Information Hiding in Image using Combined Approach of Pixel Mapping Method and Pixel Value Differencing Method

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1 Informaton Hdng n Image usng Combned Approach of Pxel Mappng Method and Pxel Value Dfferencng Method Souvk Bhattacharyya 1, Prtn Haldar 2, Indradp Banerjee 3 and Gautam Sanyal 4 1,2,3 Computer Scence & Engneerng Department, Unversty Insttute of Technology, Burdwan Unversty 4 Department of Computer Scence and Engneerng, Natonal Insttute of Technology Abstract: The staggerng growth n communcaton technology and usage of publc doman channels has greatly facltated the transfer of data. However, such open communcaton channels have greater vulnerablty to securty threats causng unauthorzed nformaton access resultng popularty of Informaton Hdng over the past few decades. The securty and far use of the nformaton wth guaranteed qualty of servces s mportant, yet challengng topcs. Steganography s an area of nformaton hdng whch means "secret or covered wrtng. In ths paper, the authors have proposed an mage based steganography technque for hdng nformaton wthn the spatal doman of the grayscale mage. The developed approach works by dvdng the cover mage nto 3 by 3 blocks and then embeds the secret nformaton n the dfference of the 8-neghborhood pxels n the two adjacent blocks usng 2-bt, 3-bt or 4-bt Pxel Mappng Method. Expermental results through qualtatve and quanttatve metrcs show that the proposed approach has better embeddng capacty compared to the orgnal 2-bt or 4-bt Pxel Mappng Method and produces stego mage wth hgh mperceptblty. Keywords: Pxel Mappng Method (PMM), Pxel Value Dfferencng (PVD), Steganography, Qualtatve and Quanttatve Smlarty Metrcs, Cover Image, Stego Image. I. INTRODUCTION Steganography s used to hde nformaton nsde other. The word steganography s derved from the Greek word, whch lterally means Covered Wrtng [1]. Steganography technques allow communcaton between two certfed users wthout an observer beng responsve that the communcaton s actually happenng. The useful steganography system must provde a method to embed data n an mperceptble manner, allow the data to be readly extracted, promote a hgh embeddng capacty and ncorporate a certan extent of robustness. In ths work the authors have presented an effcent mage steganography method for hdng nformaton wth the extended approach of Pxel Mappng Method (2-bt or 4-bt) wth a combnaton of Pxel Value Dfferencng method and try to ncorporate a 2-bt, 3-bt, 4-bt PMM approach together to hde the nformaton. The rest of ths paper s organzed as follows: Secton 2 ntroduces some data hdng methods n spatal doman. Secton 3 and Secton 4 deal wth the proposed methodology and soluton methodology. Secton 5 contracts wth algorthm and dfferent expermental measures used to test the algorthm have shown n Secton 6. Secton 7 s compared wth other exstng steganography methods and the concluson s drawn n Secton

2 II. REVIEW AND RELATED WORKS A. Data Hdng through LSB One of the most common technques of data hdng s Least-sgnfcant-bt (LSB) [2] modfcaton. It s done by replacng the LSB porton of the cover-mage wth message bts. LSB methods naturally accomplsh hgh capacty embeddng, but unluckly LSB nserton s exposed to slght mage operaton such as compresson or croppng technque. B. Gray Level Modfcaton (GLM) The GLM has proposed by Potdar et al.[3], whch s a mappng technque used to modfy the gray level value of the mage pxels. Gray level modfcaton Steganography s the technque to map data by modfyng the gray level values of the mage pxels wthout embeddng or hde. GLM technque uses the scheme of odd and even numbers for mappng the data wthn an mage. It s the one-to-one mappng concept among the bnary data and selected pxels of the mage. From a partcular mage, a set of pxels s chosen based on a mathematcal functon. The gray level values of those pxels are observed and compared to the bt stream that s to be mapped nto the mage. Gray level values of the selected pxels,.e. the odd pxels are made even by changng the gray level by one unt. Once the entre selected pxel has an even gray level, t s compared wth bt stream, whch s to be mapped. If the bt s 0, then selected pxel s not modfed. If the bt s 1, then the gray level value of selected pxel s decremented by 1 to make t odd. C. Pxel Value Dfferencng Wu and Tsa [4] proposed pxel-value dfferencng (PVD) method whch can successfully provde both hgh embeddng capacty and exceptonal mperceptblty of the stego-mage. Ths method segments the cover mage nto non overlappng blocks holdng two connectng pxels and modfes the pxel dfference n each block (n par) for data embeddng. A larger dfference n the orgnal pxel values permts a greater modfcaton. In the extracton process, the orgnal range table s ndspensable. It s used to partton the stego-mage by the same method as used n the cover mage. Varous dverse approaches have also been proposed based on ths PVD method. Chang et al. [5] developed a new method usng tr-way pxel-value dfferencng and ths s better than orgnal PVD method wth respect to embeddng capacty and PSNR value. D. Pxel Mappng Method (PMM) Pxel Mappng Method [6], [7] s a method developed for nformaton hdng wthn the spatal doman of any gray scale mage. Numbers of research work has been done n these methods. Embeddng pxels are selected based on one mathematcal functon whch s dependng on the pxel ntensty value of the seed pxel. The eght neghbors of the seed pxels are taken n a counterclockwse drecton. Before embeddng a checkng has been done to fnd out whether the selected embeddng pxels or ts neghbors are lyng at the boundary of the mage or not. Data embeddng s done by mappng par of two or four bts from the secret message n each of the neghbor pxels wth the help of some features of that pxel. Extracton process starts agan by selectng the same seed pxels that were used n embeddng. Reversal operatons are carred out to get back the orgnal message at the recever sde. III. PROPOSED METHODOLOGY The proposed method s a combnaton of Pxel Value Dfferencng (PVD) and Pxel Mappng Method (PMM) whch sgnfcantly dffers from both the conventonal PVD and PMM methods. In ths method, frst the mage s dvded nto some 3 by

3 non-overlappng blocks. Then two consecutve, adjacent blocks are selected. The 8-neghbor pxels (P ) of the frst block s chosen n ant-clockwse drecton, whereas for the other block, the neghbor pxels are selected n clockwse drecton (P +1). The dfference (d) between the pxel ntensty values (8-neghbors) of the two adjacent blocks s determned as n PVD method. Embeddng s done on the dfferences of the pxel values n PMM method. Intally, the dfference of the ntenstes of the center pxels s determned. Dependng on the dfference value of the center pxels, t s decded whether 2-bt or 3-bt or 4-bt PMM would be mplemented. Table 1 descrbes the decson of embeddng bts. TABLE I DATA EMBEDDING TECHNIQUE DETERMINATION Dfference of center pxels ODD PRIME EVEN PMM 2-bt 3-bt 4-bt Data embeddng s done by mappng two or three or four bts of the bnary form of secret message n the dfference of the neghbor pxels establshed on some features of the dfference value. Table 2, Table 3 and Table 4 shows the mappng nformaton for embeddng two bts, three bts and four bts respectvely. TABLE II PIXEL MAPPING TECHNIQUE FOR TWO BITS MSG BIT PIXEL INTENSITY NO.OF VALUE ONES(BIN) 00 EVEN EVEN 01 EVEN ODD 10 ODD EVEN 11 EVEN EVEN TABLE III PIXEL MAPPING TECHNIQUE FOR THREE BITS MSG BIT 2 ND SET-RESET BIT PIXEL INTENSITY VALUE NO.OF ONES(BIN) 000 EVEN EVEN EVEN 001 EVEN EVEN ODD 010 EVEN ODD EVEN 011 EVEN ODD ODD 100 ODD EVEN EVEN 101 ODD EVEN ODD 110 ODD ODD EVEN 111 ODD ODD ODD 2784

4 TABLE IV PIXEL MAPPING TECHNIQUE FOR THREE BITS MSG 3 RD 2 ND PIXEL NO.OF BIT SET-RESET BIT SET-RE INTENS ONES(BIN) SET BIT ITY VALUE 0000 EVEN EVEN EVEN EVEN 0001 EVEN EVEN EVEN ODD 0010 EVEN EVEN ODD EVEN 0011 EVEN EVEN ODD ODD 0100 EVEN ODD EVEN EVEN 0101 EVEN ODD EVEN ODD 0110 EVEN ODD ODD EVEN 0111 EVEN ODD ODD ODD 1000 ODD EVEN EVEN EVEN 1001 ODD EVEN EVEN ODD 1010 ODD EVEN ODD EVEN 1011 ODD EVEN ODD ODD 1100 ODD ODD EVEN EVEN 1101 ODD ODD EVEN ODD 1110 ODD ODD ODD EVEN 1111 ODD ODD ODD ODD After embeddng the dfference of the 8-neghbors get modfed. The modfed dfference s d '. The dfference of the gray value s then adjusted n each pxel par (each from dfferent block) so that the dfference value causes unnotceable and mperceptble changes. B. Mathematcs Schemes ' P P P P P P ' 1 ' ' p ; m 0 ' 1 ' 1 p p p ; m 0 p m; m 0, p p 1 p abs( m); m 0, p p m; m 0, p p 1 1 abs( m); m 0, p p.(1) where, m=d-d ; P and P +1 are modfed pxel values after adjustment of the modfed dfference value. The extracton procedure starts by choosng the same seed pxels that were used durng embeddng. The reverse operatons are

5 carred out to get back the orgnal nformaton on the recever zone. Fg.1 and Fg.2 llustrate the block dagram of proposed methodologes. IV. SOLUTION METHODOLOGY Fg.1 Sender sde block dagram of proposed method Fg.2 Recever sde Block dagram of proposed method 2786

6 A. Let s consder ths 9X9 Cover Image Fg.3 9X9 Cover Image B. The Image s dvded nto some 3 by 3 non-overlappng blocks. Then two adjacent blocks (A&B, D&E and G&H) are selected. C. The secret message s GOD BLESS U CHILD. Its bnary form s 010/001/110/101/000/001/000/100/0100/0010/0100/1100/0100/0100/0101/0100/01/01/01/00/01/ 01/01/10. D. Now fndng the dfferences of Pxel Intensty Values of neghborng pxels (Fg.4). Fg.4 Block wse dfference of cover mage 2787

7 The dfference of the center pxels s found out.e. 8-27=19, whch s a prme number. So 3-bt secret message embeddng wll be done n the dfference of the 8-nehbours of the two adjacent blocks. So 010 s embedded n (5) to produce e Smlarly n all other seven dfferences the rest of the bts wll be embedded. The modfed dfferences are 1, 8, 7, 4, 0, 8, 0, and 12 respectvely. E. Adjustments 1) Case1: m d d' ;as m>0 and P > P +1 So, P' P m ) Case: m d d' ; so no adjustment s requred. Smlarly the adjustments are done for all the 8 cases. F. Now gettng the modfed blocks (fg.5) Fg.5 Modfed block of cover mage G. The stego mage s now sent to the recever sde where the reverse operatons are performed to fnd the hdden message. Intally, the dfference of the center pxels s found out = 8-27=19, whch s a prme number. So 3-bt wll be extracted from the dfference of the 8-neghbors of two adjacent blocks accordng to the rule shown n Table 1. H. Now fndng the dfferences of Pxel Intensty Values of neghborng pxels and the hdden message are found usng the table 5. I. Now gettng the entre secret message by assemblng all the bts. The bnary form s as follows:- 010/001/110/101/000/001/000/100/0100/0010/0100/1100/0100/0100/0101/0100/01/01/01/00/01/01/01/10 The message decphered s: GOD BLESS U CHILD. Fg.6 shows the cover and stego for ths development. Cover Image StegoImage (Embeddng20000 chars) Fg. 6 Cover and Stego 2788

8 TABLE V HIDDEN MESSAGE EXTRACTION PROCESS Dfference of pxel ntensty values Pxel Intensty Value Bnary Form NO.O F ONES (BIN) 2 nd Extracted SET-RESET 3-Bt Bt 8-7 = 1 ODD EVEN EVEN = 8 EVEN ODD EVEN = 5 ODD EVEN ODD = 4 EVEN ODD ODD = 0 EVEN EVEN EVEN = 8 EVEN ODD EVEN = 0 EVEN EVEN EVEN = 12 EVEN EVEN ODD 100 V. ALGORITHMS The proposed approach s a spatal doman approach and t has been used n grayscale mages. The dfferent algorthms used n approach are shown below: A. Algorthm for Data Embeddng 1) Dvde a grayscale mage nto 3 by 3 non-overlappng blocks and select two adjacent blocks from the left sde smultaneously. 2) Consder the dfference between each 8-neghbors of one block n antclockwse drecton wth each 8-neghbors of another block n clockwse drecton. 3) The no. of bts to be embedded n each of the dfference of the value depends on the dfference of center pxels of the two adjacent blocks. 4) Convert the dfference values nto ther correspondng bnary values. 5) Select a secret message and convert t nto ts bnary form. 6) Map 2-bt or 3-bt or 4-bt of the bnary form of secret message n every dfference of the neghborng pxels based on ntensty value, no. of one s (n bnary), 2 nd set-reset and 3 rd set-reset bt present n that dfference value. 7) Modfed dfference wll be generated. Adjust t n two neghbor pxel par each belongng from one of two consecutve blocks and obtan the modfed blocks. 2789

9 8) Repeat the process for all the adjacent blocks and obtan the stego mage. B. Algorthm for Data Extracton 1) Select the stego mage and dvde nto 3 by 3 non-overlappng blocks. Select two adjacent blocks from the left sde smultaneously. 2) Consder the dfference between each pxel ntensty value of one block n antclockwse drecton wth each pxel ntensty value of another block n clockwse drecton. 3) The no. of bts to be extracted from each of the dfference of the value depends on the dfference of center pxels of the two adjacent blocks. 4) Convert the dfference values nto ther correspondng bnary values. 5) Match the bnary value of the dfferences wth the propertes of ts correspondng PMM table and obtan correspondng 2 bts or 3 bts or 4 bts of the bnary form of secret message. 6) Arrange the obtaned bts n an orderly manner and get the requred secret nformaton. VI. RESULTS AND ANALYSIS In ths secton the authors have presented expermental results of the proposed method based on two benchmark technques for evaluatng the hdng performance. Frst one s the data hdng capacty and the second one s the mperceptblty of the stego mage. The qualty of the stego mage should be acceptable to human eyes. The experments have been performed on two well-known mages: Lena and Pepper. The qualty of the stego mages created by the developed method has been tested by dfferent qualtatve and quanttatve smlarty metrcs. The quanttatve values are llustrated n Table.5. A. Qualtatve Smlarty Metrcs The qualty of stego mage produced by the proposed methods and the stego mage has been tested thorough statstcal parameters lke Mean, Standard Error Mean, Tr Mean, Standard Devaton, Varance, CoefVar, Sum, Sum of Squares, Frst quartle (Q1), Medan (Q2), Thrd quartle (Q3), Range, Interquartle (IQR), Mode, N for Mode, Skewness, Kurtoss, MSSD, Covarance etc. Then examned the relatve error for the steganography methods wth respect to embeddng rate of each methods by calculatng the parameters value. Relatve errors are plotted on a graph and t shows that the error rate of developed method s less than the LSB and PVD method. The qualty of the steganography approach s dependng upon the relatve error graph. When the relatve error s less than or equal to the others method, the performance s better. B. Mathematcal Schemes E Statstcal parameters, R Relatve Error st err Calculate E and E Average E ) st Average ( st Stego ( E Average ) Cover ( E Average ) Estmate the relatve error Rerr...( 2) Cover ( E ) All these R 0,1 err Average. Here Stego denotes the statstcal parameter values of each methods and Cover denotes the cover mage 2790

10 used n ths method. Plot the Rerr n a graph. Table 6 llustrates the parameter values as well as relatve error. In the equaton 2, Stego denotes the statstcal parameter values of LSB, PVD and PMM Varable Bt. Fgure 7 shows the graph that shows the relatve errors.the detals of the tests are dscussed below: 1) Mean: In statstcs and probablty, the mean [8] s used to denote one measure of the central tendency ether of a probablty dstrbuton or random varable whch s characterzed by dstrbuton. For a data set, the mathematcal expectaton, arthmetc mean and at tmes average are used to refer to a central value of a dscrete set of numbers: defntely, the sum of the values dvded by the number of values. For a fnte populaton, the populaton mean of a property s equal to the arthmetc mean of the gven property whle consderng every member of the populaton. For example, the populaton mean heght s equal to the sum of the heghts of every ndvdual dvded by the total number of ndvduals. The sample mean may dffer from the populaton mean, especally for small samples. The law of large numbers dctates that the larger the sze of the sample, the more lkely t s that the sample mean wll be close to the populaton mean. 2) Standard Error Mean: The standard error (SE) [9] s the standard devaton of the samplng dstrbuton of a statstc, most commonly of the mean. The term may also be used to refer to an estmate of that standard devaton, derved from a partcular sample used to compute the estmate. 3) Trmmed Mean: A truncated mean or trmmed mean [10] s a statstcal measure of central tendency, much lke the mean and medan. It nvolves the calculaton of the mean after dscardng gven parts of a probablty dstrbuton or sample at the hgh and low end, and typcally dscardng an equal amount of both. Ths number of ponts to be dscarded s usually gven as a percentage of the total number of ponts, but may also be gven as a fxed number of ponts. 4) Standard Devaton: In statstcs, the standard devaton [11] (SD, also represented by the Greek letter sgma, σ) s a measure that s used to quantfy the amount of varaton or dsperson of a set of data values. A standard devaton close to 0 ndcates that the data ponts tend to be very close to the mean (also called the expected value) of the set, whle a hgh standard devaton ndcates that the data ponts are spread out over a wder range of values. 5) Varance: In probablty theory and statstcs, varance [12] measures how far a set of numbers s spread out. A varance of zero ndcates that all the values are dentcal. Varance s always non-negatve: a small varance ndcates that the data ponts tend to be very close to the mean (expected value) and hence to each other, whle a hgh varance ndcates that the data ponts are very spread out around the mean and from each other. 6) Coeffcent of Varaton: In probablty theory and statstcs, the coeffcent of varaton (CV) [13] s a standardzed measure of dsperson of a probablty dstrbuton or frequency dstrbuton. It s defned as the rato of the standard devaton to the mean. It s also known as untzed rsk or the varaton coeffcent. The absolute value of the CV s sometmes known as relatve standard devaton (RSD), whch s expressed as a percentage. The coeffcent of varaton (CV) s defned as the rato of the standard devaton to the mean 7) Quartle: In descrptve statstcs, the quartles [14] of a ranked set of data values are the three ponts that dvde the data set 2791

11 nto four equal groups, each group comprsng a quarter of the data. A quartle s a type of quantle. The frst quartle (Q 1) s defned as the mddle number between the smallest number and the medan of the data set. The second quartle (Q 2) s the medan of the data. The thrd quartle (Q 3) s the mddle value between the medan and the hghest value of the data set. In applcatons of statstcs such as epdemology, socology and fnance, the quartles of a ranked set of data values are the four subsets whose boundares are the three quartle ponts. Thus an ndvdual tem mght be descrbed as beng "n the upper quartle". a) Frst quartle (desgnated Q 1) also called the lower quartle or the 25th percentle (splts off the lowest 25% of data from the hghest 75%) b) Second quartle (desgnated Q 2) also called the medan or the 50th percentle (cuts data set n half) c) Thrd quartle (desgnated Q 3) also called the upper quartle or the 75th percentle (splts off the hghest 25% of data from the lowest 75%) d) Interquartle range (desgnated IQR) s the dfference between the upper and lower quartles. (IQR = Q 3 - Q 1) 8) Range: In arthmetc, the range [15] of a set of data s the dfference between the largest and smallest values. However, n descrptve statstcs, ths concept of range has a more complex meanng. The range s the sze of the smallest nterval whch contans all the data and provdes an ndcaton of statstcal dsperson. It s measured n the same unts as the data. Snce t only depends on two of the observatons, t s most useful n representng the dsperson of small data sets. 9) Mode: The mode [16] s the value that appears most often n a set of data. The mode of a dscrete probablty dstrbuton s the value x at whch ts probablty mass functon takes ts maxmum value. In other words, t s the value that s most lkely to be sampled. The mode of a contnuous probablty dstrbuton s the value x at whch ts probablty densty functon has ts maxmum value, so, nformally speakng, the mode s at the peak. 10) Skewness: In probablty theory and statstcs, skewness [17] s a measure of the asymmetry of the probablty dstrbuton of a real-valued random varable about ts mean. The skewness value can be postve or negatve, or even undefned. The qualtatve nterpretaton of the skew s complcated. For a unmodal dstrbuton, negatve skew ndcates that the tal on the left sde of the probablty densty functon s longer or fatter than the rght sde t does not dstngush these shapes. Conversely, postve skew ndcates that the tal on the rght sde s longer or fatter than the left sde. In cases where one tal s long but the other tal s fat, skewness does not obey a smple rule. For example, a zero value ndcates that the tals on both sdes of the mean balance out, whch s the case both for a symmetrc dstrbuton, and for asymmetrc dstrbutons where the asymmetres even out, such as one tal beng long but thn, and the other beng short but fat. Further, n multmodal dstrbutons and dscrete dstrbutons, skewness s also dffcult to nterpret. Importantly, the skewness does not determne the relatonshp of mean and medan. 11) Kurtoss: In probablty theory and statstcs, kurtoss [17] (from Greek: κυρτός, kyrtos or kurtos, meanng "curved, archng") s any measure of the "peakedness" of the probablty dstrbuton of a real-valued random varable. In a smlar way to the concept of skewness, kurtosss a descrptor of the shape of a probablty dstrbuton and, just as for skewness, there are dfferent ways of quantfyng t for a theoretcal dstrbuton and correspondng ways of estmatng t from a sample from a populaton. There are varous nterpretatons of kurtoss, and of how partcular measures should be nterpreted; these are prmarly peakedness (wdth of peak), tal weght, and lack of shoulders (dstrbuton prmarly peak and tals, not n between). 12) MSSD: The mean of the squared successve dfferences (MSSD) [18] s used as an estmate of varance. It s calculated by takng the sum of the dfferences between consecutve observatons squared, then takng the mean of that sum and dvdng by 2792

12 two. Two common applcatons are: Basc Statstcs - A common applcaton for the MSSD s a test to determne whether a sequence of observatons s random. In ths test, the estmated populaton varance s compared wth MSSD. Control Charts - MSSD can also be used to estmate the varance for control charts when the subgroup sze s 1. 13) Covarance: In probablty theory and statstcs, covarance [19] s a measure of how much two random varables change together. If the greater values of one varable manly correspond wth the greater values of the other varable, and the same holds for the smaller values,.e., the varables tend to show smlar behavor, the covarance s postve. In the opposte case, when the greater values of one varable manly correspond to the smaller values of the other,.e., the varables tend to show opposte behavor, the covarance s negatve. The sgn of the covarance therefore shows the tendency n the lnear relatonshp between the varables. The magntude of the covarance s not easy to nterpret. The normalzed verson of the covarance, the correlaton coeffcent, however, shows by ts magntude the strength of the lnear relaton. TABLE VI RELATIVE ERROR OF STATISTICAL PARAMETERS FOR LSB, PVD & PMM VARIABLE BIT Relatve Error Error Change Rate Embedd PMM PMM Varable LSB PVD LSB PVD ng Rate Varable Bt Bt

13 It has been observed that the developed method s robust and secure, whch has been verfed wth the help of relatve error graph and varous statstcal parameters. Thus the developed method works better than LSB, PVD mechansms. C. Quanttatve Smlarty Metrcs 1) Peak Sgnal-to-Nose Rato (PSNR): A mathematcal extent of mage qualty s Sgnal to-nose rato (SNR) [20], whch s based on the pxel dfference between two mages [21]. The SNR measure the estmate of Stego mage and cover mage. PSNR s shown n equaton (3). S PSNR 10log...(3) 10 MSE 2 Where, S s for the maxmum possble pxel value of the mage. When the PSNR s greater than 36 DB, the vsblty looks same n between the cover and stego mage; n that case the HVS s not dentfyng the changes. Fg. 8 Graphcal representaton of PSNR 2794

14 2) Mean Square Error (MSE): It s computed by averagng the squared ntensty of the cover and stego mage pxels [20]. The equaton (4) and fg.9 shows the MSE. MSE NM M N e m 0 n 0 2 m, n...(4 ) Where NM s the mage sze (N x M) and e(m,n) s the reconstructed mage. Root Mean Square Error (RMSE): RMSE [22] s a frequently used measure of dfference n between Cover and Stego ntensty values. These ndvdual dfferences called resduals and RMSE aggregate them nto a sngle measure of analytcal power. The RMSE shows n equaton (5) and fg.9. RMSE n 1 ( X obs, X n model, 2 )...( 5) X obs and X model are two mage vectors,.e. cover and stego Fg. 9: Graphcal representaton of MSE and RMSE 3) Correlatons: Pearson s correlaton coeffcent [23] s wdely used n statstcal analyss as well as mage processng. Here to apply t n, Cover and Stego mage, to see the dfference between these two mages. The Correlaton shows n equaton (6) and fg.10. The X and Y are the cover mage and bar of X and Y are stego mage postons. 4) Structural Smlarty Index (SSIM): Wang et. al[24], proposed Structural Smlarty Index [21] concept between orgnal and dstorted mage. The Stego and Cover mages are dvded nto blocks of 8 x 8 and converted nto vectors. Then two means and two standard dervatons and one covarance value are computed. After that the lumnance, contrast and structure comparsons based on statstcal values are computed. Then The SSIM computed between Cover and Stego mages. SSIM shows n equaton (7) and fg.10. r SSIM n 1 1 ( x ( x x) n x) ( y 2 n 1 y) ( y y) 2...( 6) 2 x y C1 2 xy C C C x y 1 x y 2...(7) 2795

15 Fg. 10 Graphcal representaton of Correlaton and SSIM 5) KL dvergence: Wth the help of probablty densty functon (PDF) for each Image (cover and stego) estmatng the Kullback-Lebler Dvergence [25]. KL dvergence shows n equaton (8) and fg.11. D p q p x x p log q x x...(8) Fg. 11: Graphcal representaton of Kullback-Lebler Dvergence 2796

16 TABLE VII VARIOUS IMAGE SIMILARITY METRICS FOR THE PROPOSED METHOD Images Lena 512*512 Lena 256*256 Lena 128*128 Length of Embeddng Character Metrcs PSNR MSE RMSE SSIM Correlaton KL dvergence 6.81E E E E E E-04 Entropy 7.42E E E E E E-05 PSNR N/A N/A MSE N/A N/A RMSE N/A N/A SSIM N/A N/A Correlaton N/A N/A KL dvergence 1.76E E E E-04 N/A N/A Entropy N/A N/A PSNR N/A N/A N/A MSE N/A N/A N/A RMSE N/A N/A N/A SSIM N/A N/A N/A Correlaton N/A N/A N/A KL dvergence 1.06E E E-04 N/A N/A N/A Entropy N/A N/A N/A TABLE VIII COMPARISON OF EMBEDDING CAPACITY IMAGE IMAGE AHMAD PMM(2 Proposed PVD GLM SIZE et al. bt) Method Lena 512* *256 ** *128 ** Pepper 512* *256 ** *128 **

17 TABLE IX COMPARISON OF PSNR VALUES BETWEEN PMM 4-BIT AND PROPOSED METHOD Image PSNR Character length PMM(4 bt) Proposed Method Lena512* ) Entropy: Entropy [26] s a measure of the uncertanty assocated wth a random varable. Here, a 'message' means a specfc realzaton of the random varable. The equaton (9) and fg.12 shows t. dqrev Where, S s the entropy and T s the unform S. thermodynamc...(9) temperature of a closed system dvded nto an ncremental T reversble transfer of heat nto that system (dq). Fg.12 Graphcal representaton of Entropy VII. COMPARISON WITH EXISTING METHODS A comparatve study of the proposed methods wth some other exstng methods lke PVD, GLM and the methods proposed by Ahmad T et al. s dscussed n ths secton. TABLE VIII shows the comparson of dfferent methodologes wth the help of embeddng capacty. TABLE IX shows the comparson of PSNR values of PMM (4 bt) and the proposed method. VIII. CONCLUSION A new and effcent steganography method for embeddng secret messages n grayscale mages has been proposed here. The expermental results through qualtatve and quanttatve smlarty metrcs clearly ndcate that the embeddng capablty of ths 2798

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