Steganography Using Reversible Texture Synthesis

130 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 24, NO. 1, JANUARY 2015
Steganography Using Reversible Texture Synthesis
Kuo-Chen Wu and Chung-Ming Wang, Member, IEEE
Abstract—We propose a novel approach for steganography
using a reversible texture synthesis. A texture synthesis process
resamples a smaller texture image, which synthesizes a new
texture image with a similar local appearance and an arbitrary
size. We weave the texture synthesis process into steganography
to conceal secret messages. In contrast to using an existing cover
image to hide messages, our algorithm conceals the source texture
image and embeds secret messages through the process of texture
synthesis. This allows us to extract the secret messages and
source texture from a stego synthetic texture. Our approach
offers three distinct advantages. First, our scheme offers the
embedding capacity that is proportional to the size of the stego
texture image. Second, a steganalytic algorithm is not likely
to defeat our steganographic approach. Third, the reversible
capability inherited from our scheme provides functionality,
which allows recovery of the source texture. Experimental results
have verified that our proposed algorithm can provide various
numbers of embedding capacities, produce a visually plausible
texture images, and recover the source texture.
Index Terms—Data embedding, example-based approach,
reversible, steganography, texture synthesis.
I. INTRODUCTION
IN THE last decade many advances have been made in
the area of digital media, and much concern has arisen
regarding steganography for digital media. Steganography [1]
is a singular method of information hiding techniques. It
embeds messages into a host medium in order to conceal secret
messages so as not to arouse suspicion by an eavesdropper [2].
A typical steganographic application includes covert commu-
nications between two parties whose existence is unknown to
a possible attacker and whose success depends on detecting
the existence of this communication [3]. In general, the host
medium used in steganography includes meaningful digital
media such as digital image, text, audio, video, 3D model [4],
etc. A large number of image steganographic algorithms have
been investigated with the increasing popularity and use of
digital images [5], [6].
Most image steganographic algorithms adopt an existing
image as a cover medium. The expense of embedding secret
messages into this cover image is the image distortion encoun-
tered in the stego image. This leads to two drawbacks.
Manuscript received July 23, 2013; revised August 30, 2014; accepted
November 6, 2014. Date of publication November 14, 2014; date of current
version December 8, 2014. This work was supported by the Ministry of
Science and Technology, Taiwan, under Grant 101-2221-E-005-091-MY3. The
associate editor coordinating the review of this manuscript and approving it
for publication was Prof. Charles Boncelet.
The authors are with the Department of Computer Science and Engineering,
National Chung Hsing University, Taichung 40227, Taiwan (e-mail:
phd9501@cs.nchu.edu.tw; cmwang@cs.nchu.edu.tw).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIP.2014.2371246
First, since the size of the cover image is fixed, the more secret
messages which are embedded allow for more image distor-
tion. Consequently, a compromise must be reached between
the embedding capacity and the image quality which results
in the limited capacity provided in any specific cover image.
Recall that image steganalysis is an approach used to detect
secret messages hidden in the stego image. A stego image
contains some distortion, and regardless of how minute it is,
this will interfere with the natural features of the cover image.
This leads to the second drawback because it is still possible
that an image steganalytic algorithm can defeat the image
steganography and thus reveal that a hidden message is being
conveyed in a stego image.
In this paper, we propose a novel approach for steganog-
raphy using reversible texture synthesis. A texture synthesis
process re-samples a small texture image drawn by an artist or
captured in a photograph in order to synthesize a new texture
image with a similar local appearance and arbitrary size.
We weave the texture synthesis process into steganography
concealing secret messages as well as the source texture.
In particular, in contrast to using an existing cover image
to hide messages, our algorithm conceals the source texture
image and embeds secret messages through the process of
texture synthesis. This allows us to extract the secret messages
and the source texture from a stego synthetic texture. To the
best of our knowledge, steganography taking advantage of the
reversibility has ever been presented within the literature of
texture synthesis.
Our approach offers three advantages. First, since the texture
synthesis can synthesize an arbitrary size of texture images, the
embedding capacity which our scheme offers is proportional
to the size of the stego texture image. Secondly, a steganalytic
algorithm is not likely to defeat this steganographic approach
since the stego texture image is composed of a source texture
rather than by modifying the existing image contents. Third,
the reversible capability inherited from our scheme provides
functionality to recover the source texture. Since the recovered
source texture is exactly the same as the original source
texture, it can be employed to proceed onto the second round
of secret messages for steganography if needed. Experimental
results have verified that our proposed algorithm can provide
various numbers of embedding capacities, produce visually
plausible texture images, and recover the source texture.
Theoretical analysis indicates that there is an insignificant
probability of breaking down our steganographic approach,
and the scheme can resist an RS steganalysis attack [7].
The remainder of this paper is organized as follows:
in Section II, we review the texture synthesis techniques.
In Section III, we detail our algorithm including embedding
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WU AND WANG: STEGANOGRAPHY USING REVERSIBLE TEXTURE SYNTHESIS 131
and extracting procedures. We describe experimental results
and theoretical analysis in Section IV, followed by our con-
clusions and future work presented in the final section.
II. RELATED WORKS
Texture synthesis has received a lot of attention recently in
computer vision and computer graphics [8]. The most recent
work has focused on texture synthesis by example, in which a
source texture image is re-sampled using either pixel-based or
patch-based algorithms to produce a new synthesized texture
image with similar local appearance and arbitrary size.
Pixel-based algorithms [9]–[11] generate the synthesized
image pixel by pixel and use spatial neighborhood compar-
isons to choose the most similar pixel in a sample texture
as the output pixel. Since each output pixel is determined
by the already synthesized pixels, any wrongly synthesized
pixels during the process influence the rest of the result causing
propagation of errors.
Otori and Kuriyama [12], [13] pioneered the work of
combining data coding with pixel-based texture synthesis.
Secret messages to be concealed are encoded into colored
dotted patterns and they are directly painted on a blank image.
A pixel-based algorithm coats the rest of the pixels using the
pixel-based texture synthesis method, thus camouflaging the
existence of dotted patterns. To extract messages the printout
of the stego synthesized texture image is photographed before
applying the data-detecting mechanism. The capacity provided
by the method of Otori and Kuriyama depends on the number
of the dotted patterns. However, their method had a small error
rate of the message extraction.
Patch-based algorithms [14], [15] paste patches from a
source texture instead of a pixel to synthesize textures. This
approach of Cohen et al. and Xu et al. improves the image
quality of pixel-based synthetic textures because texture struc-
tures inside the patches are maintained. However, since patches
are pasted with a small overlapped region during the synthetic
process, one needs to make an effort to ensure that the patches
agree with their neighbors.
Liang et al. [16] introduced the patch-based sampling
strategy and used the feathering approach for the overlapped
areas of adjacent patches. Efros and Freeman [17] present a
patch stitching approach called “image quilting.” For every
new patch to be synthesized and stitched, the algorithm
first searches the source texture and chooses one candidate
patch that satisfies the pre-defined error tolerance with respect
to neighbors along the overlapped region. Next, a dynamic
programming technique is adopted to disclose the minimum
error path through the overlapped region. This declares an
optimal boundary between the chosen candidate patch and
the synthesized patch, producing visually plausible patch
stitching.
Ni et al. [18] proposed an image reversible data hiding
algorithm which can recover the cover image without any
distortion from the stego image after the hidden data have
been extracted. Histogram shifting is a preferred technique
among existing approaches of reversible image data hiding
because it can control the modification to pixels, thus limiting
the embedding distortion, and it only requires a small size
Fig. 1. Patch, kernel blocks, and source patch. (a) The diagram of a patch.
The central part of a patch is the kernel region; the other part around the kernel
region is the boundary region. (b) An illustration of non-overlapped kernel
blocks subdivided from the source texture. (c) The diagram of source patches
derived by the expanding process using kernel blocks. (d) The boundary
mirroring and expanding for a source patch.
location map, thereby reducing the overhead encountered. The
current state-of-the-art for reversible image data hiding is the
general framework presented by Li et al. [19].
To the best of our knowledge, we were unable to disclose
any literature that related patch-based texture synthesis with
steganography. In this paper, we present our work which
takes advantage of the patch-based methods to embed a
secret message during the synthesizing procedure. This allows
the source texture to be recovered in a message extracting
procedure, providing the functionality of reversibility.
We detail our method in the next section.
III. PROPOSED METHOD
We illustrate our proposed method in this section. First,
we will define some basic terminology to be used in our
algorithm. The basic unit used for our steganographic texture
synthesis is referred to as a “patch.” A patch represents an
image block of a source texture where its size is user-specified.
Fig. 1(a) illustrates a diagram of a patch. We can denote the
size of a patch by its width (Pw) and height (Ph). A patch
contains the central part and an outer part where the central
part is referred to as the kernel region with size of Kw × Kh,
and the part surrounding the kernel region is referred to as the
boundary region with the depth (Pd).
Next, we describe the concept of the kernel block. Given
a source texture with the size of Sw × Sh we can subdivide
the source texture into a number of non-overlapped kernel
blocks, each of which has the size of Kw × Kh, as shown as
Fig. 1(b). Let KB represent the collection of all kernel blocks
thus generated, and KB represent the number of elements in
this set. We can employ the indexing for each source patch kbi,
i.e., KB = {kbi |i = 0 to KB − 1} . As an example, given a
source texture with the size of Sw × Sh = 128×128, if we set
the size Kw × Kh as 32 × 32, then we can generate
KB = 16 kernel blocks. Each element in KB can be
identified as {kb0, kb1, . . . , kb15} .
We can expand a kernel block with the depth Pd at each
side to produce a source patch. The expanding process will
overlap its neighbor block. Fig. 1(c) indicates the boundary
region of source patch sp4 when we expand the kernel block

Fig. 2. The flowchart of the three-process message embedding procedure.
kb4 to overlap the kernel blocks kb0, kb1, kb5, kb8, and kb9.
If a kernel block is located around the boundary of a source
texture, we operate the boundary mirroring using the kernel
block’s symmetric contents to produce the boundary region,
as shown in Fig. 1(d) for the kernel block kb4.
Similar to the kernel block, we can denote SP as the
collection of all source patches and SPn = SP as the number
of elements in the set SP. We can employ the indexing for each
source patch spi, i.e., SP = {spi| i = 0 to SP − 1}.
Given a source texture with the size of Sw × Sh, we can
derive the number of source patches SPn using (1) if a kernel
block has the size of Kw × Kh. In our paper, we assume the
size of the source texture is a factor of the size of the kernel
block to ease the complexity.
SPn =
Sw
Kw
×
Sh
Kh
(1)
Our steganographic texture synthesis algorithm needs
to generate candidate patches when synthesizing synthetic
texture. The concept of a candidate patch is trivial: we employ
a window Pw × Ph and then travel the source texture (Sw ×Sh)
by shifting a pixel each time following the scan-line order.
Let CP = {cpi|i = 0, 1, . . . , CPn − 1} represent the set of the
candidate patches where CPn = CP denotes the number of
elements in CP. We can derive CPn using (2).
C Pn = C P = (Sw − Pw + 1) × (Sh − Ph + 1) (2)
When generating a candidate patch, we need to ensure that
each candidate patch is unique; otherwise, we may extract an
incorrect secret message. In our implementation, we employ
a flag mechanism. We first check whether the original source
texture has any duplicate candidate patches. For a duplicate
candidate patch, we set the flag on for the first one. For the
rest of the duplicate candidate patches we set the flag off to
ensure the uniqueness of the candidate patch in the candidate
list.
A. Message Embedding Procedure
In this section we will illustrate the message embedding
procedure. Fig. 2 shows the three processes of our message
embedding procedure. We will detail each process in the
following sections.
1) Index Table Generation Process: The first process is
the index table generation where we produce an index table
to record the location of the source patch set SP in the
synthetic texture. The index table allows us to access the
synthetic texture and retrieve the source texture completely.
Fig. 3. An illustration of two types of priority locations to paste the
source patches: (a) the first-priority locations L1 and (b) the second-priority
locations L2; (c) 9 source patches using L1 resulting in sparse distribution;
(d) 36 source patches using L1 first, and then employing the L2 leading to
the dense distribution.
Fig. 4. An illustration of composition image; (a) the source texture (96 × 96),
(b) the index table after patch distribution, (c) the composition image
(488 × 488) by referring (a) and (b).
Such a reversible embedding style reveals one of the major
benefits our proposed algorithm offers.
We first determine the dimensions of the index table
(Tpw × Tph). Given the parameters Tw and Th, which are
the width and the height of the synthetic texture we intend
to synthesize, the number of entries in this index table can
be determined using (3) where TPn denotes the number of
patches in the stego synthetic texture. For simplicity, we chose
appropriate parameters for Tw, Th, Pw, Ph, and Pd, so that the
number of entries is an integer. As an example, if Tw × Th =
488 × 488, Pw × Ph = 48 × 48, and Pd = 8, then we can
generate an index table (12 × 12) containing 144 entries.
T Pn = Tpw×Tph =
(Tw−Pw)
(Pw−Pd)
+1 ×
(Th −Ph)
(Ph −Pd)
+1 (3)
When we distribute source texture to achieve the manner
of reversibility, the source patches can be distributed in a
rather sparse manner if the synthetic texture has a resolution
that is much larger than that of the source texture, as shown
in Fig. 3(a). On the contrary, the source patches may be
distributed in a rather dense manner if the synthetic texture
has a resolution that is slightly larger than that of the source
texture, as shown in Fig. 3(b). For the patch distribution,
we avoid positioning a source texture patch on the borders
of the synthetic texture. This will encourage the borders to be
produced by message-oriented texture synthesis, enhancing the
image quality of the synthetic texture. We further define the
first-priority position L1 and the second-priority position L2,
for two types of priority locations where L1 and L2 ,
dervied in (4), represent the number in the first-priority and
second-priority positions, respectively.
⎧
⎨
⎩
L1 =
Tpw−2
2 ×
Tph−2
2
L2 =
Tpw−2
2 ×
Tph−2
2
(4)
Fig. 4 illustrates the composition image where nine
source patches are pasted. As an example, an index table

Tpw × Tph = 12 × 12 contains 144 entries so L1 = 25
and L2 = 25.
Given the number of patches SPn subdivided from the
source texture, the strategy of patch distribution is to distribute
patches perfectly on the first-priority positions before posting
patches on the second-priority positions. Based on the reso-
lution of the synthetic texture, we will have two cases: the
sparse distribution and dense distribution. These are described
below.
When the number of source patches is less than or equal
to the number of the first-priority positions (SPn ≤ L1 ), the
patch will be distributed sparsely. In the security issue section
we describe some mathematical analyses of our algorithm.
The analysis shows that the total number of patterns that
the sparse distribution can offer is C
L1
S Pn
× SPn!. On the
contrary, when the number of source patches is greater than
the first-priority position (SPn > L1 ), the patch will be
distributed densely. A mathematical analysis shows that the
total number of patterns that the dense distribution can offer
is C
L2
S Pn− L1
× SPn!.
The index table has the initial values of −1 for each
entry, which shows that the table is blank. Now, we need to
re-assign values when we distribute the source patch ID in the
synthetic texture. In our implementation, we employ a random
seed for patch ID distribution, which increases the security
of our steganographic algorithm making it more difficult for
malicious attackers to extract the source texture. As a result,
the index table will be scattered with different values as shown
in Fig. 4(b) where we have nine source patches (no. 0 to 8)
and 135 blank locations with the initial value of “−1.” In this
index table, the entries with non-negative values indicate
the corresponding source patch ID subdivided in the source
texture, while these entries with the value of −1 represent
that the patch positions will be synthesized by referring to
the secret message in the message-oriented texture synthesis.
Taking the above condition into consideration, we can now
use the random seed Rs to disarrange the ID of the source
patches subdivided in the source texture. For example, if there
are nine source patches (SPn = 9) and the synthetic texture is
synthesized with a total number of 144 patches (TPn = 144),
we can distribute the disarranged nine IDs of the source
patches resulting in a sparse distribution. Secret messages will
be encoded in the remaining 135 blank locations during the
message-oriented texture synthesis.
2) Patch Composition Process: The second process of our
algorithm is to paste the source patches into a workbench
to produce a composition image. First, we establish a blank
image as our workbench where the size of the workbench is
equal to the synthetic texture. By referring to the source patch
IDs stored in the index table, we then paste the source patches
into the workbench. During the pasting process, if no overlap-
ping of the source patches is encountered, we paste the source
patches directly into the workbench, as shown in Fig. 3(c).
However, if pasting locations cause the source patches to over-
lap each other, we employ the image quilting technique [17]
to reduce the visual artifact on the overlapped area.
3) Message-Oriented Texture Synthesis Process: We have
now generated an index table and a composition image,
TABLE I
A FUNDAMENTAL OF THREE DIFFERENCES BETWEEN THE
CONVENTIONAL TEXTURE SYNTHESIS AND OUR
MESSAGE-ORIENTED TEXTURE SYNTHESIS
Fig. 5. Five different shapes, (a) to (e), of the overlapped area may occur
during our message-oriented texture synthesis algorithm. The blank area inside
the green square frame represents the working location which is going to be
synthesized.
and have pasted source patches directly into the workbench.
We will embed our secret message via the message-oriented
texture synthesis to produce the final stego synthetic texture.
The three fundamental differences between our proposed
message-oriented texture synthesis and the conventional patch-
based texture synthesis are described in Table I. The first
difference is the shape of the overlapped area. During the
conventional synthesis process, an L-shape overlapped area is
normally used to determine the similarity of every candidate
patch. In contrast, the shape of the overlapped area in our
algorithm varies because we have pasted source patches into
the workbench. Consequently, our algorithm needs to provide
more flexibility in order to cope with a number of variable
shapes formed by the overlapped area.
The second difference lies in the strategy of candidate
selection. In conventional texture synthesis, a threshold rank is
usually given so that the patch can be randomly selected from
candidate patches when their ranks are smaller than the given
threshold. In contrast, our algorithm selects “appropriate”
patches by taking into consideration secret messages. Finally,
the output of the conventional texture synthesis is a pure
synthetic texture. However, our algorithm produces a much
different synthetic texture. The source texture being converted
into a number of source patches has been pasted as part of the
contents in the large synthetic texture. In addition, the output
large texture has been concealed with the secret message.
While the conventional texture synthesis algorithm has an
“L-shape” overlapped area, our algorithm may acquire another
four shapes of the overlapped area, as shown in Fig. 5. Assume
that the texture synthesis is carried on using the scan-line
order. The texture area reveals a typical “L-shape” of an
overlapped area, as shown in Fig. 5(a). However, when a
nearby pasted source patch has occupied the right side of
the working location, this leads to a “downward U-shape”
of the overlapped area (Fig. 5(b)). In addition, if a nearby

Fig. 6. The MSEs and rank of patches in the candidate list for the working
location.
pasted source patch has occupied the bottom side, this leads
to a “rightward U-shape” of the overlapped area (Fig. 5(c)).
If a nearby pasted source patch has occupied the lower right
corner of the working location, this leads to a disjointed
overlapped area containing an “L-shape” and a small but
isolated part (Fig. 5(d)). Finally, if two nearby pasted source
patches have occupied the right and bottom side of the working
location, this will contribute to an “O-shape” of the overlapped
area (Fig. 5(e)).
For each candidate patch within the candidate list, one
of the ﬁve shapes of overlapped area described above will
occur when referring to the synthesized area in the working
location. Thus, we can compute the mean square error (MSE)
of the overlapped region between the synthesized area and
the candidate patch. After all MSEs of the patches in the
candidate list are determined, we can further rank these candi-
date patches according to their MSEs. Fig. 6 demonstrates an
example of a candidate list where four candidate patches have
different MSEs. The candidate patch which has the smallest
MSE indicates that this candidate patch is the most similar to
the synthesized area in the working location.
Once the ranks of all candidate patches are determined,
we can select the candidate patch where its rank equals
the decimal value of an n-bit secret message. In this way,
a segment of the n-bit secret message has been concealed
into the selected patch to be pasted into the working location.
In our implementation, we employ a simple but effective
image quilting technique [17] to reduce the visual artifact
encountered in the overlapped area.
B. Capacity Determination
The embedding capacity is one concern of the data embed-
ding scheme. Table II summarizes the equations we described
to analyze the embedding capacity our algorithm can offer.
The embedding capacity our algorithm can offer is related
to the capacity in bits that can be concealed at each patch
(BPP, bit per patch), and to the number of embeddable patches
in the stego synthetic texture (EPn). Each patch can conceal
at least one bit of the secret message; thus, the lower bound of
BPP will be 1, and the the maximal capacity in bits that can be
concealed at each patch is the upper bound of BPP, as denoted
by BPPmax. In contrast, if we can select any rank from the
candidate list, the upper bound of BPP will be log2 (C Pn) .
The total capacity (TC) our algorithm can offer is shown in (5)
which is the multiplciation of BPP and EPn. The number of
the embeddable patches is the difference between the number
of patches in the synthetic texture (TPn) and the number of
TABLE II
THE EMBEDDING CAPACITY PROVIDED BY OUR ALGORITHM
Fig. 7. The ﬂowchart of the four-step message extracting procedure.
source patches subdivided in the source texture (SPn).
T C = BPP × E Pn = BPP × (T Pn − SPn) (5)
Suppose we provide a source texture Sw × Sh = 128 × 128,
and we intend to generate a synthetic texture Tw × Th =
488 × 488. We specify the patch size Pw × Ph = 48 × 48
and the boundary depth Pd = 8 pixels. This will lead to the
range of the BPP between 1 and 12. We can produce
SPn = 16 source patches and TPn = 144 patches on the
stego synthetic texture. Thus, there are EPn = 128 embeddable
patches. If we take the BPP = 12, then the total embedding
capacity is TC = 1536 bits.
C. Source Texture Recovery, Message Extraction,
and Message Authentication Procedure
The message extracting for the receiver side involves
generating the index table, retrieving the source texture,
performing the texture synthesis, and extracting and authen-
ticating the secret message concealed in the stego synthetic
texture. The extracting procedure contains four steps, as shown
in Fig. 7.
Given the secret key held in the receiver side, the same index
table as the embedding procedure can be generated. The next
step is the source texture recovery. Each kernel region with the
size of Kw × Kh and its corresponding order with respect to
the size of Sw ×Sh source texture can be retrieved by referring
to the index table with the dimensions Tpw ×Tph. We can then
arrange kernel blocks based on their order, thus retrieving the
recovered source texture which will be exactly the same as
the source texture. In the third step, we apply the composition

image generation to paste the source patches into a workbench
to produce a composition image by referring to the index table.
This generates a composition image that is identical to the one
produced in the embedding procedure.
The final step is the message extraction and authentica-
tion step, which contains three sub-steps. The first sub-step
constructs a candidate list based on the overlapped area by
referring to the current working location. This sub-step is the
same as the embedding procedure, producing the same number
of candidate lists and their corresponding ranks.
The second sub-step is the match-authentication step. Given
the current working location Cur(WL) on the workbench,
we refer to the corresponding stego synthetic texture at the
same working location Stg(WL) to determine the stego kernel
region SKw × SK h. Then, based on this stego kernel region,
we search the candidate list to determine if there is a patch in
the candidate list where its kernel region is the same as this
stego kernel region. If this patch is available, we refer to it
as the matched patch, and denote it as MKw × MK h. Clearly,
we can locate the rank R of the matched patch, and this rank
represents the decimal value of the secret bits we conveyed
in the stego patch when operating the texture synthesis in the
message embedding procedure. However, if we cannot disclose
any matched patch in the candidate list where the kernel region
is the same as the stego kernel region, it means that the stego
kernel region has been tampered with, leading to a failure of
the message authentication. In this way, we can authenticate
and extract all of the secret messages that are concealed in the
stego synthetic texture patch by patch.
Our method is resistant against malicious attacks as long as
the contents of the stego image are not changed. With some
side information, for example, our scheme can survive the
attacks of the image mirroring or image rotation by 90, 180,
or 270 degrees. Nevertheless, if malicious attacks lead to
alteration of the contents of the stego texture image, the
message authentication step will justify the authenticity of the
secret messages.
IV. EXPERIMENTAL RESULTS AND ANALYSIS
A. Results of the Embedding Capacity
We collect our experimental results on a personal computer
with an i7-2600 3.4GHz CPU and 4GB memory. We adopt
four source textures for the results of our collection. Table III
presents the total embedding capacity our algorithm can pro-
vide when different resolutions of the synthetic texture are pro-
duced by concealing various BPPs. It is interesting to point out
that given a fixed number of BPP, the larger the resolutions of
the source texture Sw ×Sh (96 × 96 vs. 192×192), the smaller
the total embedding capacity (TC) our algorithm will offer
(6160 bits vs. 5890 bits for 10 BPP). This is because the larger
source texture will contain more source patches SPn (9 vs. 36)
that we need to paste which cannot conceal any secret bits.
This will reduce the number of embeddable patches (EPn)
on the composition image (616 vs. 589), thus reducing the
total embedding capacity. Nevertheless, we can employ larger
BPP (11 vs. 14) in order to convey more secret messages
(6776 bits vs. 8246 bits). The maximal capacity provided by
our algorithm is 34398 bits.
TABLE III
TOTAL EMBEDDING CAPACITY IN BITS OUR ALGORITHM CAN PROVIDE
TABLE IV
COMPUTING TIME (SECOND)
We compare our embedding capacity with the work
presented by Otori and Kuriyama [13]. In their algorithm,
a data-coded texture image of 480 × 640 pixels contains
5×5 or 10×10 dotted patterns, thus concealing the capacity in
the range of 200 to 800 bits. In contrast, our scheme conveys
the capacity ranging from 12285 to 34398 bits in a stego
texture synthesis image of 1024 × 1024 pixels. Consequently,
the capacity we offer varies from 4.50 to 50.39 times more
than our counterparts’. Besides, our scheme extracts the secret
messages correctly, while their scheme exhibits a small error
rate when extracting secret messages.
Fig. 8 compares stego synthetic textures with different
capacities. We also present the pure synthetic texture which
does not convey any secret message. No significant visual
difference exists between the two stego synthetic textures
and the pure synthetic texture. In addition, no significant
visual difference can be perceived when comparing two stego
synthetic textures embedded by 5 BPP vs. 10 BPP.
The computing times of Fig. 8 are shown in Table IV. The
range of the computing time is 6.8% to 8.7% more than that
needed for pure texture synthesis. Nevertheless, our algorithm
is flexible enough to provide a different embedding capacity by
simply altering the patch size, satisfying the desirable capacity
or texture quality demanded by users. Also, our algorithm can
retrieve the source texture, making possible the second round
of message embedding using the recovered source texture.
B. Image Quality Comparison
We use several mechanisms to determine the image quality
of the stego synthetic texture. We define the first measure-
ment, which is called the mean squared error of the over-
lapped area (MSEO) to determine the image quality of the
synthetic results. MSEO reflects the similarity between the
candidate patch and the synthesized area where we will

Fig. 8. Comparison results for the pure synthetic texture and two stego synthetic textures with different BPP: (a) source textures, (b) pure synthetic textures,
(c) stego textures with 5 BPP, (d) stego textures with 10 BPP. No significant visual differences exist for these three synthetic textures. The patch size is
Pw × Ph = 48 × 48, the boundary depth is Pd = 8, and the resolutions of the stego synthetic textures are Tw × Th = 1008 × 1008.
specifically operate the image quilting technique during the
message-oriented texture synthesis process. Consequently, the
MSEO has a non-zero value even in the case of the pure patch-
based texture synthesis. If the MSEO produces a small value,
it implies that the synthetic texture shows a high image quality
of the overlapped areas. Obviously, the lower the MSEO value,
the higher quality of the synthetic texture image. The equation
of MSEO is shown in (6), where OLi stands for the overlapped
area of the working location, i, pc
j stands for the pixel j of
the candidate patch in OLi, and ps
j stands for the pixel j of
the synthesized area in OLi.
MSEO =
1
(E Pn)×Pw × Ph
E Pn
i=1 j∈OLi
(pc
j − ps
j )2
(6)
The MSEO can be calculated during the texture synthesis
procedure. When we synthesize a patch, we accumulate the
squared errors of all the pixels in the overlapped area between
the synthesized area and the selected candidate patch. When
the texture synthesis procedure is finished, we can divide the
summation of squared errors by the patch size and the number
of the synthesized patches to produce the MSEO. It comes
as no surprise that the MSEO is dependent on the capacity
per patch.
Table V compares the MSEO to the embedding capacity
for the four test source textures. When we consider the same
patch size, the MSEO increases as we convey more secret bits
per patch. These MSEO values coincide with the image quality
when visualizing the stego synthetic texture. For a larger patch
size, the boundary depth increases leading to a larger MSEO.
Taking the test source texture “peanuts” as an example, the
MSEO is 1034.6 when conveying 5 bits of secret message per
TABLE V
A COMPARISON OF MSEO WITH RESPECT TO EMBEDDING CAPACITY
patch, while it shows the MSEO of 1236.9 when conveying
10 bits per patch. Fig. 8(c) shows a slightly higher visual image
quality than Fig. 8(d).
The second scheme we adopt for measuring the image
quality is the Pearson Product Moment Correla-
tion (PPMC) [20]. It is employed as a measure of how
well two variables are related. The Pearson coefficient values
that this scheme produces are between 1 and −1. A result
of 1 means that there is a perfect positive correlation between
the two variables, while a result between 0.5 and 1.0 represents
a high correlation.
Table VI shows average Pearson coefficients across three
R-G-B channels measured under the base of the histogram
produced for each channel. In Case-A and Case-B, we reveal
the Pearson coefficients between the stego synthetic textures
and the pure synthetic texture. We report in Case-C the
Pearson coefficients between two stego synthetic textures with
different BPPs. The Pearson coefficients shown in Case-A
are very close to 1.0. This represents the high correlation

TABLE VI
COMPARISON OF PEARSON CORRELATION COEFFICIENTS
TABLE VII
COMPARISON OF SSIM INDEX
between the pure and stego synthetic textures. In Case-B,
although the Pearson coefficient values slightly decrease along
with the increase of the embedding capacity per patch, they
retain the feature of a close relation between the pure and stego
synthetic textures. The Pearson coefficients in Case-C are very
close as well, which indicates that the stego synthetic textures
conveying 5 BPP remain highly correlated to those conveying
10 BPP. All the Pearson coefficients shown in this table exhibit
that our steganographic algorithm is effective in producing
stego synthetic textures of high image quality in comparison
to pure synthetic textures produced by conventional texture
synthesis.
Next, we employ the SSIM (Structural SIMilarity)
index [21] to quantify the similarity between the pure and
stego synthetic textures. The SSIM is an image quality assess-
ment method for measuring the change in luminance, contrast,
and structure in an image. The SSIM index is in the range
of [−1, 1] and when it equals to 1, the two images are
identical. Table VII shows the SSIM indices for different patch
sizes. The SSIM index values are close despite their concealing
different embedding capacities. The SSIM algorithm is highly
sensitive to translation, scaling and rotation. This explains the
low index values shown in Table VII because the patch-based
method generates an entirely new synthetic texture image
from a number of patches in the source texture resulting in
a different level of image translation and scaling.
C. Results of Different Message Probabilities
The secret messages consist of bit stream “0” or “1.” The
experimental results shown so far consider that bit “0” or “1”
has equal probability of appearance. However, equal proba-
bility may not be the case for some kinds of information to
be served as a secret message. We generalize our scheme by
considering the probability of appearance.
TABLE VIII
THE PROBABILITY P TO THE MSEO OF THE
STEGO SYNTHETIC TEXTURE
Let p represent the probability of appearance of secret
bit “1.” If we consider two bits of the secret message, then the
probability for bit patterns “00” is (1−p)×(1−p). Let ER(p,2)
represent the expected rank of the selected candidate during
our message-oriented texture synthesis with BPP = 2. Then,
ER(p, 2) can be derived as a function of probability p, as
shown in (7).
E R(p, 2) = 0 × (1− p)(1− p) + 1 × (1− p)p
+ 2× p(1− p) + 3 × p2
=3p (7)
E R(p, k) = (2k
−1)p (8)
In general, when we consider BPP = k bits of the secret
message, we can express the expected rank of a selected
candidate as a more general form, as ER(p, k) shown in (8).
For example, if k = 10 and p = 0.5, ER(0.5, 10) = 511.5.
However, if p = 0.7, then ER(0.7, 10) = 716.1. If we
select the larger rank, the larger MSEO would be expected.
Consequently, the image quality of the synthetic texture is
likely to be worse than the one produced by p = 0.5.
In general, if p is smaller, we are likely to select a better
candidate of patch, which leads to producing a better stego
synthetic texture. Thus, our algorithm is general enough to
cope with the situation when given a variety of p values.
Table VIII shows the MSEO with the different probability p.
The statistics show that this larger probability causes the
increase of MSEO, as expected. This is due to the fact that
when the secret message has the larger probability p, the
candidate patch is likely to be selected at the rear part of
the candidate list, leading to larger MSEO.
To improve the probability of getting better ranks we can
conduct the “probability complement” process to decrease the
MSEO. If the probability p is larger than 0.5, we adopt the
probability of 1-p for message embedding. This can be real-
ized by flipping every bit of the secret message to its reverse
style. During the extraction stage, we extract the secret bit as
usual, and then flip it again to produce the correct message.
With this mechanism, we can ensure that the probability used
for message embedding is always less than or equal to 0.5,
which encourages our scheme to produce a stego synthetic
texture with a smaller MSEO. Clearly, we need to adopt a
secret key to record whether or not we have conducted any
flipping operation.
If we are not able to determine the probability of the secret
message, such as the example of the message being from a
streaming source, then we can use a strategy referred to as
“probability balancing” to produce a nearly even probability

TABLE IX
THE MSEO USING THE PROBABILITY BALANCING STRATEGY
of p = 0.5. In particular, we can conduct an XOR operation
between the previous message clip Mi−1 and the current
message clip Mi . For example, if we want to embed Mi to
patch i, we do the XOR operation and produce Mi where
Mi = Mi ⊕Mi−1. Then, we embed Mi to patch i. In the
extraction procedure, we recover the secret clip Mi with
another XOR operation, where Mi = Mi ⊕ Mi−1. With this
mechanism, we can produce a stego synthetic texture where
its image quality is close to the one produced by p = 0.5,
free from the effect of message probability.
Table IX shows the effect of “probability balancing.” The
results show that all of the MSEOs are close to those produced
with the probability p = 0.5 regardless of using different
message probabilities.
D. Security Issue
In this section we discuss the probability of breaking our
steganographic algorithm in order to produce a correct secret
message. We assume the resolution of the stego synthetic
texture is known by the eavesdropper.
We explain our first level of security. For four possible
squared sizes of the source texture (Sw × Sh), the probability
of breaking down is Pbi = 0.25. The probability of breaking
down five possible squared sizes of the patch (Pw × Ph) is
Pbp = 0.2. Finally, the probability of breaking down ten
possible BPPs from 2-bit to 12-bit is Pbc = 0.1. The total
probability that the eavesdropper can break down the security
of level one is Pbon
1 = Pbi × Pbp × Pbc = 5×10−3.
Next, we discuss the second level of security.
An eavesdropper might be able to perceive the index
table. If the length of the seed used to generate the index
table is a 128-bit sequence, it is highly impossible that this
seed will be revealed. The eavesdropper may try to speculate
about the contents of the index table. For the case of the
sparse distribution, the number of source patches (SPn)
is less than or equal to the number of the first-priority
position ( L1 ). Thus, the total number of patterns offered is
C L1
S Pn
× SPn!. The probability of revealing the correct order
of patches in the index table is shown in (9).
Pb
sp
2 =
( L1 − SPn) !
L1 !
(9)
For the case of the dense distribution, the number of
source patches is larger than the number of the first-priority
position (SPn > L1 ). Therefore, the total number of
permutation patterns that the dense distribution can offer is
C L2
S Pn− L1
× SPn!. Thus, the probability of revealing the
correct order of these IDs in the index table is shown in (10).
Pbde
2 =
(SPn − L1 ) !× ( L2 − SPn + L1 ) !
L2 !×SPn!
(10)
We present two examples to provide more insight for
the sparse distribution. Suppose Tw × Th = 488 × 488,
Pw × Ph = 48 × 48, Pd = 8, and Sw × Sh = 128 × 128,
where the notations of these variables can be referred to
Table II. The eavesdropper can retrieve the number of source
patches as SPn = 16, the dimensions of the index table as
Tpw × Tph = 12 × 12, the number of first-priority positions
L1 = 25, and the number of second-priority positions
L2 = 25. An eavesdropper can realize that the case of
the sparse distribution is being employed. The probability
that the index table is broken down is P
sp
2
∼= 2.35 × 10−20.
Even though the security of level one has collapsed, the
probability that an eavesdropper can retrieve source texture
will be Pbbk = Pbon
1 ×Pb
sp
2 = 1.18 × 10−22.
For the dense distribution we employ a larger source tex-
ture Sw × Sh = 192 × 192. An eavesdropper can retrieve
SPn = 36, Tpw × Tph = 12 × 12, L1 = 25, and
L2 = 25. The probability that an index table has bro-
ken down is Pde
2
∼= 8.70×10−49. The overall probability
that an eavesdropper can retrieve source texture will be
Pbbk = Pbon
1 ×Pde
2 = 4.35×10−51. Both examples illustrate
that even though the security of level one has collapsed, there
is insignificant probability that our steganographic system can
be attacked to retrieve the source texture, and consequently, the
secret message. The analysis indicates that our steganographic
system is secure against a malicious attack.
E. Steganalysis
We have determined so far that our scheme is secure.
However, we need to conduct steganalysis, the art and science
of detecting hidden messages using steganography. While
there are a number of steganalysis algorithms developed,
we employ the RS steganalytic scheme [7] since this algorithm
is well-known, having been adopted for most steganalysis
attacks.
In the RS detection method, the relative number of regular
groups for masks M = [0110] and –M = [0 − 1 − 10] is
denoted as (RM, R−M ), respectively. Similarly, the relative
number of singular groups for masks M and −M is denoted
as (SM , S−M ), respectively. If the magnitude of RM is equal
to that of R−M , or the same equivalence happens to the
singular group (SM , S−M ), the embedded image will pass the
RS steganalysis. Otherwise, it would reveal the presence of
the secret message.
In detection processing, we compute the absolute difference
of the regular group |RM–R−M | and that of the singular group
|SM–S−M | with masks M = [0110] and –M = [0 − 1 − 10].
A small difference usually means that the stego image is more
secure to the RS steganalysis.
Table X shows the detection results for the source texture
“rope net” in three primary color channels. Even though each
patch is concealed with different amounts of secret bits, the
difference between regular group RM and R−M is similar to
the values shown for the pure synthetic texture. This similar
difference invariance reflects for singular groups SM and S−M .
These statistics indicate our message-oriented texture synthesis
algorithm can resist the RS detection attack. This is due to the
fact that the secret bits are concealed by selecting different

TABLE X
THE RS STEGANALYSIS USING “ROPE NET” SOURCE TEXTURE
ranks of candidate patches rather than by modifying their
contents.
V. CONCLUSION AND FUTURE WORK
This paper proposes a reversible steganographic algorithm
using texture synthesis. Given an original source texture, our
scheme can produce a large stego synthetic texture concealing
secret messages. To the best of our knowledge, we are the
first that can exquisitely weave the steganography into a
conventional patch-based texture synthesis. Our method is
novel and provides reversibility to retrieve the original source
texture from the stego synthetic textures, making possible a
second round of texture synthesis if needed. With the two tech-
niques we have introduced, our algorithm can produce visually
plausible stego synthetic textures even if the secret messages
consisting of bit “0” or “1” have an uneven appearance of
probabilities. The presented algorithm is secure and robust
against an RS steganalysis attack. We believe our proposed
scheme offers substantial benefits and provides an opportunity
to extend steganographic applications.
One possible future study is to expand our scheme to
support other kinds of texture synthesis approaches to improve
the image quality of the synthetic textures. Another possible
study would be to combine other steganography approaches
to increase the embedding capacities.
ACKNOWLEDGMENT
The authors would like to thank the anonymous reviewers
for their valuable comments and suggestions. They would also
like to thank Dr. Evelyne Pickett for her enthusiastic assistance
in improving the clarity of this article.
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Kuo-Chen Wu is currently pursuing the
Ph.D. degree with the Department of Computer
Science and Engineering, National Chung Hsing
University, Taichung, Taiwan, where he received
the M.Sc. degree from the Department of Computer
Science and Engineering, in 2006. His current
research interests include computer graphics, color
science, image processing, watermarking, and
steganography.
Chung-Ming Wang (M’96) received the
B.S. degree in applied mathematics from National
Chung Hsing University, Taichung, Taiwan, in
1984, and the Ph.D. degree in computer science
from the University of Leeds, Leeds, U.K., in
1992. From 1986 to 1988, he was a System
Analyst with President Enterprise Cooperation,
Tainan, Taiwan, and PAL Company. He is currently
a Professor with the Department of Computer
Science and Engineering, National Chung Hsing
University. His research interests include computer
graphics, color science, virtual reality, multimedia systems, watermarking,
and steganography. He has received three Dragon Thesis Awards, funded by
the Acer Computers, and two Outstanding Paper Awards from the Computer
Society of the Republic of China (ROC). He is a member of the Association
for Computing Machinery and the IEEE Computer Society.

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