488 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL. 3, NO. 3, SEPTEMBER 2008

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1 488 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL 3, NO 3, SEPTEMBER 2008 Adaptive Data Hiding in Edge Areas of Images With Spatial LSB Domain Systems Cheng-Hsing Yang, Chi-Yao Weng, Shiuh-Jeng Wang, Member, IEEE, Hung-Min Sun Abstract This paper proposes a new adaptive least-significantbit (LSB) steganographic method using pixel-value differencing (PVD) that provides a larger embedding capacity imperceptible stegoimages The method exploits the difference value of two consecutive pixels to estimate how many secret bits will be embedded into the two pixels Pixels located in the edge areas are embedded by a -bit LSB substitution method with a larger value of than that of the pixels located in smooth areas The range of difference values is adaptively divided into lower level, middle level, higher level For any pair of consecutive pixels, both pixels are embedded by the -bit LSB substitution method However, the value is adaptive is decided by the level which the difference value belongs to In order to remain at the same level where the difference value of two consecutive pixels belongs, before after embedding, a delicate readjusting phase is used When compared to the past study of Wu et al s PVD LSB replacement method, our experimental results show that our proposed approach provides both larger embedding capacity higher image quality Index Terms Adaptive least-significant-bit (LSB) substitution, pixel-value differencing (PVD), steganography I INTRODUCTION T HE Internet is becoming increasingly popular as a communication channel However, message transmissions via the Internet have some problems, such as information security, copyright protection [1], [2], etc Therefore, we need a secure communication method to transmit messages via the Internet Encryption is one way However, encryptions result in a disordered confusing message make it suspicious enough to attract eavesdroppers Steganographic methods [3] [8] overcome this problem by hiding the secret information behind a cover, the result does not attract any special attention A well-known steganographic method is the least-significant-bit (LSB) substitution [9] [11] This method embeds secret data by replacing LSBs of a pixel with secret bits Manuscript received November 1, 2007; revised March 12, 2008 Published August 13, 2008 (projected) This research was supported in part by the National Science Council of the Republic of China under Grants NCS E in part by the TWISC@NCKU, National Science Council under Grants NSC E , NSC P Y, NSC E MY2The associate editor coordinating the review of this manuscript approving it for publication was Dr Hany Farid C-H Yang is with the Department of Computer Science, National Pingtung University of Education, Pingtung, 900, Taiwan ( chyang@mailnpue edutw) C-Y Weng H M Sun are with the Department of Computer Science, National Tsing-Hua University, Hsinchu, 300, Taiwan, ROC ( cyweng@iscsnthuedutw; hmsun@csnthuedutw) S-J Wang, corresponding author, is with the Department of Information Management, Central Police University, Taoyuan, 333, Taiwan, ROC ( sjwang@mailcpuedutw) Digital Object Identifier /TIFS directly However, not all pixels can tolerate an equal amount of change As a result, many new sophisticated LSB approaches have been proposed to improve this drawback [12], [13] Some of these methods use the concept of human vision to increase the quality of the stegoimages [14] [16] In 2003, Wu Tsai proposed a pixel-value differencing steganographic method that uses the difference value between two neighbor pixels to determine how many secret bits should be embedded [17] In 2005, Wu et al proposed the pixel-value differencing (PVD) LSB replacement method [18] In their approach, two pixels are embedded by the LSB replacement method if their difference value falls into a lower level Similarly, the PVD method is used if the difference value falls into a higher level If the embedding result causes the difference value to change from the lower level to the higher level, the two pixels values need to be readjusted such that their difference value comes back to the lower level Usually, the edge areas can tolerate more changes than the smooth areas Consider the past studies, such as Wu et al s scheme [18], that would cause pixels located in the lower level to embed more data than that in the higher level Next, the scheme in [19] provided the analyses of the PVD LSB replacement to significantly improve the works in [18] In 2005, Park et al proposed a steganographic scheme based on the information of neighboring pixels [20] In their approach, the number of bits embedded into a target pixel is determined by the difference value of its neighboring pixels, where is the upper pixel of is the left pixel of Their approach is similar to Chang Tseng s side-match method [14] However, their is embedded by LSB methods Chang Tseng s is embedded by PVD methods The embedding capacity of Park et al s method is far less than that of Wu et al s PVD LSB replacement method [18], [20] It is an important topic to find an adaptive steganographic method, which embeds data adaptively by considering the concept of human vision, with the features of high capacity low distortion A lot of approaches, including LSB techniques, PVD techniques, side-match techniques have been proposed to this topic [14] [20] Nevertheless, some of them seemed not to provide efficient capacities [14], [20], not completely obey the principle that the edge areas can tolerate more changes than smooth areas [18], [19] The fundamental analyses were also not discussed in past studies In this paper, a novel adaptive steganographic method for hiding data in gray images is proposed Our method obeys the basic concept that edge areas can tolerate more changes than smooth areas, our method can embed a large number of secret data maintain high qualities of the stegoimages First, some ranges are predefined by users /$ IEEE

2 YANG et al: ADAPTIVE DATA HIDING IN EDGE AREAS OF IMAGES WITH SPATIAL LSB DOMAIN SYSTEMS 489 level), (1) is used to readjust After the readjusting operation, the new difference then belongs to the lower level if (1) if For example, assume that, secret data The difference value is calculated by, which belongs to the lower level Therefore, the 3-bit LSB substitution method is used to embed into pixels After being embedded, Thus, After being readjusted, Hence, the new difference value is, which belongs to the lower level Fig 1 Wu et al s division of lower level higher level (Div = 15) Then, all pixels are embedded by the LSB replacement method with different numbers of secret bits Given two neighbor pixels, the number of embedding bits is evaluated by the range which their difference value falls into In addition, in order to increase the quality of stegoimages, a more skilful method is proposed to readjust the pixel values when embedding results cause the difference values to fall into another range Besides, perspective views to usher in our contributions are presented in a series of proof-based discussions in this paper The remainder of this paper is organized as follows Wu et al s pixel-value differencing LSB replacement method is introduced in Section II Our proposed method is presented in Section III, the experimental results are shown in Section IV The key fundamentals related to our ideas are discussed in lemmas theorems, shown in Section V Finally, conclusions are given in Section VI II LITERATURE REVIEW In this section, Wu et al s PVD LSB replacement method [18] is followed first Their approach uses gray-level images as cover images First, the cover image is partitioned into nonoverlapping blocks with two consecutive pixels, a division (Div) is used to partition the range [0, 255] into a lower level a higher level For example, as shown in Fig 1, Div is 15; therefore, the lower level includes range, the higher level includes ranges, Then, for the block with pixels, the difference value is calculated by, the range which falls into is determined If the difference value belongs to the higher level, the embedding method is the same as the pixel-value differencing Otherwise, the difference value belongs to the lower level, are embedded by the 3-b LSB substitution method Let be the embedded results of, respectively Note that the LSB substitution method may cause the new difference value to fall into the higher level Therefore, if the new difference value (ie, higher III OUR PROPOSED APPROACH The embedding strategy of our adaptive LSB substitution approach is based on the concept that edge areas can tolerate a larger number of changes than smooth areas Similar to Wu Tsai s scheme [17], pixel-value differencing is used to distinguish between edge areas smooth areas The range [0, 255] of difference values is divided into different levels, for instance, lower level, middle level, higher level For any two consecutive pixels, both pixels are embedded by the -bit LSB substitution, but the value is decided by the level which their difference value belongs to A higher level will use a larger value of In order to improve the quality of the stegoimages, we apply the well-known LSB substitution method, called the modified LSB substitution method [8], [11] The concept of the modified LSB substitution is to increase or decrease the most-significant-bit (MSB) part by 1 for reducing the square error between the original pixel the embedded pixel In order to extract data exactly, the difference values before after embedding must belong to the same level If the difference value changes into another level after embedding, a readjusting phase is used to readjust the pixel values The embedding extracting procedures of our approach are described in the following subsections A Embedding Procedure The cover images used in our method are 256 gray values The difference value is computed for every nonoverlapping block with two consecutive pixels The way of partitioning the cover image into two-pixel blocks runs through all of the rows in a raster scan Prior to the embedding procedure, the range [0, 255] must be divided into different levels Fig 2 shows two dividing cases: an - division an - - division In Fig 2(a), the first case has one dividing line, which divides the range [0, 255] into ranges, where the lower level contains the higher level contains Similarly, in Fig 2(b), the second case has two dividing lines;, which divide range [0, 255] into ranges,, where, belong to the lower level, middle level, higher lever, respectively The width of range is denoted as For example,, are shown in Fig 2(b) The - - division means that two-pixel blocks with difference values falling into the lower level, middle level, higher level, will be embedded by the -bit, -bit -bit LSB substitution approaches, respectively Since the edge

3 490 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL 3, NO 3, SEPTEMBER 2008 Fig 2 Two dividing cases: (a) lower level higher level (b) lower level, middle level, higher level areas can tolerate a larger number of changes, the proper relations of values, in Fig 2(a) (b) are, respectively In addition, to succeed in the readjusting phase, we apply the restrictions to the - division, restrictions to the - - division Examples in Fig 2(a) (b) show a 2 3 division a division, respectively For each block, the detailed embedding steps for an - - division are as follows Step 1) Calculate the difference value for each block with two consecutive pixels, say, using Step 2) From the - - division, find out the level to which belongs to Let,, if belongs to the lower level, middle level, higher level, respectively Step 3) By the -bit LSB substitution method, embed secret bits into secret bits into, respectively Let be the embedded results of, respectively Step 4) Apply the modified LSB substitution method to Step 5) Calculate the new difference value by Step 6) If belong to different levels, execute the readjusting phases as follows Case 61 lower-level, lower level If, readjust to being the better choice between ; otherwise, readjust to be the better choice between Case 62 middle level, lower level If, readjust to be the better choice between ; otherwise, readjust to be the better choice between Case 63 middle level, higher level If, readjust to be the better choice between ; otherwise, readjust to be the better choice between Case 64 higher level, higher level If, readjust to be the better choice between ; otherwise, readjust to be the better choice between In Step 6), the better choice, say, means that it satisfies the conditions that belong to the same level, also the value of is smaller For instance, consider the division shown in Fig 2(b) with, secret data First, the difference value is calculated by Since is the middle level, pixels are embedded by the 4-bit LSB substitution have results After the modified LSB substitution is applied, Now, belongs to the lower level In the readjusting phase, Case 62 is executed There are two readjusting results to be chosen choice, that is, B Data Extraction The first result is the better Hence, belongs to the middle level The stegoimage is partitioned into nonoverlapping blocks with two consecutive pixels, the process of extracting the embedded message is the same as the embedding process with the same traversing order of blocks Also, the same - - division, which is used in the embedding procedure, is used here For each block, the detailed steps of data extracting are as follows Step 1) Calculate the difference value for each block with two consecutive pixels, say, using Step 2) From the - - division, find out the level to which belongs to Let, if belongs to the lower level, middle level, higher level, respectively Step 3) From the -bit LSB of a pixel, extract secret bits from secret bits from The embedding example shown in the previous subsection is extracted here, where a division is used there is a block with For this block, belongs to the middle level Therefore, There are 4 bits embedded in 4 bits embedded in Thus, secret bits 1010 can be extracted from secret bits can be extracted from IV EXPERIMENTAL RESULTS In this section, we present some experiments to demonstrate that our adaptive LSB substitution approach is better than Wu et al s approach Ten cover images with size are used in the experiments, two of them are shown in Fig 3 A series of - divisions - - divisions with various dividing lines are used in the experiments We use the peak signal-to-noise ratio (PSNR) to evaluate qualities of the stegoimages Experimental results of two stegoimages are shown in Fig 4, where a 3-4 division with is used Also, two stegoimages

4 YANG et al: ADAPTIVE DATA HIDING IN EDGE AREAS OF IMAGES WITH SPATIAL LSB DOMAIN SYSTEMS 491 Fig 3 Two cover images (a) Elaine (b) Baboon a division with From Table III, we can see that our approach results in not only more capacity but also better quality On average, our approach with 3 4 division obtains more bits than Wu et al s; moreover, the PSNR value increases by 415 db For the case of the division, our approach results in more bits, the PSNR value increases by 036 db, on average In addition, other noticeable image quality measures, such as mean square error (MSE) image fidelity (IF) [21] are also applied to our method indicating the significance we contribute in this paper As shown in Table IV, it demonstrates that our approach has a characteristic of imperceptibility Since IF values are close to 1, it shows that our stegoimages remain as high fidelity Besides, from MSE values, it shows that the changed value of each pixel is between 3 6 on average Fig 4 Two stegoimages created by our approach with 3-4 division D = 7 (a) Elaine (embedded data are bits, PSNR is 3352 db) (b) Baboon (embedded data are bits, PSNR is 3301 db) Fig 5 Two stegoimages created by our approach with division D = 15 D =31 (a) Elaine (embedded data are bits, PSNR is 3782 db) (b) Baboon (embedded data are bits, PSNR is 3484 db) TABLE I RESULTS OF CAPACITIES AND PSNRS USING VARIOUS l-h DIVISIONS WITH DIVIDING LINE D =7 are shown in Fig 5, where a division with are used More experimental results using various - divisions with dividing line are shown in Table I Also, experimental results using various - divisions with dividing line are shown in Table II All results of capacities PSNRs are the averages of results created by executing different rom bit streams 100 times Table III shows the comparisons between the results of our proposed approach that of Wu et al s, in which our approach uses a 3 4 division with V FUNDAMENTALS AND DISCUSSIONS In this section, we show that our approach can embed data extract data correctly, give some discussions First of all, the restrictions of our approach are shown here For an - - division, let ranges, be the ranges of lower level, middle level, higher level, respectively In order to apply the - - division at our approach reasonably correctly, some restrictions are given to our approach all theorems in this section The restrictions are, The restriction means that the -bit modified LSB substitution used in our approach must have In the following theorems, we show that our approach succeeded in embedding extracting by proving that the readjusting phase works Definition 1: For the -bit modified LSB substitution, the range is called the Bottom extreme range the range is called the Top extreme range Both of the aforementioned ranges are called extreme ranges For the example of the 5-bit modified LSB substitution, range is the Bottom extreme range range is the Top extreme range Definition 2: For the -bit modified LSB substitution, pixel is modifiable if does not belong to the extreme ranges Note that if is modifiable, the MSB part of can be used to reduce the difference between original embedded whenever it is needed For instance, secret data, then is the embedded result using the 4-bit simple LSB substitution Now, the MSB part of is decreased by 1, which causes to reduce the difference between Therefore, is modifiable In another example, assume secret data, then is the embedded result using the 4-bit simple LSB substitution Now, the MSB part of cannot be used to reduce the difference between Therefore, is not modifiable Lemma 1: For the -bit modified LSB substitution, if pixel is modifiable, then Proof: After the -bit simple LSB substitution, the embedded result has The range is divided into three ranges,

5 492 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL 3, NO 3, SEPTEMBER 2008 TABLE II RESULTS OF CAPACITIES AND PSNRS USING VARIOUS l-h DIVISIONS WITH DIVIDING LINE D =15 TABLE III COMPARISONS OF THE RESULTS BETWEEN WU ET AL S METHOD AND OURS, WHICH USE A 3 4 DIVISION WITH D =15AND A DIVISION WITH D =15AND D =31 3) : can be modified as such that From the aforementioned discussions, we have Lemma 2: Suppose that are modifiable are embedded by -bit modified LSB substitution Then Proof: From Lemma 1, we know that Without loss of generality, let Therefore Also, Wehave TABLE IV RESULTS OF MEAN SQUARE ERROR (MSE) AND IMAGE FIDELITY (IF) USING A 3 4 DIVISION WITH D = 15 AND A DIVISION WITH D =15AND D =31,, to be considered 1) : can be modified as such that 2) : nothing to do Theorem 1: Suppose that are modifiable are embedded by the -bit modified LSB substitution, where their difference value belongs to range Then, the readjusting phase works Proof: In the conditions that fall into different ranges, Fig 6(a), (b), (d) shows the cases where belongs to the lower level, middle level, higher level, respectively From Lemma 2, the maximum difference between is, which has been pointed out in Fig 6 Since can go back to the range which belongs to by moving one of at distance Now, we show that at least one of can move by Without loss of generality, let We discuss the cases of Fig 6 one by one Case of Fig 6(a):

6 YANG et al: ADAPTIVE DATA HIDING IN EDGE AREAS OF IMAGES WITH SPATIAL LSB DOMAIN SYSTEMS 493 Fig 8 Ranges of p p, where p belongs to the extreme ranges Case of Fig 6(b): Let be the width of be the width of Since,wehave Therefore Fig 6 Cases that d d fall into difference ranges, where pixel p p are modifiable are embedded by k-bit modified LSB substitution: (a)d 2 lower level (b) One case of d 2 middle level (c) The other case of d 2 middle level (d) d 2 higher level Fig 7 Corresponding moving operations of p p in Fig 6: (a) d 2 lower level, (b) one case of d 2 middle level, (c) the other case of d 2 middle level, (d) d 2 higher level Since,wehave Therefore, both can move by The condition moving directions are shown in Fig 7(a) Therefore, at least one can move by Fig 7(b) shows the condition Case of Fig 6(c): Since,wehave Therefore, can move by Fig 7(c) shows the condition Case of Fig 6(d): Let be the width of be the width of Since,wehave Two restrictions are needed in this theorem: 1) 2) They imply that Thus, Therefore, at least one of can move by Fig 7(d) shows the condition From Definition 1, we have the following two Lemmas Lemma 3: For -bit modified LSB substitution, if Bottom extreme range, the embedded result has If Top extreme range, the embedded result has Lemma 4: For -bit modified LSB substitution, if Bottom extreme range, the embedded result has If Top extreme range, the embedded result has Fig 8 points out the ranges of, where belongs to the extreme ranges Lemma 5: Suppose that only one of is not modifiable, are embedded by -bit modified LSB substitution Then, Proof: Without loss of generality, let Suppose that Bottom extreme range does not belong to extreme ranges From Lemmas 1 3, we have

7 494 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL 3, NO 3, SEPTEMBER 2008 Therefore From (c) (d), we have (e) On the other h, suppose that does not belong to the extreme ranges Top extreme range From Lemmas 1 3, we have Therefore From (d), we have Thus, or If, from (e), can be readjusted by moving one of at distance Similar to Fig 7(b), at least one of can move by Therefore, the readjusting phase works On the other h, if, there is no need to readjust 3) higher level From Definition 1, we have Therefore, From Lemma 4, we have Therefore, From, we obtain Theorem 1 has shown that our approach is correct if none of belong to the extreme ranges Now, we discuss the cases that at least one of belong to the extreme ranges Without loss of generality, let These cases are divided into three categories: 1) Category A, 2) Category B, 3) Category C, as follows: Category A: Bottom extreme range or Top extreme range We just show the case of Bottom extreme range The proof of the other case is similar 1) lower-level From Definition 1, we have From Lemma 4, we have Therefore, there is no need to readjust 2) middle level middle level Also, we have Therefore From (a) (b), we have From Lemma 4, we have (a) (b) (c) (d) If, there is no need to readjust On the other h, if can be readjusted by moving one of at distance Similar to Fig 7(d), at least one of can move by Therefore, the readjusting phase works Category B: Bottom extreme range extreme ranges, or extreme ranges Top extreme range From Lemma 5, we have 1) lower level Fig 9(a) shows the possible location of Therefore, if can go back to by moving one at distance Thus, the readjusting phase works 2) middle level Fig 9(b) shows the possible location of If,any can go back to by moving one of at distance Thus, the readjusting phase works If, there are two conditions of Condition 1: In this condition, any can go back to by moving one at distance Thus, the readjusting phase works Condition 2: In this condition, moving one of by is not enough to send to Even worse, one cannot move by for the reason that one belong to the extreme ranges Our readjusting phase cannot work in this condition However, we propose a more sophisticated readjusting phase, which applies the method of pixel-value shifting [16] to solve this condition later 3) higher level Fig 9(c) shows the possible location of

8 YANG et al: ADAPTIVE DATA HIDING IN EDGE AREAS OF IMAGES WITH SPATIAL LSB DOMAIN SYSTEMS 495 Fig 9 Relative positions of d d, where pixel p p are embedded by k-bit modified LSB substitution: (a) d 2 lower level (b) d 2 middle-level (c) d 2 higher level If,any can go back to by moving one at distance Thus, the readjusting phase works If, there are two conditions of Condition 1: Similar to previous Condition 1, the readjusting phase works Condition 2: Similar to previous Condition 2, a more sophisticated readjusting phase is needed Category C: Bottom extreme range Top extreme range From Definition 1, we have Therefore, From Lemma 4, we have where where Therefore, there is no need to readjust From the aforementioned discussion, we have the following theorem Theorem 2: For an - - division, the readjusting phase works if It is very clear that all divisions used in Section IV satisfy Theorem 2 Therefore, all experimental cases in Section IV can be executed correctly Now, we give an example to demonstrate that the readjusting phase cannot work if the conditions in Theorem 2 are not satisfied Then, the example is solved by the sophisticated readjusting phase, which shifts parallelly moves by in different directions The example given here is in the Condition 2 of Category B3) Suppose that the division has Note that, Therefore, Let, secret data First, we calculate the difference value, find out that higher level Therefore, Note that Bottom extreme range for the reason that Also, extreme ranges for the reason that After the 5-bit modified LSB substitution, Now, belongs to the lower level In the readjusting phase, Case 62 is executed There are two readjusting choices Both choices fail, because the resulting pixel does not fall into [0, 255] or the resulting Therefore, the readjusting phase cannot work Now, we solve the problem of the aforementioned example by the sophisticated readjusting phase It is executed by the following steps Step 1) Pixel-value shifting Both are shifted by Therefore, Step 2) Embedding Both shifted are embedded by -bit modified LSB substitution After 5-bit-modified LSB substitution, we have Step 3) Readjusting If belong to different ranges, the readjusting phase is applied Now,, therefore the readjusting phase is applied Case 64 is executed There are two choices The better choice is Thus, belongs to the higher level With the sophisticated readjusting phase, which is used whenever Conditions 2 of Categories B2) B3) occur, we have the following corollary Corollary 1: For a - - division, the sophisticated readjusting phase, which involves the technique of pixel-value shifting, can work Proof: Without loss of generality, let Note that the sophisticated readjusting phase is only applied in Category B We prove this corollary by showing that if in Category B are shifted, the shifted results have extreme ranges extreme ranges In Category B, let Bottom extreme range extreme ranges That is, In the left side of Fig 10(a), the robust line is

9 496 IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY, VOL 3, NO 3, SEPTEMBER 2008 Therefore, there is no need to readjust no need to shift From Fig 9(c), the readjusting phase cannot work is too small to go back to Therefore, we consider the smallest show that it can go back to by readjusting The smallest appears when At,wehave It means that can go back to by moving one of at distance Therefore, the shifting operation is not needed The proof of the other case that extreme ranges Top extreme range is similar Fig 10(b) shows the similar condition Fig 10 Discussed ranges of p p (a) P 2 bottom extreme range p =2 extreme ranges (b) p =2 extreme ranges p =2 top extreme range the range of the total line, including the robust line the dotted line, is the range of embedded result The real values shown in Fig 10 are for the case It is clear that the shifted result of does not belong to the extreme ranges Also, in the right side of Fig 10(a), the robust line is the range in which cannot be shifted by adding or will be shifted into Top extreme range, the total line, including the robust line the dotted line, is the range of the embedded result, where falls into the range of the robust line Therefore, if, the sophisticated readjusting phase may fail Now we show that the shifting operation is never executed when Note that Therefore, or It occurs only when this case Also, it must be the case that, In From Fig 9(b), the readjusting phase cannot work if small to go back to Note that the smallest is is too VI CONCLUSIONS AND FUTURE WORK In this paper, we propose a new adaptive LSB substitution method to embed secret data into gray images without making a perceptible distortion Pixels located in edge areas are embedded by -bit LSB substitution method with a larger value of than that of the pixels located in smooth areas The PVD approach is used to distinguish between edge areas smooth areas, the level of difference value is defined by the user Also, a delicate readjusting phase is proposed to maintain the same level to which the difference value of a pair of pixels belongs to, before after embedding Experimental results show that our approach obtains both larger capacity higher image quality than that of Wu et al Our approach majors in more significant promotion in the terms of adaptability, capacity, imperceptivity The relative attacks to either destroy or detect the embedding information are not given in this paper It can be further incorporated in future works with attack-resistant discussions besides the merits achieved in this paper With regard to the division experiments, some - divisions - - divisions both yielded higher capacity higher PSNR It remains an open issue to find a method, where the cover images can be analyzed automatically, aiming to capture an adequate - - division satisfying the key requirements in information hiding REFERENCES [1] D Zou, C W Wu, G Xuan, Y Q Shi, A content-based authentication system with lossless data hiding, in Proc Multimedia Expo Int Conf, 2003, vol 2, pp 6 9 [2] T Liu Z D Qiu, The survey of digital watermarking-based image authentication techniques, in Signal Process, 2002, vol 2, pp [3] D Artz, Digital steganographic: Hiding data within data, IEEE Internet Comput, vol 5, no 3, pp 75 80, May/Jun 2001 [4] H J Highl, Data encryption: A non-mathematical approach, Comput Security, vol 16, pp , 1997 [5] Y H Chu S Chang, Dynamical cryptography based on synchronized chaotic systems, Inst Elect Eng Electron Lett, vol 35, no 12, pp , 1999 [6] D W Bender, N M Gruhl, A Lu, Techniques for data hiding, IBM Syst J, vol 35, pp , 1996 [7] R R Anderson F A P Peticolas, On the limits of steganography, IEEE J Sel Areas Commun, vol 16, no 4, pp , May 1998 [8] Y K Lee L H Chen, High capacity image steganography model, Proc Inst Elect Eng Vis Image, Signal Processing, vol 147, no 3, pp , 2000

10 YANG et al: ADAPTIVE DATA HIDING IN EDGE AREAS OF IMAGES WITH SPATIAL LSB DOMAIN SYSTEMS 497 [9] R Z Wang, C F Lin, J C Lin, Image hiding by optimal LSB substitution genetic algorithm, Pattern Recognit, vol 34, no 3, pp , 2000 [10] C C Thien J C Lin, A simple high-hiding capacity method for hiding digit-by-digit data in images based on modulus function, Pattern Recognit, vol 36, no 3, pp , 2003 [11] C K Chan L M Chen, Hiding data in images by simple LSB substitution, Pattern Recognit, vol 37, no 3, pp , 2004 [12] C C Chang, J Y Hsiao, C S Chan, Finding optimal leastsignificant-bit substitution in image hiding by dynamic programming strategy, Pattern Recognit, vol 36, no 7, pp , 2003 [13] C H Yang S J Wang, Weighted bipartite graph for locating optimal LSB substitution for secret embedding, J Discrete Math Sci Cryptograph, vol 9, no 1, pp , 2006 [14] C C Chang H W Tseng, A steganographic method for digital images using side match, Pattern Recognit Lett, vol 25, no 12, pp , 2004 [15] C M Wang, N I Wu, C S Tsai, M S Hwang, A high quality steganography method with pixel-value differencing modulus function, J Syst Softw, vol 81, pp , 2008 [16] C H Yang C Y Weng, A steganographic method for digital images by multi-pixel differencing, in Proc Int Comput Symp, Taipei, Taiwan, ROC, 2006, pp [17] D C Wu W H Tsai, A steganographic method for images by pixel-value differencing, Pattern Recognit Lett, vol 24, no 9 10, pp , 2003 [18] H C Wu, N I Wu, C S Tsai, M S Hwang, Image steganographic scheme based on pixel-value differencing LSB replacement methods, Proc Inst Elect Eng, Vis Images Signal Process, vol 152, no 5, pp , 2005 [19] C H Yang, S J Wang, C Y Weng, Analyses of pixel-value- differencing schemes with LSB replacement in stegonagraphy, in Proc 3rd Int Conf Intelligent Information Hiding Multimedia Signal Processing, Kaohsiung City, Taiwan, ROC, 2007, pp [20] Y R Park, H H Kang, S U Shin, K R Kwon, A Steganographic Scheme in Digital Images Using Information of Neighboring Pixels Berlin, Germany: Springer-Verlag, 2005, vol 3612, pp [21] M Kutter F A P Petitcolas, A fair benchmark for image watermarking systems, in Proc SPIE Conf Security Watermarking of Multimedia Contents, San Jose, CA, 1999, vol 3657, pp Cheng-Hsing Yang received the BS MS degrees in applied mathematics from National Chung- Hsing University, Hsinchu, Taiwan, ROC, in , respectively, the PhD degree in electrical engineering from National Taiwan University, Taiwan, ROC, in 1997 Currently, he is an Associate Professor in the Department of Computer Science, National Pingtung University of Education, Pingtung, Taiwan His current research interests include information hiding image watermarking Chi-Yao Weng received the MS degree in computer science from National Pingtung University of Education, Pintung, Taiwan, in 2007, is currently pursuing the PhD degree in computer science from National Tsing Hua University, Hsinchu, Taiwan, ROC His current research interests include data hiding, steganography, image processing Shiuh-Jeng Wang (M 99) was born in Taiwan, ROC, in 1967 He received the MS degree in applied mathematics from National Chung-Hsing University, Taichung, Taiwan, ROC, in 1991 the PhD degree in electrical engineering from National Taiwan University, Taipei, in 1996 Currently, he is a Full Professor with the Department of Information Management at Central Police University, Taoyuan, Taiwan, where he directs the Information Cryptology Construction Laboratory His research interests include information security, digital investigation computer forensics, steganography, cryptography, data construction, engineering Dr Wang was a recipient of the fifth Acer Long-Tung Master Thesis Award the tenth Acer Long-Tung PhD Dissertation Award in , respectively He was a Visiting Scholar with the Computer Science Department at Florida State University, Tallahassee, FL, in , respectively, a Visiting Scholar in the Department of Computer Information Science Engineering at the University of Florida (UF), Gainesville, from 2004 to 2005 He was the Editor-in-Chief of the Communications of the CCISA in Taiwan from 2000 to 2006 He was the Panel Director of Chinese Cryptology Information Security Association (CCISA) since 2006 He academically toured the CyLab with School of Computer Science with Carnegie Mellon University, Pittsburgh, PA, in 2007 for international project collaboration inspection He is also the author/coauthor of six books (written in Chinese): Information Security, Cryptography Network Security, State of the Art on Internet Security Digital Forensics, Eyes of Privacy-Information Security Computer Forensics, Information Multimedia Security, Computer Forensics Digital Evidence published in 2003, 2004, 2006, 2007, respectively He is a member of the ACM Hung-Min Sun received the BS degree in applied mathematics from National Chung-Hsing University, Taiwan, ROC, in 1988, the MS degree in applied mathematics from National Cheng-Kung University, Taiwan, ROC, in 1990, the PhD degree in computer science information engineering from National Chiao-Tung University, Taiwan, in 1995, respectively He was an Associate Professor with the Department of Information Management, Chaoyang University of Technology, Taiwan, from 1995 to 1999, the Department of Computer Science Information Engineering, National Cheng-Kung University, from 1999 to 2002 Currently, he is an Associate Professor with the Department of Computer Science, National Tsing Hua University He has published more than 100 international journal conference papers His research interests include information security, cryptography, network security, multimedia security, image compression Dr Sun was the Program Co-Chair of the 2001 National Information Security Conference the program committee member of the Information Security Conference; 2000 Workshop on Internet Distributed Systems; 2001, 2002, 2005 Workshop on the 21st Century Digital Life Internet Technologies; National Conference on Information Security, ACISP 04