Proceedngs of the World Congress on Engneerng 2011 Vol II, July 6-8, 2011, London, U.K. Inverse Halftonng Method Usng Pattern Substtuton Based Data Hdng Scheme Me-Y Wu, Ja-Hong Lee and Hong-Je Wu Abstract The objectve of nverse halftonng s to reconstruct hgh qualty grayscale mages from b-level halftone mages. Dfferent from the prevous nverse halftonng approaches, our algorthm computes the dfference mage between the predcted mage usng Gaussan flterng from a halftone mage and the orgnal grayscale one. The dfference mage s then compressed and embedded nto the halftone mage usng a reversble data hdng method. In the mage reconstructon process, the marked halftone mage s scanned to extract the embedded data. Fnally, a better qualty of reconstructed mage can be generated by addng the extracted dfference mage to the predcted mage. Expermental results show that the proposed approach can effcently mprove the qualty of reconstructed mages for nverse halftonng when compared to the prevous approaches. Index Terms nverse halftonng, pattern substtuton, reversble data hdng, Gaussan flterng H I. INTRODUCTION ALFTONE technques have been wdely appled to many felds, ncludng the prntng of newspapers, magaznes, books, and dsplay devces. It s a process of convertng grayscale mages nto halftone mages for the devces that can only process blevel mages. Halftone mages are bnary mages that provde a rendton of gray-scale mages and conssts of 0 and 1. In the halftonng process, t needs to use a kernel to carry out the converson, and the common kernel s such as Floyd-Stenberg kernel, and s dffcult to recover a contnuous-tone mage through halftone manpulaton, converson, compresson, etc. Inverse halftonng s a process whch transforms halftone mages nto grayscale mages. The objectve of nverse halftone reconstructon s to convert halftone blevel mages nto gray-level mages wth the mnmum dstorton. In the past few years, many effcent nverse halftonng algorthms have been proposed, but there s no way to construct a perfect gray-scale mage from a gven halftone mage. There exst several nverse halftonng methods, ncludng kernel estmaton [1], wavelet [2], flterng [3][4], and set theoretc approaches[5]. Most of these methods can obtan good Manuscrpt receved March 19, 2011; revsed Aprl 15, 2011. Ths work was Me-Y Wu. Author s wth General Educaton Center, Natonal Kaohsung Unversty of Hosptalty and Toursm. No.1, Songhe Rd., Xaogang Dst., Kaohsung Cty 81271, Tawan (e-mal:barbara @mal.nkuht.edu.tw) Ja-Hong Lee. Author s wth Informaton Management Department, the Natonal Kaohsung Frst Unversty of Scence and Technology, 2 Jhuoyue Rd., Nanzh, Kaohsung Cty, 811, Tawan (correspondng author, phone: 886-7-6011000; fax: 886-7-6011069; e-mal: jhlee@ nkfust.edu.tw). Hong-Je Wu. Author s wth Informaton Management Department, the Natonal Kaohsung Frst Unversty of Scence and Technology.. ISSN: 2078-0958 (Prnt); ISSN: 2078-0966 (Onlne) reconstructon mage qualty but requre relatvely hgh computatonal complexty. The halftonng and nverse halftonng processes can be regarded as the encodng and decodng processes of vector quantzaton. Therefore, the codebook desgn methods can be appled to buld the nverse halftonng lookup tables [6] [7]. The content of a table entry s the centrod of the nput samples that are mapped to ths entry. The results are optmal n the sense of mnmzng the MSE for a gven halftone method. Although the table lookup method has the advantages of good reconstructed qualty and fast speed, t faces the empty cell problem n whch no or very few tranng samples are mapped to a specfc halftone pattern. In ths paper, a reversble data hdng scheme s proposed to embed some useful nformaton nto the halftone mages. Then users can extract the embedded nformaton and reconstruct the orgnal halftone mage from the marked halftone mage. The extracted nformaton can mprove the qualty of generated grayscale mages by usng a flter based nverse halftonng method. II. REVIEW OF INVERSE HALFTONING AND REVERSIBLE DATA HIDING A. LUT-based Inverse Halftonng (LIH) Method The LUT-based method ncludes two procedures: the LUT buld-up and the LUT-based nverse halftonng (LIH) procedures. The LUT buld-up procedure s to buld the LUT nformaton by scannng selected grayscale mages and ther correspondng halftone mages wth a 3 3 or 4 4 template. Template s used as a sldng wndow to buld up the LUT. In the LIH procedure, a grayscale mage can be reconstructed from a gven halftone mage usng the LUT nformaton. The LUT nformaton contans a set of pars of bnary pattern and ts correspondng estmated gray value. Assume that there are L tranng mage par sets and {( O, H ) 1 L} represents the th par, where O denotes the th orgnal mage and H the correspondng halftone mage of O. The LUT buld-up and LIH procedures usng 4 4 template F are descrbed as follows: Procedure LUT buld-up: Step 1: Let arrays LUT[] and N [] be zero as the ntal values. LUT[] s used to record the mapped gray value correspondng to a specfc bnary template wth ndex I whch s appeared n the nput halftone mage and N[] s used to store the occurrence frequency of ths specfc bnary template n the halftone mage. Select L tranng grayscale mages and generate ther correspondng halftone mages, respectvely.
Proceedngs of the World Congress on Engneerng 2011 Vol II, July 6-8, 2011, London, U.K. Step2: Select one mage from the L tranng grayscale mages. Scan the selected mage and ts correspondng halftone mage n raster order wth the template F. Let P k be the bnary value of a pxel located on X n a halftone mage and the gray value wth the same locaton X n a tranng mage s denoted as G(X). The ndex I and LUT[ can be calculated usng equaton (1) where k represents dfferent locaton on the template F. Snce there are totally 16 locatons on the template F, the value of I ranges from 0 to 65535. Then, the sum of the template occurrence frequences and the sum of the gray values on the tranng mage wth the same poston X can be computed as the equaton (2). 15 (1) I 2 K Pk k0 N[ N[ 1 (2) LUT[ LUT[ G( X ) Step3: Repeat Step 2, untl all L mages are selected. Step4: The predcted gray value for a specfed 4 4 pattern wth ndexed I can be computed as Procedure LIH: LUT[ LUT[ (3) N[ Step1:Perform the above-mentoned LUT buld-up algorthm to buld LUT. Step2: Scan a halftone mage n raster order wth template F, and compute the template ndex I usng equaton (1). The estmated gray value G (X) on the locaton X can be obtaned and denoted as G' ( X ) LUT[. Step3: Output the estmated grayscale mage. Note that, some bnary patterns n the nput halftone mage may not exst n the tranng mages. In ths stuaton, we wll apply Gaussan flter method to estmate the mean gray value. Thought the LUT-based nverse halftonng method s easly mplemented, there exsts a dsadvantage of ths method, the constructed LUT nformaton must be sent to the recever. B. Gaussan Flterng Method Gaussan flterng s a smoothng algorthm for mages. Equaton (4) denotes a 2D Gaussan functon, where s the standard devaton of a Gaussan dstrbuton. In the mplementaton of nverse halftonng usng Gaussan flterng, the bnary pxel value 0 and 1 n the nput halftone mage wll be regarded as 0 and 255, respectvely. A weght mask wth specfed sze and contents should be determned accordng to the use of Gaussan dstrbuton wth parameter. G 2 2 x y 1 2 2 ( x, y) e 2 (4) 2 In the nverse halftonng process, the halftone mage s scanned pxel by pxel n a raster order by movng the sldng mask. The output gray value on the correspondng central pxel of the mask s estmated va the summaton of the weght value on the mask content multplyng by the bnary values on the neghborng pxels. III. THE PROPOSED METHOD A. Dagram of the Proposed Method Orgnal Halftone (2)Gaussan flterng (5)Lossy Compresson (1)Halftonng by error-dffuson Predcted (4)Subtracton Dfference Bnary Fle (6) Reversble data hdng (3)Pattern selecton Selected Pars Marked Output Predcted (4)Gaussan flterng Halftone Decompressed Bnary Fle (1) Data extractng (5)Addton (3)Restore (2)Decompresson Fg. 1. The embeddng and extractng dagram of proposed method. To mprove the reconstructed mage qualty for nverse halftonng, the proposed reversble data hdng technque s appled and dvded nto two phases: the embeddng process and the extractng process. Fgure 1 shows the dagram of the proposed method. In the embeddng process, a grayscale mage G s transferred nto a halftone mage H by error dffuson process wth Floyd-Stenberg kernel. The halftone mage H can be used as an nput to obtan a predcted mage G when a Gaussan flter s appled. Then we can obtan a dfference mage D by a subtracton operaton D=G-G. In our opnon, the orgnal grayscale mage s lossless reconstructed f we can lossless embed the entre dfference mage D nto the halftone mage H. In the embeddng phase, a marked halftone mage H s output after data s embedded nto H. On the other hand, the dfference mage D and the orgnal halftone mage H can be extracted from the marked halftone mage H snce the embeddng process s reversble. The predcted mage G s computed by applyng the Gaussan flter to the halftone mage H agan. Then the orgnal mage G can be reconstructed as G=G +D. However, the embedded capacty of a halftone mage s not enough to carry the whole dfference mage. Therefore, a lossy mage compresson s used to reduce the mage fle sze to ft the capacty lmt of data embeddng. In our study, dgt wavelet transformaton (DWT) s appled to compress the dfference mage nto a small scale of sze mage for embeddng. Ths process s descrbed as a flowchart n Fgure 2. Although the mage qualty of the reconstructed grayscale mage s not perfect when compared wth the orgnal one, the obtaned mage qualty s better than the tradtonal nverse halftonng methods. ISSN: 2078-0958 (Prnt); ISSN: 2078-0966 (Onlne)
Proceedngs of the World Congress on Engneerng 2011 Vol II, July 6-8, 2011, London, U.K. It s not dscernble to human eyes f we modfy or add a pxel on the edge of a bnary mage. Therefore, the mage flppng operaton of Ho s method s to fnd the boundares where black and whte pxels meet. The flppng formula s as follows. P(, D(, P(, P( j 1, ) P(, P( j, 1) f j 1 f j 1 otherwse and and 1 1 (5) Fg. 2. The process of generatng a dfference mage. B. Reversble Data Hdng for Bnary s Reversble data hdng can embed secret message n a reversble way. Relatvely large amounts of secret data are embedded nto a cover mage so that the decoder can extract the hdden secret data and restore the orgnal cover mage wthout any dstorton. Recent, a boundary-based PWLC method s presented [8]. Ths method defnes the same contnuous 6 edge pxels as an embeddable block through searchng for bnary mage edges. And then one can embed data n the par of the thrd and fourth edge pxels. A reversble data hdng method for error dffused halftone mages s proposed[9] (Pan, Luo & Lu, 2007). Ths method employs statstcs feature of pxel block patterns to embed data, and utlzes the HVS characterstcs to reduce the ntroduced vsual dstorton. The method s sutable for the applcatons where the content accuracy of the orgnal halftone mage must be guaranteed, and t s easly extended to the feld of halftone mage authentcaton. However, these two methods both have a drawback that the capacty of data hdng s stll lmt. Recently, Ho et al. [10] proposed a hgh-capacty reversble data hdng method for bnary mages usng pattern substtuton. The method s capable of both successful extracton of secret data from a stego-mage and restorng the bnary mage completely after the extracton of secret data. Ther method gathers statstcal data concernng the occurrence frequences of varous patterns and establshes the pattern exchange relatonshps. Pattern substtuton can be used accordng to the pattern relatonshps for data hdng. In ths paper, Ho s scheme s appled to embed some useful nformaton nto the halftone mages and the nformaton can be extracted and used to mprove the qualty of generated grayscale mages. The flowchart of Ho s method s dsplayed n Fgure 3. Cover mage Secret data flppng Bt stream Pattern selecton for modfcaton Pattern substtuton Marker mage Capacty computaton Hdng by key Fg. 3. The flowchart of data embeddng process n Ho s method. For a flpped mage, we dvde t nto non-overlapped 4 1 mage blocks. Each four-pxel block from the flpped mage can be regarded as a pattern. Then we can compute the occurrence frequences for each knd of pattern type. TABLE I s the computed results for Lena mage. In ths study, we modfed Ho s method to embed more capacty. All patterns are classfed nto two groups, hgh frequent pattern and low frequent pattern. For each hgh frequent pattern A, a low frequent pattern B whch content s the most closest to pattern A wll be selected to form a par for data embeddng. In the data embeddng process, the orgnal halftone mage s parttoned nto a group of 4 1 non-overlappng patterns. Then, any pattern p on the halftone mage wth the same content of A wll be selected to embed 1-bt data. If a data bt 0 s embedded on p, then the content of p s remaned as A. If a data bt 1 s embedded on p, then the content of p s updated as the content of pattern B. In data extracton process, the embedded message s obtaned dependng on the pattern A, B when the test mage s scanned. For example, assume that the hghest frequent pattern n the mage s PH=1111 and ts correspondng lowest frequent pattern s PL=0101. If the content of the pattern PH s encountered, then check the bt value whch s currently embedded. If the bt value s 0 then reman the content as PH. If the value s 1 then we replace PH wth the PL pattern. Fgure 4 shows an example of the data embeddng and extractng processes for the used method. However, we had found that the usage of pattern type wth PL=0000 would cause black spot effect n the marked mage. Therefore, we avod the selecton of ths pattern type n the data embeddng process. Fgure 5 s an example to demonstrate the results wth and wthout the usage of pattern type PL=0000. TABLE I shows the frequences of dfferent 4 1 patterns appeared n Lena of sze 512 512. TABLE I THE FREQUENCIES OF DIFFERENT PATTERNS APPEARED IN LENA IMAGE Pattern type Frequency Pattern type Frequency P 0000 4615 P 0001 2115 P 0011 3620 P 0010 103 P 1100 244 P 1000 122 P 1001 5281 P 1001 4486 P 1010 1526 P 1110 2226 P 0101 230 P 0101 6068 P 0110 3600 P 1101 6072 P 1111 20913 P 1011 4315 ISSN: 2078-0958 (Prnt); ISSN: 2078-0966 (Onlne)
Proceedngs of the World Congress on Engneerng 2011 Vol II, July 6-8, 2011, London, U.K. Fg. 4. The processes of data embeddng/extractng for the used reversble data hdng scheme. Benft (# PH # PL ) (# PL *18 4) t t t (7) where #PH and #PL s the frequences of the hgh and low frequent pattern appeared n the mage, and the overhead s for keep the coordnates of the PL patterns (9 bts for x coordnate and 9 bts for y coordnate f the sze of the test mage s 512 512) and the PL content. Step 4. Search all blocks n the orgnal mage. As long as we come across a pattern n the embedded, the block s remaned as block s updated as the pattern PL. PH, f a bt 0 s PH ; Otherwse the The dstance defnton for two patterns n equaton 1 means the count of dfferent appearance n the same postons on patterns. The Maxmum capacty for dfferent halftoned mages usng the proposed method s lsted as follows. TABLE II The Maxmum Capacty of the embeddng method Maxmum Capacty(bts) Lena 27849 Pepper 26612 Arplane 14849 Baboon 6912 (a) Fg. 5. Marked mages of the data embeddng (a)usng the pattern type PL=0000 (b) wthout usng the pattern type PL=0000. For the purpose of reversblty, we should record the coordnates of the used lowest frequent patterns appeared n the test mage. In addton, to acheve a hgher capacty of embeddng data, more pattern pars should be determned, whose steps can be presented as below. Procedure-Par Selecton and Pattern Substtuton method for halftone mages Step1. Partton the orgnal mage nto non-overlappng 4 1 blocks. Step2. Compute the occurrence frequences for all appeared patterns. Sort these patterns decreasngly and denoted them as PH accordng to ther occurrence frequences. Step3. Fnd out all low frequent patterns PL. Assume that there are totally k low frequent patterns, k pars of patterns ( PH, PL ) should be constructed to perform the (b) data embeddng. Here the pattern matchng operaton should follow the mnmum dstance rule and the beneft rule, where the dstance computaton of two patterns s defned as 3 Dst ( PH, PL ) PH t PL (6) t t0 The embeddng capacty beneft of the th par of pattern wth pattern type PH t and PL t s determned by the followng equaton. C. Overhead Informaton There are two knds of data should be embedded nto the halftone mage to acheve the reversble data hdng and the hgh qualty of recovery mage, they are the selected pars nformaton (SH) and the compressed dfference mage(dh), respectvely. In the data extracton process, the recever should know the predefned patterns ( PH, PL ) n the data embeddng process to extract data correctly. Assume that there are totally TC pars of patterns used n the data embeddng process, the followng data depcted n Fgure 6(a) should be embedded sequentally. The sze the overhead nformaton s 3 + 9 2 TC bts. We use 3 bts to store the TC value snce the total count of pattern pars for 4 1 dfferent bnary patterns s 16=2 2 3. On the other hand, assume the compressed fle sze of the dfference mage s DH, the compressed fle of the dfference mage s arranged n bt streams for embedded nto the halftone mage after the embeddng of par nformaton. The data structure s shown n Fgure 6(b). TC 0 PH DH 0 PL TC1 PH (a) SH (selected par header) D ' D ' 0 1 (b) DH (Data header) TC1 PL D ' DL2 D ' DL1 Fg. 6. The data structures of the overhead nformaton: (a) pars nformaton and (b) the compressed mage nformaton. ISSN: 2078-0958 (Prnt); ISSN: 2078-0966 (Onlne)
Proceedngs of the World Congress on Engneerng 2011 Vol II, July 6-8, 2011, London, U.K. D. Data Embeddng and Extractng The way to embed SH nformaton s mportant snce the recever cannot extract any data from the marked mages f he doesn t have the SH nformaton before data extractng. We dvded the halftone mage nto two regons: one s the place to embed SH sequence and the other one s the place to embed the DH sequence. Snce the sze of SH nformaton s very small when compared to the entre mage sze. Two knds of embeddng data can be chosen here. One s the fxed poston method to arrange the SH and DH n faxed regons, such as the example n Fgure 7(a) and the other s the random poston method to randomly select dfferent pxels for embeddng DH nformaton. Then we drectly replace the selected pxels wth the SH sequence. The mplementaton of the second method requres a secret key K to select the postons for embeddng SH sequence and the recever should also have the key to extract the data. Although the second method needs more computaton n SH embeddng, t owns a hgher securty than the frst method. IV. EXPERIMEANT RESULTS Four 512 512 error dffused halftone mages, Lena, Baboon, Arplane, and Pepper are selected to evaluate the performance of the proposed method, as shown n Fgure 8. These halftones are obtaned by performng Floyd Stenberg error dffuson flterng on the 8-bt gray-scale mages. Comparson of dfferent nverse halftonng methods, ncludng Gaussan flterng, LIH, ELIH are mplemented. The PSNR values of the predcted mage from dfferent nverse halftonng method and the orgnal grayscale mage are computed as lsted n Table III. The marked mages of the proposed methods are shown n Fgure 8. Fg. 7. Two knds of methods to embed SH and DH. The block dagram of data extracton s shown n Fgure 1, wth steps as follows. Procedure-Data Extracton from a marked halftone mage Step1. The SH and DH sequence reconstructon: we use the same Key K to fnd the 3 + 9 2 TC pxel locatons and arrange the pxel values nto the selected pattern pars ( PH, PL ). Extract the embedded DH sequence by scannng the entre mage accordng to the SH nformaton. If a pattern n the PH s found then output bt 0. If a pattern n the pattern PL s found then output bt 1. Step2. Decompresson: DH sequence s decoded usng nverse dgtal wavelet transform (IDWT) and a predcted dfference mage D s obtaned. Step3. Restore the orgnal halftone mage H: The scan of the whole marked mage s performed. If a pattern belongs to the pattern PL then replace the pattern wth the correspondng pattern PH. Then, we wll update a part of patterns orgnal PH usng the coordnate nformaton of all PL extracted from SH. Step4. Compute the predcted mage G : A predcted mage of the halftone mage H s output usng a Gaussan flter. Step5. reconstructon: A recovery mage s obtaned by addng the mage D to the predcted mage G. Fg. 8. The marked mages wth dfferent amount of data bts embedded usng the proposed method.(a)(c) two pars of patterns were used (e)(g)three pars of patterns were used;(b)(d)(f)(h) maxmum capacty of data were embedded. In addton, mage qualty of restored grayscale mages was evaluated. Three sub-mages extracted from the restored mages usng dfferent nverse halftonng methods are shown n Fgure 9. We can found that the prnt words n the reconstructed mage n Fgure (c) look clearer than the other two methods. ISSN: 2078-0958 (Prnt); ISSN: 2078-0966 (Onlne)
Proceedngs of the World Congress on Engneerng 2011 Vol II, July 6-8, 2011, London, U.K. TABLE III Comparson of dfferent nverse halftonng methods Gaussan flterng PSNR(dB) Capacty(bts) LIH ELIH[7] Lena 29.40 27.53 28.54 Pepper 29.30 27.33 29.29 Arplane 28.29 26.94 28.05 Baboon 22.22 22.35 22.22 Proposed method 30.61 (27849) 32.42 (26612) 30.60 (14849) 22.58 (6912) (a) REFERENCES [1] P. W. Wong, Inverse halftonng and kernel estmaton for error dffuson, IEEE Transactons on Processng, vol. 4, pp. 486 498, Aprl, 1995. [2] Z. Xong, M. T. Orchard and K. Ramchandran, Inverse halftonngusng wavelets, Proceedngs of the IEEE nternatonal conference on mage processng, vol. 1, pp. 569 572, 1996. [3] Z. Fan, Retreval of mages from dgtal halftones, Proceedngs of the IEEE nternatonal symposum on crcuts systems pp. 313 316, 1992. [4] T. D. Kte, N. D. Venkata, B. L. Evans and A. C. Bovk, A fast hgh qualty nverse halftonng algorthm for error dffused halftones, IEEE Transactons on Processng, vol. 9, pp. 1583 1592, 2000. [5] P.C. Chang, C. S. Yu and T. H. Lee, Hybrd LMS-MMSE nverse halftonng technque, IEEE Transactons on Processng, vol. 10, pp. 95 103, 2001. [6] M. Mese, P.P. Vadyanathan, Look-up Table (LUT) Method for Inverse Halftonng, IEEE Transactons on Processng, vol. 10, pp.1566-1578, October 2001. [7] K.L. Chung, S.T. Wu, Inverse Halftonng Algorthm Usng Edge-Based Lookup Table Approach, IEEE Transactons on Processng, vol. 10, pp.1583-1589, 2005. [8] C.L. Tsa, H. F. Chang, K.C. Fan, C.D. Chung, Reversble data hdng and lossless reconstructon of bnary mages usng par-wse logcal computaton mechansm, Pattern Recognton, 38. 1993-2006, 2005. [9] J.S. Pan, H. Luo, Z.M. Lu, Look-up Table Based Reversble Data Hdng for Error Dffused Halftone s. INFORMATICA, Vol. 18, No. 4, 615 628, 2007. [10] Yu-An Ho, Yung-Kuan Chan, Hsen-Chu Wu, Yen-Png Chu, Hgh-capacty reversble data hdng n bnary mages usng pattern substtuton. Computer Standards & Interfaces 31(4): 787-794, 2009. (b) (c) Fg. 9. qualty comparson of restored mages usng dfferent nverse halftonng methods (a) Gaussan flterng method (b) LIH method (c)the proposed method. V. CONCLUSION In ths paper, a reversble data hdng scheme s ntroduced to embed some useful nformaton nto halftone mages. The proposed approach frstly computes the dfference mage between the predcted mage usng Gaussan flterng and the orgnal grayscale one. The dfference mage s then compressed and embedded nto the halftone mage usng a reversble data hdng method. In the mage reconstructon process, the marked halftone mage s scanned to extract the embedded dfference mage. Fnally, a better qualty of reconstructed mage wll be generated by addng the extracted dfference mage to the predcted mage usng Gaussan flterng. Expermental results show that the proposed approach can effcently mprove the qualty of reconstructed mages for nverse halftonng. ISSN: 2078-0958 (Prnt); ISSN: 2078-0966 (Onlne)