HONG AND CHEN: NOVEL DATA EMBEDDING METHOD USING ADAPTIVE PIXEL PAIR MATCHING 177embedding is done by modifying the pixel pairs in the cover stego image quality. In this section, OPAP and DE will be brieﬂyimage according to their DCV’s neighborhood set and the given reviewed.message digit. Chao used an embedding parameter to controlthe payload, in which a digit in a -ary notational system A. Optimal Pixel Adjustment Process (OPAP)can be concealed into two pixels, where . The OPAP method proposed by Chan et al. in 2004 greatlyIf , , i.e., digits in a 5-ary notational system improved the image distortion problem resulting from LSB re-are concealed, the resultant payload is equivalent to EMD. If placement. The OPAP method is described as follows , . , ; if , . Note that is signiﬁcantly Suppose a pixel value is , the value of the right-most LSBsincreased as is only increased by one. Instead of enhancing of is . Let be the pixel value after embedding mes-the payload of EMD, Wang et al.  in 2010 proposed a sage bits using the LSB replacement method and be the dec-novel section-wise exploring modiﬁcation direction method to imal value of these message bits. OPAP employs the followingenhance the image quality of EMD. Their method segments the equation to adjust so that the embedding distortion can becover image into pixel sections, and each section is partitioned minimizedinto the selective and descriptive groups. The EMD embeddingprocedure is then performed on each group by referencing apredeﬁned selector and descriptor table. This method combinesdifferent pixel groups of the cover image to represent more otherwiseembedding directions with less pixel changes than that of the where denotes the result obtained by OPAP embedding. NoteEMD method. By selecting the appropriate combination of that and have the same right-most LSBs and thus, thepixel groups, the embedding efﬁciency and the visual quality embedded data can be extracted directly from the right-mostof the stego image is enhanced. LSBs. Here is a simple example. Suppose a pixel value Another group of rather practical data-hiding methods con- and the bits to be embedded are . Insiders security as a guiding principle for developing a less de- this case, and . After is embedded, we obtainedtectable embedding scheme. These methods may either be im- . Because andplemented by avoiding embedding the message into the con- , we obtainedspicuous part of the cover image, or by improving the embed- . Thus, after embedding , the pixel value 160 isding efﬁciency, that is, embed more messages per modiﬁcation changed to 157. To extract the embedded data, we simply extractinto the cover . The former can behttp://ieeexploreprojects.blogspot.com of 157. achieved, for example, the right-most three LSBsusing “the selection channel” such as the wet paper code pro-posed by Fridrich et al. . The latter can be done by en- B. Diamond Encodingcoding the message optimally with the smallest embedding im- In 2009, Chao et al. proposed a DE method based on PPM.pact using the near-optimal embedding schemes , , . This method conceals a secret digit in a -ary notational systemIn these methods, the data bits were not conveyed by individual into two pixels, where , . The payload ofpixels but by groups of pixels and their positions. DE is bpp. Note that when , DE This paper proposes a new data embedding method to re- is equivalent to EMD in which both methods conceal digits in aduce the embedding impact by providing a simple extraction 5-ary notational system. The DE method is brieﬂy described asfunction and a more compact neighborhood set. The proposed follows.method embeds more messages per modiﬁcation and thus in- Let the size of bits cover image be , message digitscreases the embedding efﬁciency. The image quality obtained be , where the subscript represents is in a -ary no-by the proposed method not only performs better than those ob- tational system. First, the smallest integer is determined totained by OPAP and DE, but also brings higher payload with satisfy the following equation:less detectability. Moreover, the best notational system for dataconcealing can be determined and employed in this new methodaccording to the given payload so that a lower image distortioncan be achieved. The rest of this paper is organized as follows. Section II is a where denotes the number of message digits in a -arybrief review of OPAP and DE. The proposed method is given in notational system. To conceal a message digit into pixel pairSection III. Experimental results are given in Section IV, and the , the neighborhood set is determined bysteganalysis of the proposed method is presented in Section V.Section VI includes the conclusions and remarks. where represents the set of the coordinates ’s whose absolute distance to the coordinate is smaller or II. RELATED WORKS equal to . A diamond function is then employed to calculate the DCV of , where . OPAP effectively reduces the image distortion compared with After that, the coordinates belong to the set are searchedthe traditional LSB method. DE enhances the payload of EMD and DE ﬁnds a coordinate satisfying ,by embedding digits in a -ary notational system. These two and then is replaced by . Repeat these proceduresmethods offer a high payload while preserving an acceptable until all the message digits are embedded. In the extraction
178 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 1, FEBRUARY 2012 in DE is deﬁned by a diamond shape, which may lead to some unnecessary distortion when . In fact, there exists a better other than diamond shape resulting in a smaller embedding distortion. In Section III-A, we redeﬁne as well as and then propose a new embedding method based on PPM. The proposed method not only allows concealing digits in any notational system, but also provides the same or even smaller embedding distortion than DE for various payloads. Fig. 1. Neighborhood set for . A. Extraction Function and Neighborhood Set The deﬁnitions of and signiﬁcantly affect the stego image quality. The designs of and havephase, pixels are scanned using the same order as in the em- to fulﬁll the requirements: all values of in havebedding phased. The DCV value of a pixel pair is then to be mutually exclusive, and the summation of the squared dis-extracted as a message digit. tances between all coordinates in and has to be the Here is a simple example. Let and , smallest. This is because, during embedding, is replacedthen . The neighborhood by one of the coordinates in . Suppose there are coor-set and its corresponding DCV values are shown dinates in , i.e., digits in a -ary notational system are toin Fig. 1. If a digit in a 25-ary notational system needs be concealed, and the probability of replacing by one ofto be embedded, then in the region deﬁned by , the coordinates in is equivalent. The averaged MSE canwe ﬁnd the DCV value of . There- be obtained by averaging the summation of the squared distancefore, we simply replace (12,10) by (11,12) and the digit between and other coordinates in . Thus, given ais embedded. To extract the embedded digits, we calculate , the expected MSE after embedding can be calculated ; the bycalculation result 14 is then the embedded digit. http://ieeexploreprojects.blogspot.com III. ADAPTIVE PIXEL PAIR MATCHING (APPM) The basic idea of the PPM-based data-hiding method is to use Here we will propose an adaptive pixel pair matching (APPM)pixel pair as the coordinate, and searching a coordinate data-hiding method to explore better and so that within a predeﬁned neighborhood set such that MSE is minimized. Data is then embedded by using PPM , where is the extraction function and is based on these and . Letthe message digit in a -ary notational system to be concealed.Data embedding is done by replacing with . For a PPM-based method, suppose a digit is to be con- The solution of and is indeed a discrete opti-cealed. The range of is between 0 and , and a coordi- mization problemnate has to be found such that .Therefore, the range of must be integers between 0 and , and each integer must occur at least once. In addition,to reduce the distortion, the number of coordinates inshould be as small as possible. The best PPM method shallsatisfy the following three requirements: 1) There are exactly coordinates in . 2) The values of extraction function (1)in these coordinates are mutually exclusive. 3) The design of and should be capable of embedding digits in Given an integer and an integer pair , (1) can beany notational system so that the best can be selected to solved to obtain a constant and pairs of . Theseachieve lower embedding distortion. pairs of are denoted by . Note that DE is a data-hiding method based on PPM. DE greatly en- represents a neighborhood set of . Table I lists the constanthances the payload of EMD while preserving acceptable stego satisfying (1) for the payloads under 3 bpp. Note that, for aimage quality. However, there are several problems. First, the given , it is possible to have more than one andpayload of DE is determined by the selected notational system, satisfying (1). Table I only lists the smallest .which is restricted by the parameter ; therefore, the notational Fig. 2 shows some representative and their cor-system cannot be arbitrarily selected. For example, when is responding satisfying (1), where the center of is1, 2, and 3, then digits in a 5-ary, 13-ary, and 25-ary notational shaded with lines. Note that, in DE, setting and ,system are used to embed data, respectively. However, embed- respectively, embeds digits in the 25-ary and 41-ary notationalding digits in a 4-ary (i.e., 1 bit per pixel) or 16-ary (i.e., 2 bits systems. We also depict the of DE when settingper pixel) notational system are not supported in DE. Second, and in Fig. 2. Note that the four corners of the diamond
HONG AND CHEN: NOVEL DATA EMBEDDING METHOD USING ADAPTIVE PIXEL PAIR MATCHING 179 TABLE I LIST OF THE CONSTANT FOR Fig. 3. Neighborhood set and , where . In real applications, we can solve all and at once. With the knowledge of and , there is no need to perform Step 2 in the embedding phase. Let and . If an overﬂow or underﬂow problem occurs, that is, or , then in the neighborhood of ﬁnd a nearest such that . This can be done by solving the optimization problem Fig. 2. Neighborhood set (shaded region) for APPM. We use a simple example to illustrate the embedding proce-shape may cause larger MSE but ours selects a more compact re- dure. Suppose a cover image of size 512 512 with embed-gion for embedding, and thus smaller distortion can be achieved. ding requirement of 520 000 bits. The minimum satisfying is 16; therefore, we choose http://ieeexploreprojects.blogspot.com the 16-ary notational system as the embedding base. After theB. Embedding Procedure notational system is known, and can be ob- tained by solving (1). The 16 ’s in such that Suppose the cover image is of size , is the message , are recorded. The neighborhoodbits to be concealed and the size of is . First we calculate set and , where , are shownthe minimum such that all the message bits can be embedded. in Fig. 3. Suppose a pixel pair (10,11) that is to be concealedThen, message digits are sequentially concealed into pairs of a digit in a 16-ary notational system. The modulus dis-pixels. The detailed procedure is listed as follows. tance between and is and ; therefore, we replace (10, 11) byInput: Cover image of size , secret bit stream , . and key .Output: Stego image , , , and . C. Extraction Procedure To extract the embedded message digits, pixel pairs are1. Find the minimum satisfying , and scanned in the same order as in the embedding procedure. The convert into a list of digits with a -ary notational system embedded message digits are the values of extraction function . of the scanned pixel pairs.2. Solve the discrete optimization problem to ﬁnd and . Input: Stego image , , , and .3. In the region deﬁned by , record the coordinate Output: Secret bit stream . such that , . 1. Construct the embedding sequence using the key .4. Construct a nonrepeat random embedding sequence using 2. Select two pixels according to the embedding a key . sequence .5. To embed a message digit , two pixels in 3. Calculate , the result is the embedded digit. the cover image are selected according to the embedding sequence , and calculate the modulus distance  4. Repeat Steps 2 and 3 until all the message digits are between and , then extracted. replace with . 5. Finally, the message bits can be obtained by converting6. Repeat Step 5 until all the message digits are embedded. the extracted message digits into a binary bit stream.
180 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 1, FEBRUARY 2012 Continue from the previous example. Let the scanned pixelpair be . The embedded digit in a 16-arynotational system can be extracted by calculating . Fig. 4. Calculation of theoretical averaged MSE for APPM with . IV. QUALITY ANALYSIS AND EXPERIMENTAL RESULTS Image distortion occurs when data are embedded because TABLE IIpixel values are modiﬁed. We use MSE to measure the image MSE COMPARISON OF THE PROPOSED METHOD WITH LSB AND OPAPqualitywhere denotes the image size, and denote thepixel values of the original image and the stego image, respec-tively. MSE represents the mean square error between the coverimage and stego image. A smaller MSE indicates that the stego where is the embedding parameters of DE. For embeddingimage has better image quality. digits in a -ary notational system using APPM, assume that the probability of replacing with each in isA. Analysis of Theoretical MSE identical. With the knowledge of , the averaged MSE can be obtained by In this section, we analyze the averaged MSE of LSB, OPAP,DE, and APPM so that the stego image quality obtained fromeach method can be theoretically measured. When data are em-bedded using LSBs of each pixel, each bit valued 0 or 1 hasequal probability. The squared error caused by embedding a bit (5)in the th LSB is ; therefore, the averaged MSE ofembedding LSBs is given by For example, the http://ieeexploreprojects.blogspot.com that allows concealing digits with the 16-ary notational system is depicted in Fig. 4. The squared distances between and the center position (2) in are marked in the corresponding positions. The av- eraged MSE is then calculated by the averaged squared distance Now we analyze the averaged MSE of OPAP when messagebits are embedded in each pixel. Let the original pixel value beand the stego pixel value be . The probability ofor is ; the probability of to bewithin the range is . Therefore, the averagedMSE caused by embedding bits is LSB and OPAP employ every pixel in the cover image as an embedding unit, and bits can be embedded into each pixel. Therefore, the payload is bpp. For the PPM-based embedding (3) method, a payload with bpp is equivalent to embedding bits for every two pixels, which is equivalent to concealing digits in Note that when , OPAP and LSB have the same MSE. a -ary notational system. Because DE does not allow embed-In other words, OPAP cannot reduce the distortion caused by ding digits exactly in a -ary notational system, we compareLSB embedding at 1 bpp. the MSE of APPM with LSB and OPAP ﬁrst. The results are For the DE method, assume that the probability of selecting shown in Table II. Note that the results listed in Table II are ob-a coordinate in the diamond shape to replace tained by using (2)–(5), i.e., the theoretically value of MSE. Aa pixel pair is the same. Therefore, the averaged MSE very similar result can also be obtained if these methods are ap-caused by embedding digits in a -ary notational system is plied in nature images. Table II reveals that the MSE of APPM is smaller than those of LSB and OPAP in all payloads. For example, when the pay- load is 1 bpp, both OPAP and LSB have the same MSE MSE . However, the MSE of APPM is 0.375, which is 1/4 re- duction in MSE. For a high payload, e.g., 3 or 4 bpp, the MSE of OPAP is about one half that of LSB; however, the MSE of APPM is decreased by 0.297 and 0.982 for 3 and 4 bpp, respec- tively, than those of OPAP. Fig. 5 shows the cover image Lena (4) along with the stego images under various payloads. As shown
HONG AND CHEN: NOVEL DATA EMBEDDING METHOD USING ADAPTIVE PIXEL PAIR MATCHING 181 Fig. 6. MSE comparison of various PPM-based methods. The payload-MSE relationship of APPM is denoted by circles. The -ary digits used for a given payload are marked beside the circle.Fig. 5. Cover image and stego images under various payloads. (a) Cover image. TABLE IV(b) Stego image, 2 bpp at 46.86 dB. (c) Stego image, 3 bpp at 40.97 dB. (d) Stego MSE COMPARISON Payload bits bppimage, 4 bpp at 34.90 dB. TABLE III MSE COMPARISON OF THE PROPOSED METHOD WITH CHAO ’S DE METHOD http://ieeexploreprojects.blogspot.com to choose a better notational system for data embedding to de- crease the image distortion. Fig. 6 shows the MSE comparison of some PPM-based data- hiding methods for payload less than 2 bpp. It can be seen that the MSEs of APPM are always smaller or equal to other PPM- based methods. For example, when digits in a 4-ary notational system are embedded, the MSEs of APPM and LSB matching are the same. When embedding digits in a 13-ary notationalin the ﬁgures, the stego images are visually indistinguishable system, APPM and DE have the same MSE. How-from the cover images. ever, when embedding 16-ary digits, APPM outperforms OPAP. The comparison of theoretical MSEs under various payloads APPM not only greatly increases the payload of EMD, but alsofor APPM and DE is shown in Table III. Note that for the DE enable users to freely select the desired notational system formethod, only digits in some speciﬁc notational system can be data embedding so that a better image quality can be obtained.concealed, and the notational system used for concealing datais determined by the parameter . Therefore, we choose B. Comparison of Experimental Results to compare the MSE. Six images Lena, Jet, Boat, Elaine, Couple, and Peppers, When digits in a 5-ary notational system are embedded each sized 512 512, are taken as test images to compare the , EMD, DE, and APPM obtain the same MSE because these MSE obtained by APPM, OPAP, and DE. The payloads werethree methods share the same neighborhood set. When , set to 400 000, 650 000, and 1 000 000, respectively. MessageAPPM and DE share the same neighborhood set and thus their bits were generated by using a pseudorandom number generatorMSEs are the same. However, when , the MSEs of APPM (PRNG). The results are shown in Tables IV–VI.are lower than those of DE. It is worth mentioning that APPM is Tables IV–VI reveal that the performance of the proposedcapable of embedding digits in any notational system, while DE APPM method is the best under various payloads. For example,can only embed digits in -ary notational system with the payload 400 000 bits, the averaged MSE of 2-bit OPAPand must be an integer. Therefore, APPM has the ﬂexibility is 1.244, whereas the averaged MSE of DE is 0.887. However,
182 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 1, FEBRUARY 2012 TABLE V TABLE VII MSE COMPARISON Payload bits bpp MINIMAL ERROR RATE OBTAINED BY SPAM USING UCID IMAGE DATABASE TABLE VI MSE COMPARISON Payload bits bpp TABLE VIII MINIMAL ERROR RATE OBTAINED BY SPAM USING RSP IMAGE DATABASEthe proposed method has the smallest averaged MSE, 0.640. Forlarger payload, such as 650 000 and 1 000 000 bits, the proposedmethod also performs better than OPAP and DE because APPM is calculated to evaluate the security of a data-hiding methodselects the smallest notational system that provides just enough against the detection of SPAM, where and is the prob-embedding capacity to accommodate the given payload with the ability of false positive and false negative, respectively. Theleast distortion. http://ieeexploreprojects.blogspot.com lower the detectability. higher the error rate, the To evaluate the detectability of APPM using SPAM, we V. SECURITY ANALYSIS trained the SPAM steganalyzer on images obtained from UCID The goal of steganography is to evade statistical detection. It and RSP image databases, respectively. UCID consists of 1338is apparent that MSE is not a good measure of security against uncompressed images with size 512 384. RSP consists ofthe detection of steganalysis. For example, low-MSE embed- 10 000 gray-scale images with size 512 512 coming fromding such as LSB replacement is known to be highly detectable cropped and resized natural images. The implementation of, . In this section, we analyze the security of APPM under SPAM features is obtained from . The ﬁve-fold cross-val-two statistical steganalysis schemes, including Subtractive idation is employed to compute the classiﬁcation error. ThePixel Adjacency Matrix (SPAM) steganalyzer proposed by simulated annealing (SA) optimization is used to ﬁnd thePevný et al.  and the HVDH scheme proposed by Zhao et penalization parameter and the kernel parameter such thatal. . SPAM steganalyzer is a novel Steganographic method the error rate is the lowest.for detecting stego images with low-amplitude independent Because SPAM is effective to detect the embeddingstego signal, while the HVDH scheme is used to detect the methods such as LSB matching (LSB-M), which randomlypresence of hiding message according to the distance between increases or decreases the pixel values by one for matching thevertical and horizontal histograms. All the test images used in LSBs with the message bits, we use the SPAM steganalyzer tothis section are obtained from the UCID  and RSP  detect the APPM in 4-, 5-, and 9-ary notational systems and theimage database, where some literature ,  also adopt this LSB-M method with the payloads 0.25 and 0.5 bpp. Note thatdatabase for their experiments. for both the LSB-M method and APPM with these notational systems, the pixel values of each embedding unit are modiﬁedA. Security Analysis Under SPAM at most by one. The results are shown in Tables VII and VIII, SPAM is a modern technique for detecting stego images with respectively.independent random stego signal for which typically not found As shown in Tables VII and VIII, the error rates obtainedin natural digital images . SPAM obtains the features of by the APPM method are signiﬁcantly higher than those ob-images by calculating the transition probabilities along eight tained by the LSB-M, indicating that APPM is less detectabledirections, and the number of features is determined by the than LSB-M under the same payload. For example, for theSPAM order and the range of difference . A soft-margin sup- UCID image database with payload 0.25 bpp, the error rateport vector machine (SVM) with Gaussian kernel is employed of LSB-M using the second-order SPAM is 0.039, while theto implement the steganalyzer. The error rate error rate of APPM with a 5-ary notational system is 0.243. The undetectability is signiﬁcantly higher than that of LSB-M. Experiments on the RSP image database also revealed similar
HONG AND CHEN: NOVEL DATA EMBEDDING METHOD USING ADAPTIVE PIXEL PAIR MATCHING 183 http://ieeexploreprojects.blogspot.comFig. 7. Comparison of the averaged vertical and horizontal difference histograms of APPM and DE. (a) AMMP , (53-ary notational system).(b) DE , (53-ary notational system). (c) AMMP , (221-ary notational system). (d) DE , (221-arynotational system).results. The experimental results agree with the fact that APPM for DE, which were equivalent to embed digits in 53-aryis more secure against SPAM steganalyzer than LSB-M. and 221-ary notational systems, respectively. Digits in the same notational systems were used in APPM. All the test images wereB. Statistical Analysis of the Histogram Differences fully embedded, and was used in the experiments, as In 2009, Zhao et al.  proposed a detection method based suggested in . The results are shown in Fig. 7.on the statistical analysis of histogram differences. Zhao et al. As can be seen in Fig. 7(a) and (c), the averaged horizontalobserved that for many pairwise embedding methods, the differ- and vertical difference histograms obtained by APPM are al-ence between the horizontal difference histograms and ver- most the same ( and , respectively), whereas thetical difference histograms are signiﬁcantly altered. Zhao et difference histograms shown in Fig. 7(b) and (d) obtained byal. use the distance between and as a statistical detector DE are signiﬁcantly altered ( and , respectively).to detect the abnormality of histogram. The distance is deﬁned The results show that APPM preserves the shape of differenceas histogram even at high payload, which indicates that the pro- posed method is secure under Zhao et al.’s method. On the other hand, DE deviates the distance between the horizontal and ver- tical histograms signiﬁcantly, and the presence of the embedded message is likely to be detected.where is a predeﬁned threshold. A larger indicates thatand have larger differences and thus, the image is likely VI. CONCLUSIONto have messages embedded. We compare APPM with DE at This paper proposed a simple and efﬁcient data embeddinghigh payload because the abnormality of histograms often oc- method based on PPM. Two pixels are scanned as an embeddingcurs when the payload is high. In the experiment, we randomly unit and a specially designed neighborhood set is employed toselected 100 images from , and averaged the horizontal and embed message digits with a smallest notational system. APPMvertical difference histograms of the stego images obtained by allows users to select digits in any notational system for data em-APPM and DE. We chose the embedding parameter and bedding, and thus achieves a better image quality. The proposed
184 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 7, NO. 1, FEBRUARY 2012method not only resolves the low-payload problem in EMD, but  J. Fridrich and D. Soukal, “Matrix embedding for large payloads,”also offers smaller MSE compared with OPAP and DE. More- IEEE Trans. Inf. Forensics Security, vol. 1, no. 3, pp. 390–394, Sep. 2006.over, because APPM produces no artifacts in stego images and  C. H. Yang, “Inverted pattern approach to improve image quality ofthe steganalysis results are similar to those of the cover images, information hiding by LSB substitution,” Pattern Recognit., vol. 41,it offers a secure communication under adjustable embedding no. 8, pp. 2674–2683, 2008.  T. Pevný, P. Bas, and J. Fridrich, “Steganalysis by subtractive pixelcapacity. adjacency matrix,” IEEE Trans. Inf. Forensics Security, vol. 5, no. 2, pp. 215–224, Jun. 2010. REFERENCES  H. Zhao, H. Wang, and M. K. Khan, “Statistical analysis of several reversible data hiding algorithms,” in Proc. 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