steganography using reversible texture synthesis

130 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 24, NO. 1, JANUARY 2015

Steganography Using Reversible Texture SynthesisKuo-Chen Wu and Chung-Ming Wang, Member, IEEE

Abstract— We propose a novel approach for steganographyusing a reversible texture synthesis. A texture synthesis processresamples a smaller texture image, which synthesizes a newtexture image with a similar local appearance and an arbitrarysize. We weave the texture synthesis process into steganographyto conceal secret messages. In contrast to using an existing coverimage to hide messages, our algorithm conceals the source textureimage and embeds secret messages through the process of texturesynthesis. This allows us to extract the secret messages andsource texture from a stego synthetic texture. Our approachoffers three distinct advantages. First, our scheme offers theembedding capacity that is proportional to the size of the stegotexture image. Second, a steganalytic algorithm is not likelyto defeat our steganographic approach. Third, the reversiblecapability inherited from our scheme provides functionality,which allows recovery of the source texture. Experimental resultshave verified that our proposed algorithm can provide variousnumbers of embedding capacities, produce a visually plausibletexture 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 inthe area of digital media, and much concern has arisen

regarding steganography for digital media. Steganography [1]is a singular method of information hiding techniques. Itembeds messages into a host medium in order to conceal secretmessages 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 toa possible attacker and whose success depends on detectingthe existence of this communication [3]. In general, the hostmedium used in steganography includes meaningful digitalmedia such as digital image, text, audio, video, 3D model [4],etc. A large number of image steganographic algorithms havebeen investigated with the increasing popularity and use ofdigital images [5], [6].

Most image steganographic algorithms adopt an existingimage as a cover medium. The expense of embedding secretmessages 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; acceptedNovember 6, 2014. Date of publication November 14, 2014; date of currentversion December 8, 2014. This work was supported by the Ministry ofScience and Technology, Taiwan, under Grant 101-2221-E-005-091-MY3. Theassociate editor coordinating the review of this manuscript and approving itfor 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:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline 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 secretmessages which are embedded allow for more image distor-tion. Consequently, a compromise must be reached betweenthe embedding capacity and the image quality which resultsin the limited capacity provided in any specific cover image.Recall that image steganalysis is an approach used to detectsecret messages hidden in the stego image. A stego imagecontains 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 possiblethat an image steganalytic algorithm can defeat the imagesteganography and thus reveal that a hidden message is beingconveyed in a stego image.

In this paper, we propose a novel approach for steganog-raphy using reversible texture synthesis. A texture synthesisprocess re-samples a small texture image drawn by an artist orcaptured in a photograph in order to synthesize a new textureimage with a similar local appearance and arbitrary size.We weave the texture synthesis process into steganographyconcealing secret messages as well as the source texture.In particular, in contrast to using an existing cover imageto hide messages, our algorithm conceals the source textureimage and embeds secret messages through the process oftexture synthesis. This allows us to extract the secret messagesand the source texture from a stego synthetic texture. To thebest of our knowledge, steganography taking advantage of thereversibility has ever been presented within the literature oftexture synthesis.

Our approach offers three advantages. First, since the texturesynthesis can synthesize an arbitrary size of texture images, theembedding capacity which our scheme offers is proportionalto the size of the stego texture image. Secondly, a steganalyticalgorithm is not likely to defeat this steganographic approachsince the stego texture image is composed of a source texturerather than by modifying the existing image contents. Third,the reversible capability inherited from our scheme providesfunctionality to recover the source texture. Since the recoveredsource texture is exactly the same as the original sourcetexture, it can be employed to proceed onto the second roundof secret messages for steganography if needed. Experimentalresults have verified that our proposed algorithm can providevarious numbers of embedding capacities, produce visuallyplausible texture images, and recover the source texture.Theoretical analysis indicates that there is an insignificantprobability 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 resultsand 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 incomputer vision and computer graphics [8]. The most recentwork has focused on texture synthesis by example, in which asource texture image is re-sampled using either pixel-based orpatch-based algorithms to produce a new synthesized textureimage with similar local appearance and arbitrary size.

Pixel-based algorithms [9]–[11] generate the synthesizedimage pixel by pixel and use spatial neighborhood compar-isons to choose the most similar pixel in a sample textureas the output pixel. Since each output pixel is determinedby the already synthesized pixels, any wrongly synthesizedpixels during the process influence the rest of the result causingpropagation of errors.

Otori and Kuriyama [12], [13] pioneered the work ofcombining data coding with pixel-based texture synthesis.Secret messages to be concealed are encoded into coloreddotted patterns and they are directly painted on a blank image.A pixel-based algorithm coats the rest of the pixels using thepixel-based texture synthesis method, thus camouflaging theexistence of dotted patterns. To extract messages the printoutof the stego synthesized texture image is photographed beforeapplying the data-detecting mechanism. The capacity providedby the method of Otori and Kuriyama depends on the numberof the dotted patterns. However, their method had a small errorrate of the message extraction.

Patch-based algorithms [14], [15] paste patches from asource texture instead of a pixel to synthesize textures. Thisapproach of Cohen et al. and Xu et al. improves the imagequality of pixel-based synthetic textures because texture struc-tures inside the patches are maintained. However, since patchesare pasted with a small overlapped region during the syntheticprocess, one needs to make an effort to ensure that the patchesagree with their neighbors.

Liang et al. [16] introduced the patch-based samplingstrategy and used the feathering approach for the overlappedareas of adjacent patches. Efros and Freeman [17] present apatch stitching approach called “image quilting.” For everynew patch to be synthesized and stitched, the algorithmfirst searches the source texture and chooses one candidatepatch that satisfies the pre-defined error tolerance with respectto neighbors along the overlapped region. Next, a dynamicprogramming technique is adopted to disclose the minimumerror path through the overlapped region. This declares anoptimal boundary between the chosen candidate patch andthe synthesized patch, producing visually plausible patchstitching.

Ni et al. [18] proposed an image reversible data hidingalgorithm which can recover the cover image without anydistortion from the stego image after the hidden data havebeen extracted. Histogram shifting is a preferred techniqueamong existing approaches of reversible image data hidingbecause it can control the modification to pixels, thus limitingthe 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 kernelregion is the boundary region. (b) An illustration of non-overlapped kernelblocks subdivided from the source texture. (c) The diagram of source patchesderived by the expanding process using kernel blocks. (d) The boundarymirroring and expanding for a source patch.

location map, thereby reducing the overhead encountered. Thecurrent state-of-the-art for reversible image data hiding is thegeneral framework presented by Li et al. [19].

To the best of our knowledge, we were unable to discloseany literature that related patch-based texture synthesis withsteganography. In this paper, we present our work whichtakes advantage of the patch-based methods to embed asecret message during the synthesizing procedure. This allowsthe source texture to be recovered in a message extractingprocedure, 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 ouralgorithm. The basic unit used for our steganographic texturesynthesis is referred to as a “patch.” A patch represents animage block of a source texture where its size is user-specified.Fig. 1(a) illustrates a diagram of a patch. We can denote thesize of a patch by its width (Pw) and height (Ph). A patchcontains the central part and an outer part where the centralpart is referred to as the kernel region with size of Kw × Kh ,and the part surrounding the kernel region is referred to as theboundary region with the depth (Pd ).

Next, we describe the concept of the kernel block. Givena source texture with the size of Sw × Sh we can subdividethe source texture into a number of non-overlapped kernelblocks, each of which has the size of Kw × Kh , as shown asFig. 1(b). Let KB represent the collection of all kernel blocksthus generated, and ‖KB‖ represent the number of elements inthis set. We can employ the indexing for each source patch kbi ,i.e., KB = {kbi | i = 0 to ‖KB‖ − 1} . As an example, given asource texture with the size of Sw × Sh = 128×128, if we setthe size Kw × Kh as 32 × 32, then we can generate‖KB‖ = 16 kernel blocks. Each element in KB can beidentified as {kb0, kb1, . . . , kb15} .

We can expand a kernel block with the depth Pd at eachside to produce a source patch. The expanding process willoverlap its neighbor block. Fig. 1(c) indicates the boundaryregion 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 sourcetexture, we operate the boundary mirroring using the kernelblock’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 thecollection of all source patches and SPn = ‖SP‖ as the numberof elements in the set SP. We can employ the indexing for eachsource patch spi , i.e., SP = {spi | i = 0 to ‖SP‖ − 1}.

Given a source texture with the size of Sw × Sh , we canderive the number of source patches SPn using (1) if a kernelblock has the size of Kw × Kh . In our paper, we assume thesize of the source texture is a factor of the size of the kernelblock to ease the complexity.

S Pn = Sw

Kw× Sh

Kh(1)

Our steganographic texture synthesis algorithm needsto generate candidate patches when synthesizing synthetictexture. The concept of a candidate patch is trivial: we employa 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 thecandidate patches where CPn = ‖CP‖ denotes the number ofelements 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 thateach candidate patch is unique; otherwise, we may extract anincorrect secret message. In our implementation, we employa flag mechanism. We first check whether the original sourcetexture has any duplicate candidate patches. For a duplicatecandidate patch, we set the flag on for the first one. For therest of the duplicate candidate patches we set the flag off toensure the uniqueness of the candidate patch in the candidatelist.

A. Message Embedding Procedure

In this section we will illustrate the message embeddingprocedure. Fig. 2 shows the three processes of our messageembedding procedure. We will detail each process in thefollowing sections.

1) Index Table Generation Process: The first process isthe index table generation where we produce an index tableto record the location of the source patch set SP in thesynthetic texture. The index table allows us to access thesynthetic texture and retrieve the source texture completely.

Fig. 3. An illustration of two types of priority locations to paste thesource patches: (a) the first-priority locations L1 and (b) the second-prioritylocations L2; (c) 9 source patches using L1 resulting in sparse distribution;(d) 36 source patches using L1 first, and then employing the L2 leading tothe 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 majorbenefits our proposed algorithm offers.

We first determine the dimensions of the index table(Tpw × Tph). Given the parameters Tw and Th , which arethe width and the height of the synthetic texture we intendto synthesize, the number of entries in this index table canbe determined using (3) where TPn denotes the number ofpatches in the stego synthetic texture. For simplicity, we choseappropriate parameters for Tw, Th , Pw, Ph , and Pd , so that thenumber of entries is an integer. As an example, if Tw × Th =488 × 488, Pw × Ph = 48 × 48, and Pd = 8, then we cangenerate 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 mannerof reversibility, the source patches can be distributed in arather sparse manner if the synthetic texture has a resolutionthat is much larger than that of the source texture, as shownin Fig. 3(a). On the contrary, the source patches may bedistributed in a rather dense manner if the synthetic texturehas a resolution that is slightly larger than that of the sourcetexture, as shown in Fig. 3(b). For the patch distribution,we avoid positioning a source texture patch on the bordersof the synthetic texture. This will encourage the borders to beproduced by message-oriented texture synthesis, enhancing theimage quality of the synthetic texture. We further define thefirst-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 andsecond-priority positions, respectively.⎧⎨

⎩‖L1‖ =

⌈Tpw−2

2

⌉×

⌈Tph−2

2

⌉

‖L2‖ =⌊

Tpw−22

⌋×

⌊Tph−2

2

⌋ (4)

Fig. 4 illustrates the composition image where ninesource patches are pasted. As an example, an index table


Tpw × Tph = 12 × 12 contains 144 entries so ‖L1‖ = 25and ‖L2‖ = 25.

Given the number of patches SPn subdivided from thesource texture, the strategy of patch distribution is to distributepatches perfectly on the first-priority positions before postingpatches on the second-priority positions. Based on the reso-lution of the synthetic texture, we will have two cases: thesparse distribution and dense distribution. These are describedbelow.

When the number of source patches is less than or equalto the number of the first-priority positions (SPn ≤ ‖L1‖), thepatch will be distributed sparsely. In the security issue sectionwe describe some mathematical analyses of our algorithm.The analysis shows that the total number of patterns thatthe sparse distribution can offer is C‖L1‖

S Pn× S Pn!. On the

contrary, when the number of source patches is greater thanthe first-priority position (SPn > ‖L1‖ ), the patch will bedistributed densely. A mathematical analysis shows that thetotal number of patterns that the dense distribution can offeris C‖L2‖

S Pn−‖L1‖ × S Pn !.The index table has the initial values of −1 for each

entry, which shows that the table is blank. Now, we need tore-assign values when we distribute the source patch ID in thesynthetic texture. In our implementation, we employ a randomseed for patch ID distribution, which increases the securityof our steganographic algorithm making it more difficult formalicious attackers to extract the source texture. As a result,the index table will be scattered with different values as shownin Fig. 4(b) where we have nine source patches (no. 0 to 8)and 135 blank locations with the initial value of “−1.” In thisindex table, the entries with non-negative values indicatethe corresponding source patch ID subdivided in the sourcetexture, while these entries with the value of −1 representthat the patch positions will be synthesized by referring tothe secret message in the message-oriented texture synthesis.Taking the above condition into consideration, we can nowuse the random seed Rs to disarrange the ID of the sourcepatches subdivided in the source texture. For example, if thereare nine source patches (SPn = 9) and the synthetic texture issynthesized with a total number of 144 patches (TPn = 144),we can distribute the disarranged nine IDs of the sourcepatches resulting in a sparse distribution. Secret messages willbe encoded in the remaining 135 blank locations during themessage-oriented texture synthesis.

2) Patch Composition Process: The second process of ouralgorithm is to paste the source patches into a workbenchto produce a composition image. First, we establish a blankimage as our workbench where the size of the workbench isequal to the synthetic texture. By referring to the source patchIDs stored in the index table, we then paste the source patchesinto the workbench. During the pasting process, if no overlap-ping of the source patches is encountered, we paste the sourcepatches 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 havenow 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 occurduring our message-oriented texture synthesis algorithm. The blank area insidethe green square frame represents the working location which is going to besynthesized.

and have pasted source patches directly into the workbench.We will embed our secret message via the message-orientedtexture synthesis to produce the final stego synthetic texture.

The three fundamental differences between our proposedmessage-oriented texture synthesis and the conventional patch-based texture synthesis are described in Table I. The firstdifference is the shape of the overlapped area. During theconventional synthesis process, an L-shape overlapped area isnormally used to determine the similarity of every candidatepatch. In contrast, the shape of the overlapped area in ouralgorithm varies because we have pasted source patches intothe workbench. Consequently, our algorithm needs to providemore flexibility in order to cope with a number of variableshapes formed by the overlapped area.

The second difference lies in the strategy of candidateselection. In conventional texture synthesis, a threshold rank isusually given so that the patch can be randomly selected fromcandidate patches when their ranks are smaller than the giventhreshold. In contrast, our algorithm selects “appropriate”patches by taking into consideration secret messages. Finally,the output of the conventional texture synthesis is a puresynthetic texture. However, our algorithm produces a muchdifferent synthetic texture. The source texture being convertedinto a number of source patches has been pasted as part of thecontents in the large synthetic texture. In addition, the outputlarge texture has been concealed with the secret message.

While the conventional texture synthesis algorithm has an“L-shape” overlapped area, our algorithm may acquire anotherfour shapes of the overlapped area, as shown in Fig. 5. Assumethat the texture synthesis is carried on using the scan-lineorder. The texture area reveals a typical “L-shape” of anoverlapped area, as shown in Fig. 5(a). However, when anearby pasted source patch has occupied the right side ofthe 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 workinglocation.

pasted source patch has occupied the bottom side, this leadsto a “rightward U-shape” of the overlapped area (Fig. 5(c)).If a nearby pasted source patch has occupied the lower rightcorner of the working location, this leads to a disjointedoverlapped area containing an “L-shape” and a small butisolated part (Fig. 5(d)). Finally, if two nearby pasted sourcepatches have occupied the right and bottom side of the workinglocation, this will contribute to an “O-shape” of the overlappedarea (Fig. 5(e)).

For each candidate patch within the candidate list, oneof the five shapes of overlapped area described above willoccur when referring to the synthesized area in the workinglocation. Thus, we can compute the mean square error (MSE)of the overlapped region between the synthesized area andthe candidate patch. After all MSEs of the patches in thecandidate list are determined, we can further rank these candi-date patches according to their MSEs. Fig. 6 demonstrates anexample of a candidate list where four candidate patches havedifferent MSEs. The candidate patch which has the smallestMSE indicates that this candidate patch is the most similar tothe synthesized area in the working location.

Once the ranks of all candidate patches are determined,we can select the candidate patch where its rank equalsthe decimal value of an n-bit secret message. In this way,a segment of the n-bit secret message has been concealedinto the selected patch to be pasted into the working location.In our implementation, we employ a simple but effectiveimage quilting technique [17] to reduce the visual artifactencountered 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 describedto analyze the embedding capacity our algorithm can offer.The embedding capacity our algorithm can offer is relatedto the capacity in bits that can be concealed at each patch(BPP, bit per patch), and to the number of embeddable patchesin the stego synthetic texture (EPn). Each patch can concealat least one bit of the secret message; thus, the lower bound ofBPP will be 1, and the the maximal capacity in bits that can beconcealed at each patch is the upper bound of BPP, as denotedby BPPmax . In contrast, if we can select any rank from thecandidate 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 ofthe embeddable patches is the difference between the numberof 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 − S Pn) (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 × 48and the boundary depth Pd = 8 pixels. This will lead to therange of the BPP between 1 and 12. We can produceSPn = 16 source patches and TPn = 144 patches on thestego synthetic texture. Thus, there are EPn = 128 embeddablepatches. If we take the BPP = 12, then the total embeddingcapacity is TC = 1536 bits.

C. Source Texture Recovery, Message Extraction,and Message Authentication Procedure

The message extracting for the receiver side involvesgenerating the index table, retrieving the source texture,performing the texture synthesis, and extracting and authen-ticating the secret message concealed in the stego synthetictexture. The extracting procedure contains four steps, as shownin Fig. 7.

Given the secret key held in the receiver side, the same indextable as the embedding procedure can be generated. The nextstep is the source texture recovery. Each kernel region with thesize of Kw × Kh and its corresponding order with respect tothe size of Sw ×Sh source texture can be retrieved by referringto the index table with the dimensions Tpw ×Tph . We can thenarrange kernel blocks based on their order, thus retrieving therecovered source texture which will be exactly the same asthe source texture. In the third step, we apply the composition


image generation to paste the source patches into a workbenchto produce a composition image by referring to the index table.This generates a composition image that is identical to the oneproduced in the embedding procedure.

The final step is the message extraction and authentica-tion step, which contains three sub-steps. The first sub-stepconstructs a candidate list based on the overlapped area byreferring to the current working location. This sub-step is thesame as the embedding procedure, producing the same numberof candidate lists and their corresponding ranks.

The second sub-step is the match-authentication step. Giventhe current working location Cur(WL) on the workbench,we refer to the corresponding stego synthetic texture at thesame working location Stg(WL) to determine the stego kernelregion SKw × SK h . Then, based on this stego kernel region,we search the candidate list to determine if there is a patch inthe candidate list where its kernel region is the same as thisstego kernel region. If this patch is available, we refer to itas the matched patch, and denote it as MKw × M K h . Clearly,we can locate the rank R of the matched patch, and this rankrepresents the decimal value of the secret bits we conveyedin the stego patch when operating the texture synthesis in themessage embedding procedure. However, if we cannot discloseany matched patch in the candidate list where the kernel regionis the same as the stego kernel region, it means that the stegokernel region has been tampered with, leading to a failure ofthe message authentication. In this way, we can authenticateand extract all of the secret messages that are concealed in thestego synthetic texture patch by patch.

Our method is resistant against malicious attacks as long asthe contents of the stego image are not changed. With someside information, for example, our scheme can survive theattacks of the image mirroring or image rotation by 90, 180,or 270 degrees. Nevertheless, if malicious attacks lead toalteration of the contents of the stego texture image, themessage authentication step will justify the authenticity of thesecret messages.

IV. EXPERIMENTAL RESULTS AND ANALYSIS

A. Results of the Embedding Capacity

We collect our experimental results on a personal computerwith an i7-2600 3.4GHz CPU and 4GB memory. We adoptfour source textures for the results of our collection. Table IIIpresents 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 outthat given a fixed number of BPP, the larger the resolutions ofthe source texture Sw ×Sh (96 × 96 vs. 192×192), the smallerthe total embedding capacity (TC) our algorithm will offer(6160 bits vs. 5890 bits for 10 BPP). This is because the largersource 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 thetotal embedding capacity. Nevertheless, we can employ largerBPP (11 vs. 14) in order to convey more secret messages(6776 bits vs. 8246 bits). The maximal capacity provided byour 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 workpresented by Otori and Kuriyama [13]. In their algorithm,a data-coded texture image of 480 × 640 pixels contains5×5 or 10×10 dotted patterns, thus concealing the capacity inthe range of 200 to 800 bits. In contrast, our scheme conveysthe capacity ranging from 12285 to 34398 bits in a stegotexture synthesis image of 1024 × 1024 pixels. Consequently,the capacity we offer varies from 4.50 to 50.39 times morethan our counterparts’. Besides, our scheme extracts the secretmessages correctly, while their scheme exhibits a small errorrate when extracting secret messages.

Fig. 8 compares stego synthetic textures with differentcapacities. We also present the pure synthetic texture whichdoes not convey any secret message. No significant visualdifference exists between the two stego synthetic texturesand the pure synthetic texture. In addition, no significantvisual difference can be perceived when comparing two stegosynthetic textures embedded by 5 BPP vs. 10 BPP.

The computing times of Fig. 8 are shown in Table IV. Therange of the computing time is 6.8% to 8.7% more than thatneeded for pure texture synthesis. Nevertheless, our algorithmis flexible enough to provide a different embedding capacity bysimply altering the patch size, satisfying the desirable capacityor texture quality demanded by users. Also, our algorithm canretrieve the source texture, making possible the second roundof message embedding using the recovered source texture.

B. Image Quality Comparison

We use several mechanisms to determine the image qualityof 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 thesynthetic results. MSEO reflects the similarity between thecandidate 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 isPw × 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 themessage-oriented texture synthesis process. Consequently, theMSEO 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 qualityof the overlapped areas. Obviously, the lower the MSEO value,the higher quality of the synthetic texture image. The equationof MSEO is shown in (6), where OLi stands for the overlappedarea of the working location, i , pc

j stands for the pixel j ofthe candidate patch in OLi , and ps

j stands for the pixel j ofthe synthesized area in OLi .

MSEO = 1

(E Pn)×Pw × Ph

∑E Pn

i=1

∑j∈OLi

(pcj − ps

j )2 (6)

The MSEO can be calculated during the texture synthesisprocedure. When we synthesize a patch, we accumulate thesquared errors of all the pixels in the overlapped area betweenthe synthesized area and the selected candidate patch. Whenthe texture synthesis procedure is finished, we can divide thesummation of squared errors by the patch size and the numberof the synthesized patches to produce the MSEO. It comesas no surprise that the MSEO is dependent on the capacityper patch.

Table V compares the MSEO to the embedding capacityfor the four test source textures. When we consider the samepatch size, the MSEO increases as we convey more secret bitsper patch. These MSEO values coincide with the image qualitywhen visualizing the stego synthetic texture. For a larger patchsize, the boundary depth increases leading to a larger MSEO.Taking the test source texture “peanuts” as an example, theMSEO 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 conveying10 bits per patch. Fig. 8(c) shows a slightly higher visual imagequality than Fig. 8(d).

The second scheme we adopt for measuring the imagequality is the Pearson Product Moment Correla-tion (PPMC) [20]. It is employed as a measure of howwell two variables are related. The Pearson coefficient valuesthat this scheme produces are between 1 and −1. A resultof 1 means that there is a perfect positive correlation betweenthe two variables, while a result between 0.5 and 1.0 representsa high correlation.

Table VI shows average Pearson coefficients across threeR-G-B channels measured under the base of the histogramproduced for each channel. In Case-A and Case-B, we revealthe Pearson coefficients between the stego synthetic texturesand the pure synthetic texture. We report in Case-C thePearson coefficients between two stego synthetic textures withdifferent BPPs. The Pearson coefficients shown in Case-Aare 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 alongwith the increase of the embedding capacity per patch, theyretain the feature of a close relation between the pure and stegosynthetic textures. The Pearson coefficients in Case-C are veryclose as well, which indicates that the stego synthetic texturesconveying 5 BPP remain highly correlated to those conveying10 BPP. All the Pearson coefficients shown in this table exhibitthat our steganographic algorithm is effective in producingstego synthetic textures of high image quality in comparisonto pure synthetic textures produced by conventional texturesynthesis.

Next, we employ the SSIM (Structural SIMilarity)index [21] to quantify the similarity between the pure andstego 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 rangeof [−1, 1] and when it equals to 1, the two images areidentical. Table VII shows the SSIM indices for different patchsizes. The SSIM index values are close despite their concealingdifferent embedding capacities. The SSIM algorithm is highlysensitive to translation, scaling and rotation. This explains thelow index values shown in Table VII because the patch-basedmethod generates an entirely new synthetic texture imagefrom a number of patches in the source texture resulting ina different level of image translation and scaling.

C. Results of Different Message Probabilities

The secret messages consist of bit stream “0” or “1.” Theexperimental 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 tobe served as a secret message. We generalize our scheme byconsidering 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 secretbit “1.” If we consider two bits of the secret message, then theprobability for bit patterns “00” is (1−p)×(1−p). Let ER(p,2)represent the expected rank of the selected candidate duringour message-oriented texture synthesis with BPP = 2. Then,ER(p, 2) can be derived as a function of probability p, asshown in (7).

E R(p, 2) = 0 × (1− p)(1− p) + 1 × (1− p)p

+ 2× p(1− p) + 3 × p2 =3 p (7)

E R(p, k) = (2k−1)p (8)

In general, when we consider BPP = k bits of the secretmessage, we can express the expected rank of a selectedcandidate 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 weselect the larger rank, the larger MSEO would be expected.Consequently, the image quality of the synthetic texture islikely to be worse than the one produced by p = 0.5.In general, if p is smaller, we are likely to select a bettercandidate of patch, which leads to producing a better stegosynthetic texture. Thus, our algorithm is general enough tocope 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 theincrease of MSEO, as expected. This is due to the fact thatwhen the secret message has the larger probability p, thecandidate patch is likely to be selected at the rear part ofthe candidate list, leading to larger MSEO.

To improve the probability of getting better ranks we canconduct the “probability complement” process to decrease theMSEO. If the probability p is larger than 0.5, we adopt theprobability of 1-p for message embedding. This can be real-ized by flipping every bit of the secret message to its reversestyle. During the extraction stage, we extract the secret bit asusual, and then flip it again to produce the correct message.With this mechanism, we can ensure that the probability usedfor message embedding is always less than or equal to 0.5,which encourages our scheme to produce a stego synthetictexture with a smaller MSEO. Clearly, we need to adopt asecret key to record whether or not we have conducted anyflipping operation.

If we are not able to determine the probability of the secretmessage, such as the example of the message being from astreaming 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 operationbetween the previous message clip M ′

i−1 and the currentmessage clip Mi . For example, if we want to embed Mi topatch i , we do the XOR operation and produce M ′

i whereM ′

i = Mi ⊕M ′i−1. Then, we embed M ′

i to patch i . In theextraction procedure, we recover the secret clip Mi withanother XOR operation, where Mi= M ′

i ⊕ Mi−1. With thismechanism, we can produce a stego synthetic texture whereits 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.” Theresults show that all of the MSEOs are close to those producedwith the probability p = 0.5 regardless of using differentmessage probabilities.

D. Security Issue

In this section we discuss the probability of breaking oursteganographic algorithm in order to produce a correct secretmessage. We assume the resolution of the stego synthetictexture is known by the eavesdropper.

We explain our first level of security. For four possiblesquared sizes of the source texture (Sw × Sh), the probabilityof breaking down is Pbi = 0.25. The probability of breakingdown five possible squared sizes of the patch (Pw × Ph) isPbp = 0.2. Finally, the probability of breaking down tenpossible BPPs from 2-bit to 12-bit is Pbc = 0.1. The totalprobability that the eavesdropper can break down the securityof 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 indextable. If the length of the seed used to generate the indextable is a 128-bit sequence, it is highly impossible that thisseed will be revealed. The eavesdropper may try to speculateabout the contents of the index table. For the case of thesparse distribution, the number of source patches (SPn)is less than or equal to the number of the first-priorityposition (‖L1‖). Thus, the total number of patterns offered isC‖L1‖

S Pn× S Pn!. The probability of revealing the correct order

of patches in the index table is shown in (9).

Pbsp2 = (‖L1‖ − S Pn) !

‖L1‖ ! (9)

For the case of the dense distribution, the number ofsource patches is larger than the number of the first-priorityposition (SPn > ‖L1‖). Therefore, the total number ofpermutation patterns that the dense distribution can offer isC‖L2‖

S Pn−‖L1‖ × S Pn !. Thus, the probability of revealing thecorrect order of these IDs in the index table is shown in (10).

Pbde2 = (S Pn − ‖L1‖) !× (‖L2‖ − S Pn + ‖L1‖) !

‖L2‖ !×S Pn ! (10)

We present two examples to provide more insight forthe 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 toTable II. The eavesdropper can retrieve the number of sourcepatches as SPn = 16, the dimensions of the index table asTpw × 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 ofthe sparse distribution is being employed. The probabilitythat the index table is broken down is Psp

2∼= 2.35 × 10−20.

Even though the security of level one has collapsed, theprobability that an eavesdropper can retrieve source texturewill be Pbbk = Pbon

1 ×Pbsp2 = 1.18 × 10−22.

For the dense distribution we employ a larger source tex-ture Sw × Sh = 192 × 192. An eavesdropper can retrieveSPn = 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 bePbbk = Pbon

1 ×Pde2 = 4.35×10−51. Both examples illustrate

that even though the security of level one has collapsed, thereis insignificant probability that our steganographic system canbe attacked to retrieve the source texture, and consequently, thesecret message. The analysis indicates that our steganographicsystem 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 scienceof detecting hidden messages using steganography. Whilethere are a number of steganalysis algorithms developed,we employ the RS steganalytic scheme [7] since this algorithmis well-known, having been adopted for most steganalysisattacks.

In the RS detection method, the relative number of regulargroups for masks M = [0110] and –M = [0 − 1 − 10] isdenoted as (RM , R−M ), respectively. Similarly, the relativenumber of singular groups for masks M and −M is denotedas (SM , S−M ), respectively. If the magnitude of RM is equalto that of R−M , or the same equivalence happens to thesingular group (SM , S−M ), the embedded image will pass theRS steganalysis. Otherwise, it would reveal the presence ofthe secret message.

In detection processing, we compute the absolute differenceof 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 moresecure to the RS steganalysis.

Table X shows the detection results for the source texture“rope net” in three primary color channels. Even though eachpatch is concealed with different amounts of secret bits, thedifference between regular group RM and R−M is similar tothe values shown for the pure synthetic texture. This similardifference invariance reflects for singular groups SM and S−M .These statistics indicate our message-oriented texture synthesisalgorithm can resist the RS detection attack. This is due to thefact 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 theircontents.

V. CONCLUSION AND FUTURE WORK

This paper proposes a reversible steganographic algorithmusing texture synthesis. Given an original source texture, ourscheme can produce a large stego synthetic texture concealingsecret messages. To the best of our knowledge, we are thefirst that can exquisitely weave the steganography into aconventional patch-based texture synthesis. Our method isnovel and provides reversibility to retrieve the original sourcetexture from the stego synthetic textures, making possible asecond round of texture synthesis if needed. With the two tech-niques we have introduced, our algorithm can produce visuallyplausible stego synthetic textures even if the secret messagesconsisting of bit “0” or “1” have an uneven appearance ofprobabilities. The presented algorithm is secure and robustagainst an RS steganalysis attack. We believe our proposedscheme offers substantial benefits and provides an opportunityto extend steganographic applications.

One possible future study is to expand our scheme tosupport other kinds of texture synthesis approaches to improvethe image quality of the synthetic textures. Another possiblestudy would be to combine other steganography approachesto increase the embedding capacities.

ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewersfor their valuable comments and suggestions. They would alsolike to thank Dr. Evelyne Pickett for her enthusiastic assistancein improving the clarity of this article.

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Kuo-Chen Wu is currently pursuing thePh.D. degree with the Department of ComputerScience and Engineering, National Chung HsingUniversity, Taichung, Taiwan, where he receivedthe M.Sc. degree from the Department of ComputerScience and Engineering, in 2006. His currentresearch interests include computer graphics, colorscience, image processing, watermarking, andsteganography.

Chung-Ming Wang (M’96) received theB.S. degree in applied mathematics from NationalChung Hsing University, Taichung, Taiwan, in1984, and the Ph.D. degree in computer sciencefrom the University of Leeds, Leeds, U.K., in1992. From 1986 to 1988, he was a SystemAnalyst with President Enterprise Cooperation,Tainan, Taiwan, and PAL Company. He is currentlya Professor with the Department of ComputerScience and Engineering, National Chung HsingUniversity. His research interests include computer

graphics, color science, virtual reality, multimedia systems, watermarking,and steganography. He has received three Dragon Thesis Awards, funded bythe Acer Computers, and two Outstanding Paper Awards from the ComputerSociety of the Republic of China (ROC). He is a member of the Associationfor Computing Machinery and the IEEE Computer Society.

steganography using reversible texture synthesis

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