Abstract—In normal Steganography, the main motivation isto maintain high quality of the stego image, so that one isnot suspicious that there is a hidden image. At times, it isimportant that the hidden image quality needs to be maintainedafter recovery. How to achieve high quality of hidden imageis the motivation of this work. To solve this problem, beforethe hiding procedure, pixels of the secret image are analyzed togenerate the optimum code book. Most frequently occurring pixelvalue is encoded with the shortest code to minimize stego-imagedistortion. For evaluation, we not only tested the distortion ofsimple hidden images like a logo, but also high resolution images.Using the proposed method, PSNR value of more than 45.6 dbfor the stedo-image was achieved even for high resolution hiddenimage. Secret image PSNR after recovery was 50 db or more. Wecould conclude that the proposed method can yield good resultsregardless of the type of hidden image.Keywords: Data hiding, Secret Symbol, Re-Encoding Strategy.
I. INTRODUCTION
How to make sure that the important information in thehidden file can be delivered to receiver without distortion?To solve this problem, the motivation of Steganography isbe changed. Many scholars proposed an information hidingalgorithm where the motivation is to enhance the security ofinformation[4]. In other words, attaining high PSNR for thestego image is the main aim of all previous works (i.e., PSNR1in Fig. 1). Steganography involves hiding secret information indifferent media such as image, audio, text, video, or characterin different ways to produce the stego-media. The property ofstego-media is same as original media. The aim is that theexistence of secret information in the hiding media shouldnot be noticeable. As a result, the multimedia can be securelytransmitted without being noticed.
As a general rule, Data hiding techniques can be classifiedas reversible or irreversible, depending on whether the stego-media can be restored or not. In reversible data hiding (RDH),the stego-media can be recovered to its original state withoutdistortion, after it is extracted. RDH is often used in medicalor military application. In irreversible data hiding, after theinformation have been extracted, it is partially damaged[1][2].It could not be recovered to the original form, but the requiredamount of information, which depends on application, couldbe recovered. While hiding large amount of data, like image,irreversible data hiding is used. In most of the applications, ifthe extracted image quality is reasonable, the performance is
Fig. 1. The Concept of Steganography.
satisfactory. In other words, very high PSNR between hiddendata and extracted data were never considered (PSNR2 inFig. 1).
To achieve larger amount of data hiding, many researcheson Irreversible data hiding technique have been proposed.The pixel value differencing (PVD) technique is one of theimportant method proposed by Wu and Tasi [1]. An originalimage is divided into several non-overlapping 1×2 sizedblocks and computed the error value of neighboring pixels ineach pair. How many hidden bits should be embedded into anoriginal image are determined through these difference values.If the difference value is large, it means that the pair is inan area where every pixel value is important which shouldbe considered while hiding secret information. Otherwise, ifthe difference value is small, then we know that the pair isin a smooth area of the image. Values for all pixels are lessimportant. The final motivation is to hide as much data aspossible, causing as little distortion of the stego-image. Basedon this idea, several novel methods based on PVD techniquehave been proposed to improve their capacity and stego imagequality [2][3][4].
Most of the data hiding techniques focused on proposing anovel algorithm to embed secret information into an originalimage, and ensure that the stego image does not suffer distor-tion detectable by human eye. In 2014, Chang et al. proposeda novel method called the turtle shell method [5] (Please referto Fig. 2 for locations of the 8 pixels). In their study, twocontinuous pixels of the original image are considered as agroup, the pixel value of the first being abscissa and second
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the ordinate on the referenece matrix (Fig. 2). Secret data isembedded by mapping the reference matrix. A turtle shell isa hexagon that contains 8 different digits from 0 to 7, threebit data from (000)2 to (111)2 in binary form. Each pair canembed 3 bits of secret data. Several methods, to obtain highcapacity and high quality stego image, have been proposed[6][7][8]. However, its disadvantage is its inflexibility due tothe fixed turtle shell matrix structure by which hidden secretbit length is limited.
In this study, we proposed a novel method that generatedan optimal code book based on secret information. This re-encoding strategy enhances the hiding performance. First, thereference matrix is constructed by proposed function insteadof turtle shell, n×n sized square blocks. n in our algorithmcould be 3 or 4. The block size is determined depending onthe number of bits to be hidden. For maintaining the imagequality, we used images as secret information encoded to abinary string. Meanwhile, the re-encoding strategy is used togenerate the new code for the secret information accordingto its frequency of occurrence. Finally, the secret informationis embedded using the new code. The hiding procedure issame as Chang et al.’s method [5]. The experimental resultsshow that the proposed method has better flexibility forconstructing the reference matrix and the number of bits thatcould be hidden. Proposed algorithm also facilitates higherhiding capacity and better quality of both stego and hiddenimage.
The rest of this paper is organized as follows. In section 2,we review Chang et al. proposed technique [5]. In section3, we describe the concept of the proposed scheme anddemonstrate its performance using simulation experiment. Insection 4, we evaluate our experimental results, and we drawour conclusions in section 5.
II. RELATED WORK
The turtle shell method is proposed by Chang et al in 2014[5], where 3 bits of secret information could be hidden inone pair. A turtle shell is a hexagon that accommodate 8different digits from 0 to 7, in binary (000)2 to (111)2. Beforeembedding, 3 bits of hiding image is read and convertedinto decimal format. The secret value will be hidden throughreference matrix.
1) The Embedding Procedure: In their method two pixlesare consider as a pair of original image.The first is abbsassicaand second oridnate of the reference matrix location. If thereference matrix loaction matches with the secret infroamtion,original image pixels are unchanged. If it is not, nearsetlocation of reference matrix containing the hiding informationis selected. This referenece martix loaction become, the newpixel value of the original image. Due to the hexagon turtlestructure, new reference matrix contain will change only alittle. Therefore, distortion in the original image is low.
The reference matrix is constructed first. First row startswith 0 and serially goes to 7, from pixel to pixel, as shownin Fig. 2. The same sequence is repeated along the row.Upper rows are filled out using two rules. At the bottom
row, the first pixel starts with 0. For the next upper row,it starts with 2 (=0+2), and the row above starts with 5(=2+3). This difference of 2 and then 3, continues for allsubsequent upper rows. When it crosses 8, modulo 7 is used.The counting on the right pixel increment by 1 to next pixel,until it reaches 8 when it is reset to 0. We continue in thismanner to populate the entire reference matrix. Please notethat all concatenated hexagons will contain distinct digits from0 to 7. The matrix is shown in Fig. 2. Suppose the original
Fig. 2. The Reference Matrix.
image is X = (p1,1, p1,2, p1,3, ..., ph,w), where h is heightand w is width of the original image, respectively. For hiding,the location of each pixel pair (pi, pi+1) is mapped on thereference matrix, where pi the abscissa and the pi+1 as theordinate in the reference matrix. Reference matrix value at(pi, pi+1) is compared to the next 3 bits of the hiding data. Ifthey are same, no modification of the original image is done.If they are different then the one of the following the threerules is used to embed the hidden value into the pixel pair:
Rule 1: The corresponding reference matrix value is withinthe turtle shell.When the value of secret inforamtion is within the samehexagon turtle of the reference matrix, its coordinate replaces(pi, pi+1) of the original image.
Rule 2: The corresponding reference matrix value is locatedon the overlapping edge of the turtle shell.If the corresponding reference matrix value is located on theoverlapping edge of the turtle shell, the hidden value searchwill include the adjacent turtle shell. While selecting locationin the reference matrix form the adjacent turtle shells, we willminimize modification of (pi, pi+1).
Rule 3: The corresponding reference matrix value is notlocated on any turtle shell.The searched area is replaces by a 3×3 square block wherethe pair is located, on which it includes 8 different values.
We explain the above with examples in Fig. 3. For example,let us assume that at pixel pairs (4,3), and (1,1), the secretvalues are (000)2 and (010)2. We find the correspondingreference matrix value. We realize that the hidden value and
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Fig. 3. The Sample of Hidden Procedure.
corresponding reference matrix value are different. Followingthe embedding rule, we find that corresponding referencematrix value is located on the overlapping edge of the turtleshell. Therefore, the hidden value need to be found from theadjacent three turtle shells. Here, the three candidates stegopairs are (3,2), (4,5), and (6,4). For maintaining the quality ofstego image, pixel pair (4,5) is selected as stego pixel, becausethen the difference between original pixel (4,3) and stego pixelis the smallest. Following the same logic, the hidden value2 (=010) is hidden in (1,1). In case, when according to theposition of pixel pair the corresponding reference matrix valueis not located on any turtle shell, we obey rule 3 for hiding.Therefore, searching the candidate pixel through 3×3 squareblock, then (0,1) is taken as stego pixel.
2) The Extracting Procedure: The hidden value is extractedbased on the reference matrix. From the stego image, thecoordinate of each pair of the hidden value is known, andtherefore the position in the reference matrix can be deter-mined. Converting the value into binary string, the originalsecret value will be recovered. For the above example, forstego pair (4,5) the hidden value is extracted by mappingto the reference matrix. The obtained secret value 0 is thentransformed into binary (000)2. For the next pair (2,0), usingthe same procedure we extract the hidden value as 2, whichis then converted into binary string (010)2. Fig. 3 illustratesthe procedure for extraction.
III. PROPOSED METHOD
Embedding secret information in an otherwise clean imagecause image distortion. In addition, depending on how thesecret information is embedded and extracted, some noise isadded to the secret information too. The aim of our method isnot only to achieve a high quality stego-image, but also lowdistortion for the secret information after extraction. In thiswork, in all our experiments both the secret information aswell as the hiding media are images.The secret image is encoded so that frequently occurring
information are encoded to shorter length. For proper encodingscheme, the pixels of the secret image is scanned. Next,the secret information is encode based on their frequencyand the new encoded secret information is created, which isthen hidden in the original image. In the next subsection, weprovided the detail of the algorithm. The steps are summarizedin Fig. 4.
Fig. 4. Flow of the proposed algorthim.
1) Pre-Processing : Let SI the secret image, SI =(SI1,1, SI1,2, SI1,3, ..., SIh,w), h is the height and w is thewidth of the secret image. Next, convert all the pixels intobinary string. If every pixel is represented by 8-bits, it willbe 8×h×w bits. We consider 3 or 4 secret bits 4 for moresignificant bits and 3 for least significant bits ignoring the LSBas a set and calculate their frequency of occurrence. In orderto get an efficient coding, frequently occurring set of bits willbe represented by a shorter code than that code used for a lessfrequent set of bits. Any 8-bit information of the secret fileis first divided into two parts, first part being the first 4 bits,and the second part the first 3 bits of 4 bits. As an example,let SI = (25, 24, 23, ..., 50). We convert SI1,1 = (25)10 intobinary (00011001)2. The first 4 bits, (0001)2 is kept as it is,i.e., the first secret code is S1 = (0001)2. The next 4 bits, i.e.,(1001)2 is reduced to 3 bits by deleting the LSB. It becomesS2 = (100)2 = (4)10. Once recovered, it will be (00011000)2which is 24, one less than the original 25. We ignored the leastsignificant bits, because distortion introduced will be small.We calculated all pixels of the secret file in decimal formatand generated a new code book depending on their frequencyof occurrence. That will improve Bit Per Pixel of the hidingalgorithm. It will also lead to high quality of stego image. Thesample of code book in Nike logo is shown as below:
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Frequently occurring pixel values will use smaller code.In Table I and Table II, the most frequently occurring secretinformation is 0. Its corresponding new code is also 0. Thisis because the background of Nike image is black.
2) Embedding Process : Once pixel value in the secretimage is divided into two parts: (1) 4-bit part and (2) 3-bitpart, as already explained. To hide these two parts, we usefour pixels of the original image, two pixels say (pi, pi+1) forhiding 4-bit part, and next two pixels (pi+2, pi+3) to hide 3-bitpart. For 4-bit part, we need 4×4 block reference matrix andfor 3-bit part, we need 3×3 block reference matrix. Due tothe number of hidden bits are different, we need two types ofreference matrix to conceal 4-bits pair and 3-bits pair of thesecret image.First type: Hiding 4 bits of secret data.In this section, a reference matrix is first constructed for hiding4-bits pairs. To hide 4-bits, whose value could be 0 to 15,we need a hiding block of size 4×4. This corresponds tobinary from (0000)2 to (1111)2. Following function is usedto generate the reference matrix M:
y = ((pi × n− pi+1(n+ 1)) + (n+ 1))mod(n+ 1) (1)
On pi and pi+1 are coordinate values of a pixel pair, wherethey range from 0 to 255, because the image is 8-bitsgreyscale. For 4×4 block reference matrix n = 4, and for3×3 block reference matrix n = 3. Thus, a reference matrixM with size of 256×256 is be constructed. In our study, thestructure of the reference matrix is simple, we only need tocalculate the first block where the pixel value is from 0 to 4.The remaining pixels are repeated using the same value as thefirst block. As a result, we do not need to store the referencematrix as an extra information. Fig. 5 illustrates the referencematrix M based on 4×4 block. 4 secret bits will be hiddeninto the pixel pair (pi, pi+1), pi represents the vertical axis andpi+1 represents the horizontal axis, respectively. According tothe position, the corresponding reference matrix value C in4×4 block is found. The value of pixel will not be changedwhen the value of C is equal to secret value, otherwise itsvalue will be changed. This will create some distortion in thestego-image.Second type: Hiding 3 bits of secret data.Similar to the above section, we need to generate a referencematrix to hide for 3-bits of information. The reference matrixM based on 3×3 block is shown in Fig. 6. After the referencematrix is constructed, the secret value is to be hidden intothe pixel pair, the hiding procedure is similar as Chang et al[5]. For instance, assume the first pixel pair is (5,2), and thesecond pixel pair is (3,5), the secret value being (0000)2 and(011)2. (As mentioned earlier, in our study, the secret valueis translated to different code by encoding strategy, as shownin Table I and Table II. The encoded symbols are used forhiding.) In the first pixel pair, we hide 4 bits secret information.The original secret value in decimal format is 0. Based onthe code book (Table I), we obtain the new secret symbol,which is 0 too. Next, we find the corresponding value 0 in the4×4 block matrix. Here, the secret symbol and corresponding
Fig. 5. An example of the reference matrix M in 4 × 4 block.
value is same. There is no change in (5,2), which is alsoconverted as stego pixel. In the second pixel pair (3,5), wehide 3 bits secret information. The original secret value indecimal format is 3. Based on the code book (Table II) thesecret value is converted to 5. Next, depending on the pixel pairwe obtained the corresponding reference matrix value 8 in the3×3 block matrix. Here, the secret symbol and correspondingreference matrix values are different. We search through 3×3block matrix to find which matches the value correspondingto secret symbol. Finally, (3,4) is taken as stego pixel.
Fig. 6. An example of the reference matrix M in 3 × 3 block.
3) Extraction Process: In the extraction procedure, we caneasily extract the secret information by drawing out pixelpairs sequentially and use them to map in different typesof reference matrix. In this procedure, the embedded secretinformation is extracted correctly from pixel pair (pi, pi+1). Itis then mapped to 4×4 block matrix to find the correspondingvalue which indicates the hidden secret information. The nextpair (pi+2, pi+3), following the same way, is extracted from3×3 block matrix. After all stego pairs are mapped within thereference matrix M, the extracted secret image is recovered bymapping to the original value using the code book and finallyconverting those values to binary.
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IV. EXPERIMENTAL RESULTS
Six standard gray-level images were used for testing theperformance of the proposed method. The test images areoriginal images in Fig. 7 and secret images in Fig. 8. Theoriginal are color images, which we converted to grey-scalefor our experiments. All original images are of size 512×512.The secret information to hide are six secret images as shown
(a) Lena (b) Baboon (c) Pepper
(d) Jet (e) Lake (f) House
Fig. 7. Testing images.
in Fig 8. The secret images are in color. Before hiding wemust convert them to gray level. All secret images are of size256×256. The proposed algorithm was developed in MatlabR2015b. The PSNR value is used for evaluating the quality of
(a) Nike (b) Puma (c) Cameraman
(d) GitHub (e) Girl (f) Korea
Fig. 8. Secret images.
stego-image and extreacted secret image. Before embedding,the secret image is transferred into binary format first. Forexample, the size of Nike logo is 256×256. Thus the totalnumber of secret bits is 256×256×8 = 524,288, where everypixel is expressed as 8-bit grey-scale value. 3 to 4 consecutivebits of secret information is grouped together and convertedinto its decimal value. Whether it will be 3-bits or 4-bits, willbe explained soon. Many of the secret pictures are with blackbackground for which the pixel value is 0. Depending on the
reference matrix, the modification of pixel value will be small.In order to achieve high hiding capacity, re-encoding strategyis introduced. This encoding depends on the frequency of thehiding data, more frequent data are encoded to shortest bit-length. The bpp and PSNR value is shown in Table III. Thesecret image is Nike logo and the size of hidden matrix is 4×4and 3×3. The average PSNR value of the stego-image is morethan 47.45 db, which is good enough to retain the quality of theoriginal image. In our method, the 8-bits pixel value of secretimage is split into two parts: the Most Significant Bit (MSB)part and Least Significant Bit (LSB) part. 4-bits are used forMSB part (to keep the quality good) and 3-bits are used forLSB part. We ignore the very least significant bit, and whenit is 1, some distortion is added to the hidden image afterextraction. Using the proposed method, the extracted secretimage keeps very high PSNR value of 60.36 db. Obviously, itis same for all mother images. Depending on the hiding image,it will vary a little, but will always maintain a high value. InTable IV to Table VIII, performance of our method in terms ofbpp and PSNR values (for both original and hidden images)are shown. The secret images, as shown in Fig 8, are Nike,Puma, Cameraman, GitHub, Girl, and Korea, respectively.In Table IV, the peformance for secret image Puma logo isshown. Puma logo is like Nike with many black pixels. Hence,the value of the stego-image of PSNR is not much differentbetween Nike and Puma secret images. The PSNR value ofextracted image are different, because Puma image has morewhite pixel compared to Nike.
TABLE IIIRESULT FOR SECRET IMAGE NIKE LOGO
Test Image Proposed Method Extracted ImageBPP PSNR PSNR
Lena 1.75 47.46
60.36
Baboon 1.75 47.45Pepper 1.75 47.47
Jet 1.75 47.47Lake 1.75 47.45
House 1.75 47.42
TABLE IVRESULT FOR SECRET IMAGE PUMA LOGO
Test Image Proposed Method Extracted ImageBPP PSNR PSNR
Lena 1.75 47.46
56.66
Baboon 1.75 47.45Pepper 1.75 47.47
Jet 1.75 47.47Lake 1.75 47.45
House 1.75 47.42
Table V and Table VI, are results for secret images GitHuband Korea. Both have many white pixels, which are all 1. Theextracted image quality not only depends on the optimal codebook but also on the reference matrix. The best code bookis constructed through re-encoding strategy, but the referencematrix is fixed. The extracted secret image quality is lowerwhen background is white, as shown in Table V and Table VI.
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Of course, the PSNR value of extracted image is still around 50db. If we want to improve the secret image quality further, weneed to change the reference matrix depending on the secretimage.
TABLE VRESULT FOR SECRET IMAGE GITHUB LOGO
Test Image Proposed Method Extracted ImageBPP PSNR PSNR
Lena 1.75 46.99
51.83
Baboon 1.75 47.00Pepper 1.75 46.99
Jet 1.75 47.01Lake 1.75 47.00
House 1.75 46.97
TABLE VIRESULT FOR SECRET IMAGE KOREA LOGO
Test Image Proposed Method Extracted ImageBPP PSNR PSNR
Lena 1.75 46.91
49.21
Baboon 1.75 46.90Pepper 1.75 46.92
Jet 1.75 46.93Lake 1.75 46.90
House 1.75 46.87
To ensure that our method is not limited to simple images,we tested hiding performance on different types of testingimages such as Girl, and Cameraman. Performance resultsare shown in Table VII and Table VIII. Results are worsecompared to those shown in Table III to Table VII. Due tocomplex nature of the secret images, the modification of theoriginal image is large. The PSNR value of the stego-imageusing the proposed method is on an average slightly higherthan 45.6 db. PSNR of the extracted image is very high, atmore than 51 db.
TABLE VIIRESULT FOR SECRET IMAGE CAMERAMAN LOGO
Test Image Proposed Method Extracted ImageBPP PSNR PSNR
Lena 1.75 45.56
51.16
Baboon 1.75 45.60Pepper 1.75 45.61
Jet 1.75 45.59Lake 1.75 45.59
House 1.75 45.60
TABLE VIIIRESULT FOR SECRET IMAGE GIRL LOGO
Test Image Proposed Method Extracted ImageBPP PSNR PSNR
Lena 1.75 45.52
51.14
Baboon 1.75 45.50Pepper 1.75 45.50
Jet 1.75 45.51Lake 1.75 45.51
House 1.75 45.49
Form the tables, for black background secret images suchas Nike, and Puma, we can see that for these pictures per-formance is better than other pictures. For white backgroundsecret images such as Korea, and GitHub, the proposedmethod still have a good performance (for stego-image) butworse compared to secret imges with black background. Thereason is because the reference matrix is suitable for blackbackground. Because most white pixels are located at thecenter position of the reference matrix therefore the error is0. The stego-pixels are not shifted from its original position.It is suitable for hiding smooth secret images like flags andlogos. For complex images too, we could achieve high PSNRvalue. The proposed method can yield good results regardlessof image type.
V. CONCLUSION
In this paper, we proposed a new method to generate thereference matrix. For increasing the PSNR value of the secretimage after extraction, we encoded pixels in the secret imageby using the proposed re-encoding strategy. Most frequentlyoccurring secret value is encoded with the shortest code.Conversely, the least frequent secret value is encoded withthe longest code. The new encoded data is concealed as thesecret data in the original image.
The experiment results show that the PSNR value usingthe proposed method is high, irrespective of the secret imagesbeing smooth or complex. One drawback is that we used fixedreference matrix. If the reference matrix is changed, dependingon the contents of the secret file, the performance (PSNRvalues) would improve. In future work, we will find flexiblemethod to construct the reference matrix based on the secretimage characteristics to achieve better quality of the stegoimage.
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