1) : can be modified as
such that .
2) : nothing to do.
3) : can be modified as
such that .
From the aforementioned discussions, we have
.
Lemma 2: Suppose that and are modifiable and
are embedded by -bit modified LSB substitution. Then
.
Proof: From Lemma 1, we know that
and
Without loss of generality, let . Therefore
Also, . We have
Theorem 1: Suppose that and are modifiable and are
embedded by the -bit modified LSB substitution, where their
difference value belongs to range and . Then,
the readjusting phase works.
Proof: In the conditions that and fall into different
ranges, Fig. 6(a), (b), and (d) shows the cases where belongs
to the lower level, middle level, and higher level, respectively.
From Lemma 2, the maximum difference between and is
, which has been pointed out in Fig. 6. Since
and can go back to the range which belongs to
by moving one of and at distance . Now, we show
that at least one of and can move by . Without loss of
generality, let . We discuss the cases of Fig. 6 one by
one.
Case of Fig. 6(a):

Fig. 6. Cases that d and d fall into difference ranges, where pixel p and p
are modifiable and are embedded by k-bit modified LSB substitution: (a)d 2
lower level. (b) One case of d 2 middle level. (c) The other case of d 2
middle level. (d) d 2 higher level.
Fig. 7. Corresponding moving operations of p and p in Fig. 6: (a) d 2
lower level, (b) one case of d 2 middle level, (c) the other case of d 2 middle
level, and (d) d 2 higher level.
Since , we have .
Therefore, both and can move by . The condition
and moving directions are shown in Fig. 7(a).
Fig. 8. Ranges of ppp and ppp , where ppp belongs to the extreme ranges.
Case of Fig. 6(b):
Let be the width of and be the width of
. Since , we have . Therefore
Therefore, at least one and can move by .
Fig. 7(b) shows the condition.
Case of Fig. 6(c):
Since , we have .
Therefore, and can move by . Fig. 7(c) shows
the condition.
Case of Fig. 6(d):
Let be the width of and be the width of
.
Since , we have .
Two restrictions are needed in this theorem: 1)
and 2) .
They imply that .
Thus, .
Therefore, at least one of and can move by .
Fig. 7(d) shows the condition.
From Definition 1, we have the following two Lemmas.
Lemma 3: For -bit modified LSB substitution, if Bottom
extreme range, the embedded result has
. If Top extreme range, the embedded result has
.
Lemma 4: For -bit modified LSB substitution, if Bottom
extreme range, the embedded result has . If
Top extreme range, the embedded result has
.
Fig. 8 points out the ranges of and , where belongs to
the extreme ranges.
Lemma 5: Suppose that only one of and is not mod-
ifiable, and and are embedded by -bit modified LSB
substitution. Then, .
Proof: Without loss of generality, let . Suppose
that Bottom extreme range and does not belong to
extreme ranges.
From Lemmas 1 and 3, we have

Therefore
On the other hand, suppose that does not belong to the
extreme ranges and Top extreme range.
From Lemmas 1 and 3, we have
Therefore
Theorem 1 has shown that our approach is correct if none
of and belong to the extreme ranges. Now, we discuss
the cases that at least one of and belong to the extreme
ranges. Without loss of generality, let . These cases
are divided into three categories: 1) Category A, 2) Category B,
and 3) Category C, as follows:
Category A: Bottom extreme range or
Top extreme range.
We just show the case of Bottom extreme range.
The proof of the other case is similar.
1) lower-level.
From Deﬁnition 1, we have and
.
From Lemma 4, we have and
.
Therefore, .
and there is no need to readjust.
2) middle level. middle level
(a)
Also, we have and .
Therefore (b)
From (a) and (b), we have
(c)
(d)
From (c) and (d), we have
(e)
From (d), we have
.
Thus, or .
If , from (e), can be readjusted by moving one
of and at distance . Similar to Fig. 7(b), at least
one of and can move by .
Therefore, the readjusting phase works. On the other hand,
if , there is no need to readjust.
3) higher level.
From Deﬁnition 1, we have and
.
Therefore, .
.
Therefore, .
From and , we obtain
If , there is no need to readjust. On the other hand,
if can be readjusted by moving one of and
at distance . Similar to Fig. 7(d), at least one of
and can move by . Therefore, the readjusting phase
works.
Category B: Bottom extreme range and extreme
ranges, or extreme ranges and Top extreme range.
From Lemma 5, we have
1) lower level.
Fig. 9(a) shows the possible location of . Therefore, if
can go back to by moving one at
distance . Thus, the readjusting phase works.
2) middle level.
Fig. 9(b) shows the possible location of .
If , any can go back to by moving
one of and at distance . Thus, the readjusting
phase works.
If , there are two conditions of .
Condition 1: .
In this condition, any can go back to by moving
one and at distance . Thus, the readjusting phase
works.
Condition 2: .
In this condition, and moving one of and
by is not enough to send to . Even worse, one
and cannot move by for the reason that one and
belong to the extreme ranges. Our readjusting phase
cannot work in this condition. However, we propose a more
sophisticated readjusting phase, which applies the method
of pixel-value shifting [16] to solve this condition later.
3) higher level.
Fig. 9(c) shows the possible location of .

Fig. 9. Relative positions of d and d , where pixel ppp and p are embedded
by k-bit modified LSB substitution: (a) d 2 lower level. (b) d 2 middle-level.
(c) d 2 higher level.
If , any can go back to by
moving one and at distance . Thus, the readjusting
phase works.
If , there are two conditions of .
Condition 1: .
Similar to previous Condition 1, the readjusting phase works.
Condition 2: .
Similar to previous Condition 2, a more sophisticated read-
justing phase is needed.
Category C: Bottom extreme range and Top
extreme range.
From Definition 1, we have
and
and
where
Therefore,
From Lemma 4, we have
and
where
Therefore, there is no need to readjust.
From the aforementioned discussion, we have the following
theorem.
Theorem 2: For an - - division, the readjusting phase
works if and .
It is very clear that all divisions used in Section IV satisfy
Theorem 2. Therefore, all experimental cases in Section IV can
be executed correctly.
Now, we give an example to demonstrate that the readjusting
phase cannot work if the conditions in Theorem 2 are not sat-
isfied. Then, the example is solved by the sophisticated read-
justing phase, which shifts and parallelly and moves
and by in different directions. The example given here is
in the Condition 2 of Category B3). Suppose that the 3-4-5 divi-
sion has and . Note that
, and . Therefore, . Let
, and secret data . First,
we calculate the difference value , and find
out that higher level. Therefore, . Note that
Bottom extreme range for the reason that .
Also, extreme ranges for the reason that
and . After the 5-bit modified LSB sub-
stitution, and . Now,
belongs to the lower level. In the readjusting phase, Case 6.2 is
executed. There are two readjusting choices and
. Both choices fail, because the resulting pixel does
not fall into [0, 255] or the resulting . Therefore, the
readjusting phase cannot work.
Now, we solve the problem of the aforementioned example
by the sophisticated readjusting phase. It is executed by the fol-
lowing steps.
Step 1) Pixel-value shifting.
Both and are shifted by . Therefore,
and .
Step 2) Embedding.
Both shifted and are embedded by -bit
modified LSB substitution. After 5-bit-modified
LSB substitution, we have and .
Step 3) Readjusting.
If and belong to different ranges, the read-
justing phase is applied. Now,
and , therefore the
readjusting phase is applied and Case 6.4 is ex-
ecuted. There are two choices and
. The better choice is
. Thus,
belongs to the higher level.
With the sophisticated readjusting phase, which is
used whenever Conditions 2 of Categories B2) and
B3) occur, we have the following corollary.
Corollary 1: For a - - division, the sophisticated read-
justing phase, which involves the technique of pixel-value
shifting, can work.
Proof: Without loss of generality, let . Note that
the sophisticated readjusting phase is only applied in Category
B. We prove this corollary by showing that if and in
Category B are shifted, the shifted results have extreme
ranges and extreme ranges.
In Category B, let Bottom extreme range and
extreme ranges. That is, and
. In the left side of Fig. 10(a), the robust line is

Fig. 10. Discussed ranges of p and p . (a) P 2 bottom extreme range and
p =2extreme ranges. (b) p =2extreme ranges and p =2top extreme range.
the range of and the total line, including the robust
line and the dotted line, is the range of embedded result . The
real values shown in Fig. 10 are for the case . It is clear that
the shifted result of does not belong to the extreme ranges.
Also, in the right side of Fig. 10(a), the robust line is the range
in which cannot be
shifted by adding or will be shifted into Top extreme range,
and the total line, including the robust line and the dotted line,
is the range of the embedded result , where falls into
the range of the robust line. Therefore, if
, the sophisticated readjusting phase may
fail.
Now we show that the shifting operation is never executed
when and
. Note that
Therefore, or
It occurs only when . Also, it must be the case that
, and . In
this case
and
From Fig. 9(b), the readjusting phase cannot work if is too
small to go back to . Note that the smallest is
Therefore, there is no need to readjust and no need to shift
From Fig. 9(c), the readjusting phase cannot work. is too
small to go back to . Therefore, we consider the smallest
and show that it can go back to by readjusting. The smallest
appears when . At , we have
It means that can go back to by moving one of and
at distance . Therefore, the shifting operation is not needed.
The proof of the other case that extreme ranges and
Top extreme range is similar. Fig. 10(b) shows the sim-
ilar condition.
VI. CONCLUSIONS AND FUTURE WORK
In this paper, we propose a new adaptive LSB substitution
method to embed secret data into gray images without making
a perceptible distortion. Pixels located in edge areas are em-
bedded by -bit LSB substitution method with a larger value
of than that of the pixels located in smooth areas. The PVD
approach is used to distinguish between edge areas and smooth
areas, and the level of difference value is defined by the user.
Also, a delicate readjusting phase is proposed to maintain the
same level to which the difference value of a pair of pixels be-
longs to, before and after embedding. Experimental results show
that our approach obtains both larger capacity and higher image
quality than that of Wu et al.
Our approach majors in more significant promotion in the
terms of adaptability, capacity, and imperceptivity. The relative
attacks to either destroy or detect the embedding information
are not given in this paper. It can be further incorporated in fu-
ture works with attack-resistant discussions besides the merits
achieved in this paper. With regard to the division experiments,
some - divisions and - - divisions both yielded higher ca-
pacity and higher PSNR. It remains an open issue to find a
method, where the cover images can be analyzed automatically,
aiming to capture an adequate - - division satisfying the key
requirements in information hiding.
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Cheng-Hsing Yang received the B.S. and M.S. de-
grees in applied mathematics from National Chung-
Hsing University, Hsinchu, Taiwan, R.O.C., in 1980
and 1992, respectively, and the Ph.D. degree in elec-
trical engineering from National Taiwan University,
Taiwan, R.O.C., in 1997.
Currently, he is an Associate Professor in the
Department of Computer Science, National Ping-
tung University of Education, Pingtung, Taiwan. His
current research interests include information hiding
and image watermarking.
Chi-Yao Weng received the M.S. degree in com-
puter science from National Pingtung University of
Education, Pintung, Taiwan, in 2007, and is currently
pursuing the Ph.D. degree in computer science from
National Tsing Hua University, Hsinchu, Taiwan,
R.O.C.
His current research interests include data hiding,
steganography, and image processing.
Shiuh-Jeng Wang (M’99) was born in Taiwan,
R.O.C., in 1967. He received the M.S. degree in
applied mathematics from National Chung-Hsing
University, Taichung, Taiwan, R.O.C., in 1991 and
the Ph.D. degree in electrical engineering from
National Taiwan University, Taipei, in 1996.
Currently, he is a Full Professor with the Depart-
ment of Information Management at Central Police
University, Taoyuan, Taiwan, where he directs the In-
formation Cryptology and Construction Laboratory.
His research interests include information security,
digital investigation and computer forensics, steganography, cryptography, data
construction, and engineering.
Dr. Wang was a recipient of the ﬁfth Acer Long-Tung Master Thesis Award
and the tenth Acer Long-Tung Ph.D Dissertation Award in 1991 and 1996, re-
spectively. He was a Visiting Scholar with the Computer Science Department at
Florida State University, Tallahassee, FL, in 2002 and 2004, respectively, and a
Visiting Scholar in the Department of Computer and Information Science and
Engineering at the University of Florida (UF), Gainesville, from 2004 to 2005.
He was the Editor-in-Chief of the Communications of the CCISA in Taiwan from
2000 to 2006. He was the Panel Director of Chinese Cryptology and Information
Security Association (CCISA) since 2006. He academically toured the CyLab
with School of Computer Science with Carnegie Mellon University, Pittsburgh,
PA, in 2007 for international project collaboration inspection. He is also the au-
thor/coauthor of six books (written in Chinese): Information Security, Cryptog-
raphy and Network Security, State of the Art on Internet Security and Digital
Forensics, Eyes of Privacy-Information Security and Computer Forensics, In-
formation Multimedia Security, and Computer Forensics and Digital Evidence
published in 2003, 2004, 2006, and 2007, respectively. He is a member of the
ACM.
Hung-Min Sun received the B.S. degree in applied
mathematics from National Chung-Hsing University,
Taiwan, R.O.C., in 1988, the M.S. degree in applied
mathematics from National Cheng-Kung University,
Taiwan, R.O.C., in 1990, and the Ph.D. degree in
computer science and information engineering from
National Chiao-Tung University, Taiwan, in 1995,
respectively.
He was an Associate Professor with the De-
partment of Information Management, Chaoyang
University of Technology, Taiwan, from 1995 to
1999, and the Department of Computer Science and Information Engineering,
National Cheng-Kung University, from 1999 to 2002. Currently, he is an
Associate Professor with the Department of Computer Science, National
Tsing Hua University. He has published more than 100 international journal
and conference papers. His research interests include information security,
cryptography, network security, multimedia security, and image compression.
Dr. Sun was the Program Co-Chair of the 2001 National Information Security
Conference and the program committee member of the 1997 and 2005 Informa-
tion Security Conference; 2000 Workshop on Internet and Distributed Systems;
2001, 2002, and 2005 Workshop on the 21st Century Digital Life and Internet
Technologies; 1998-1999 and 2002-2008 National Conference on Information
Security, and ACISP’04.

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