340 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 10, NO. 3, APRIL 2008 A. Morphological Binary Wavelet Transform Consider a family of signal space and detail space at level . The 1-D wavelet decomposition scheme comprises of one signal analysis operator and one detail analysis operator . In addition, it also consists of one signal synthesis operator and one detail synthesis operator . Here “ ” indicatesFig. 1. Illustration of changes in coefﬁcients due to ﬂipping pixels [(a) and (b)] that the corresponding operator maps a signal to a higher level,and the “edge shifting” phenomenon [(c) and (d)]. towards the direction of reducing the information. Whereas “ ” indicates that the operator maps a signal to a lower level, towards the direction of restoring the information. The signal analysisnot affected by ﬂipping the candidates of another for data em- operator maps a signal, , from levelbedding, namely “orthogonal embedding”. This addresses the to for the scaled signal , .problem of the capacity decrease due to the un-embeddability of The detail analysis operator maps a signalthe block boundaries, sharing rows and columns in block-based from level to for the detail signal ,approaches . As a result, signiﬁcant gains in capacity can . On the other hand, the signal synthesis operatorbe achieved, which also improves the efﬁciency of utilizing the maps a signal from level back to level toﬂippable pixels. Implementing the transforms by the “Exclusive obtain an approximation of , i.e., . The detailOR (XOR)” operation addresses the quantization error issue in synthesis operator maps a detail signal backa DCT-based approach . The major advantages of the pro- to level so as to obtain the detail signal . Theposed scheme lie in its larger capacity (e.g., compared with , signal at level is reconstructed by, , , ), better visual quality (e.g., compared with–) and lower computational complexity (e.g., compared (1)with , , ). In addition, unlike , our present schemedoes not suffer the capacity decrease and computational load As discussed in , , perfect reconstruction of the originalincrease in order to incorporate the cryptographic signature for signal is possible if the operators satisfyauthentication. This paper is organized as follows. A brief review on existing (2)1-D morphological binary wavelet transform (MBWT), our (3)proposed extension to 2-D MBWT and the interlaced MBWT (4)(IMBWT) are presented in Section II. The authenticationscheme employing IMBWT and elimination of the redundancy where “ ” and “ ” represent the identity and zero operators, re-in IMBWT by the proposed prediction and update lifting MBWT spectively. Note that is a set of biorthog-(PUMBWT) are discussed in Section III. Experimental results onal ﬁlter operators if the conditions in (2)–(4) are satisﬁed.and discussions are presented in Sections IV and V concludes For the morphological analysis and synthesis scheme discussedthe paper. in this paper, the bi-orthogonality is formulated in the operator terms. For simplicity, we shall delete the index in the corre- II. INTERLACED MORPHOLOGICAL TRANSFORM sponding analysis and synthesis operators due to only one step One intuitive idea in utilizing MBWT for data hiding is to use decomposition between and is considered. Letthe detail coefﬁcients as a location map to determine the data- “ ” denote the “Exclusive OR (XOR)” operation. The signalshiding locations, since these coefﬁcients contain the edge infor- at level by applying the analysis operators for a 1-D signalmation in horizontal, vertical and diagonal directions. However, are given byﬂipping a pixel involves changing the coefﬁcients, as illustratedin Fig. 1(a) and (b). It can be seen that the same edges used to (5)determine the data-hiding locations cannot be found in the wa- (6)termarked image [e.g., Fig. 1(b)]. We observe that ﬂipping anedge pixel in binary images is equivalent to shifting the edge where and are the coarse and detail signals obtained atlocation horizontally one pixel [e.g., vertical edge shifting from level , respectively; denotes the index of the signal at levelFig. 1(c) to (d)] and vertically one pixel [e.g., horizontal edge and for a 1-D signal of size . Theshifting from Fig. 1(c) to (d)]. In the ﬁgure, “1” and “0” rep- detail signal contains 1 s at each transition from 0 to 1 orresent the black and white pixels, respectively. To this end, we vice versa in signal . The synthesis operators are given bydesign an IMBWT to keep track of the shifted edges to achieveblind watermark extraction. (7) In this section, we start the discussion with signal analysis (8)and synthesis which is similar to . A brief review on the1-D signal decomposition given in  is also included. Based The signal at level is reconstructed byon this, we further extend the decomposition scheme to 2-Dsignal and subsequently propose an interlaced transform for the (9)data-hiding application. (10)
YANG et al.: ORTHOGONAL DATA EMBEDDING FOR BINARY IMAGES IN MORPHOLOGICAL TRANSFORM DOMAIN-A HIGH-CAPACITY APPROACH 341 Finally, the signal at level can be reconstructed by (20) Fig. 2. Designation of samples in a 2 2 2 block. (21)B. 2-D and Interlaced Morphological Binary Wavelet (22)Transform We now extend the 1-D wavelet decomposition scheme  (23)to a 2-D signal by deﬁning a non-separable 2-D transform. Let and represent the indices of the signal at level , where Since the coarse signals obtained from (11) are at the odd-odd and for a 2-D locations, the transitions from odd-odd to other coordinates incoarse signal of size . Designation of the samples in the 2 2 block may be easily assessed from the detail signalsa 2 2 block is shown in Fig. 2, where denotes the obtained by (12)–(14). However, the transitions from odd-even,signal (“0” or “1”) located at row and column at level . even-odd and even-even coordinates to other coordinates mayTo deﬁne a 2-D transform, one sample in a 2 2 block can be not be so readily assessable. This motivates the design of com-sub-sampled as the coarse signal. The horizontal, vertical and plementary wavelet transforms operating on the 2 2 blocksdiagonal detail signals are derived from the difference between starting from the even-odd, odd-even and odd-odd coordinatesthe sub-sampled sample and its vertical, horizontal and diagonal of the signal. Based on the starting absolute coordinates(including diagonal and anti-diagonal) neighbors. The resultant in the top left position shown in Fig. 3, each 2 2 blocktransformed signal remains binary while the coarse and detail in a 2-D image can be classiﬁed as an even-even block (EEB),signals will each be 1/4 the size of the original signal. Let the or an even-odd block (EOB), or an odd-even block (OEB), or anoperators for the coarse signal, horizontal, vertical, and diagonal odd-odd block (OOB), which is given bydetail signals be , , and , respectively, where forthe superscript “ ” denotes “even-even”. The obtained trans- forform is named the even-even transform since it is operated on a for2 2 block starting from the even-even coordinates. The coarse forsignal, vertical, horizontal and diagonal detail signals at level (24) are obtained by applying the analysis operators to yield where denotes row and column of an image, denotes the index of the current 2 2 block, denotes a (11) modulo operation and “ ” represents logical “AND” operation. Hence, three additional transforms, i.e., even-odd, odd-even and (12) odd-odd, can be deﬁned. These transforms, together with the even-even transform, are collectively called interlaced morpho- logical binary wavelet transform (IMBWT). (13) Let the operators for the even-odd transforms be , the signals obtained by applying the (14) analysis operators for the even-odd transform are given bywhere and (25) . The synthesis operators of a 2-D wavelet transform aregiven by (26) (27) (28) (15) (16) The odd-even and odd-odd transforms can be deﬁned in (17) the same way. For simplicity, we use , , and , , to represent the signals obtained from different transforms. There are four single processing cases (18) (SPCs): even-even, even-odd, odd-even and odd-odd that are (19) determinant on the main processing blocks to be EEBs, EOBs,
342 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 10, NO. 3, APRIL 2008 Fig. 3. Four different 2 2 2 blocks in a 3 2 3 block of a binary image. be ﬂippable if . Since , , , and , we have , , and , where is the complement of . Flipping causes each coefﬁcient to become its complement and as a result, the ﬂippability condition becomes Fig. 4. Main processing block and its subsidiary blocks. (30)OEBs and OOBs. Consider the even-even processing casewhere the main processing blocks are EEBs and EOBs, OEBs Intuitively, in deﬁning the ﬂippability condition as such, weand OOBs which are interlaced with the EEBs are shown as the relax the condition as “either the edge exists in the current trans-subsidiary blocks in Fig. 4. form or its interlaced transform, both for horizontal and vertical In applying the IMBWT for data hiding in binary images, the edges”. Hence, the shifted edges can be tracked, i.e., the sameprocessing of images is always based on 2 2 blocks (i.e., main set of operations can be employed to ﬁnd the ﬂippable locationsprocessing blocks). However, the ﬂippability of a coarse signal for the extraction process.is determined by considering 3 3 blocks, which consist of both Let us now consider a 3 3 block of an input image . Thethe main processing blocks and the subsidiary blocks. number of transitions from the current candidate pixel (the center pixel) to its 4-neighbors in the horizontal and verticalC. Single Processing directions are represented by and , respectively, which As discussed earlier, ﬂipping an edge pixel in binary images are calculated from the center pixel to its 4-neighbors. Assumeis equivalent to shifting the edge location horizontally one pixel the center pixel is [see Fig. 3(a)], andand vertically one pixel. A horizontal edge exists if there is a are given bytransition between two neighboring pixels vertically and a ver-tical edge exists if there is a transition between two neighboring (31)pixels horizontally. To deﬁne the ﬂippability condition for acoarse signal, we actually consider the 3 3 block in such away that the shifted edges can be tracked for the convenience (32)of blind watermark extraction. The ﬂippability condition (orcross condition) for a SPC is deﬁned as follows: a coarse signal(in a main processing block) is ﬂippable if both horizontal and By satisfying the cross condition that , andvertical edges exist. Speciﬁcally, consider the even-even pro- do not change when the center pixel is ﬂipped. Hence, thecessing case, a horizontal edge exists if either or equals 4-connectivity from the center pixel to its 4-neighbors is pre-to 1 and a vertical edge exists if either or equals to 1. served. Further, the center pixel has a white 4-neighbor pixel inThe ﬂippability condition is given by both horizontal and vertical directions, which makes it an edge pixel both horizontally and vertically. Similarly, the ﬂippability conditions for the odd-odd, even-odd, and odd-even processing (29) cases are given byEquation (29) thus determines a coarse signal [i.e.,pixel at the lower right location in Fig. 3(b)] to (33)
YANG et al.: ORTHOGONAL DATA EMBEDDING FOR BINARY IMAGES IN MORPHOLOGICAL TRANSFORM DOMAIN-A HIGH-CAPACITY APPROACH 343 (34) (35)Equation (29) and (33)–(35) can be further expressed in termsof pixel values as (36) (37) Fig. 5. Checking of the ﬂippability conditions for even-even and odd-odd pro- (38) cessing cases of IMBWT. (39)where the candidate pixels are: , , and , respectively. In summary, the ﬂippability conditions help identify all thecandidate pixels for which the pixels directly above and belowthe candidate pixel have different colors (“0” and “1”) and thepixels immediately to the left and right of the candidate pixelhave different colors. In addition, in applying these ﬂippabilityconditions for data hiding, we require that the two chosen can-didate pixels should not be 4-adjacent, i.e., horizontally or verti-cally adjacent to each other to avoid poor visual quality. It can be Fig. 6. Designated 2 2 2 blocks.seen that the ﬂippability of the center pixel in each 3 3 blockis independent of the center pixel value. , there is no quantization involved to embed the information by employing a pair case in the present approach.D. Double Processing We deﬁne a designated 2 2 block as the 2 2 block The capacity of the proposed scheme is determined by the that contains the two candidate pixels for a pair case, whichnumber of pixels that satisfy the ﬂippability condition. This is shown in Fig. 6. The designated 2 2 block can be chosencapacity can be increased signiﬁcantly by combining the two from one of the two processing blocks of a pair case, but onlysingle processing cases, namely, Double Processing Case one candidate pixel is chosen to hide data in each .(DPC). Based on the observations of (36) and (37), the ﬂippa- Hence, the maximum capacity is upper bounded bybility condition of the even-even processing case (i.e., ) . To achieve higher security, the choice of anis not affected by ﬂipping the candidates in the odd-odd pro- embedder in each using DPC can depend on acessing case (e.g., ) and vice versa, as illustrated in random key , where . For example, for theFig. 5. This “nonintersection” property of the two processing block, we choose when andcases renders the processing of the even-even and odd-odd choose when . By choosing , we checkcases can be done together. The same applies to the even-odd ﬁrst, mark the current candidate pixel as embeddableand odd-even processing cases. For convenience, we call the if and proceed to the next . Otherwise,two combined processing cases as a “Pair Case”. As evidenced will be checked (i.e., when ). Similarly,from the increase in the number of candidate pixels, i.e., from is checked ﬁrst by choosing . From the above dis- to for an image of size cussion, it is noticed that there may be two candidate pixels , the capacity can be approximately doubled by com- being ﬂipped in some 2 2 blocks (not ), e.g., the OOBsbining the two processing cases. This idea is motivated by the in Fig. 6.quantization index modulation based data-hiding method .The even-even and odd-odd processing cases can be viewed as E. Double Processing With Distortion Controltwo orthogonal sets of embedders indexed at the 2 2 blocks The “nonintersection” property of the even-even and odd-starting from even-even and odd-odd coordinates, denoted as odd, or even-odd and odd-even processing cases renders the and , respectively. In this paper, the embedders are an possibility to combine the two processing cases to minimizeensemble of the embedding functions of a “Pair Case”, e.g., the the distortion, namely, double processing with distortion con-embedding functions of even-even and odd-odd cases. Unlike trol (DPDC). Embedding data using either DPC or DPDC is
344 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 10, NO. 3, APRIL 2008described as orthogonal embedding. Consider processing the using DPDC, an index (which is subsequentlyused to choose the corresponding embedder to determine theembeddable location) is chosen such that the distortion betweenthe original pattern and watermarked patternwith respect to embedder is minimized by (40)where and represents the distortion mea- Fig. 7. Illustration of the increase in capacity by orthogonal embedding in thesures such as the visual distortion tables ,  and other mea- 2 proposed approach (b) versus the interlaced 3 3 block scheme in  (a).sures , . To compare the vi- Here, the grid being shaded in gray represents a black pixel.sual distortion caused by employing different embedders, thelist of patterns that satisfy the ﬂippability conditions should beranked ﬁrst. Minimization by only considering the two candi- Hence, the corresponding diagonal detail coefﬁcient of the maindates determined by the two embedders in each may processing blocks can be used (e.g., to be ﬂipped when neces-cause the increase in distortion to the neighboring ﬂippable can- sary) to hide information when the embeddable candidate pixeldidates, which ultimately may consume the reduced distortion is in the subsidiary block, namely “swap embedding”. In thisgained by minimization. To minimize the overall distortion, we way, the processing can still be based on the main processingconsider backwardly those neighboring processed embeddable blocks. The increase in capacity with orthogonal embedding,candidates (e.g., C, D and E of EEBs in Fig. 6 which are af- i.e., via DPC or DPDC, over that of the interlaced 3 3 blockfected by ﬂipping A in OOB) and consider forwardly those un-  is illustrated in Fig. 7. Observe from the ﬁgure that theprocessed ﬂippable candidates (e.g., F, G and H of OOBs in good candidates being missed out in the interlaced 3 3 blockFig. 6 which are affected by ﬂipping B in EEB), namely, Back- scheme (due to being not a candidate), e.g., the center pixel ofward-Forward Minimization (BFM). Let be the embedder the “L” pattern, have been successfully identiﬁed by our pro-in the neighboring 2 2 blocks to be considered, here posed orthogonal embedding. Hence, signiﬁcant increase in ca-only takes one value from ; is an indicator pacity can be achieved.function to represent whether is chosen (“1”) or not (“0”)in the processed neighboring 2 2 blocks for backward min-imization, or ﬂippable (“1”) or not (“0”) in the unprocessed III. HIGH-CAPACITY DATA HIDING USINGneighboring 2 2 blocks for forward minimization. Further, let ORTHOGONAL EMBEDDING and , and and be the watermarked A. Authentication Watermark Generation, Embedding andand original patterns, before and after ﬂipping the candidate in Veriﬁcationthe by choosing , respectively. The accumu-lated change in distortion in the neighboring 2 2 blocks In the watermark generation and embedding process, ﬁrstlybecause of choosing is given by (41), as shown at the bottom we set , 1 and 2 to represent SPC, DPC and DPDCof the page, where for an image with payload watermark . Secondly weand for backward and choose a random key to determine the sequenceforward minimization, respectively. is subsequently em- of choosing the two orthogonal embedders in DPC. Finally, weployed to update the distortion generated by choosing embedder set or 0 to indicate whether or not a watermark is , (40) thus becomes embedded in the current and to be the odd-even feature of . The strategies for the hard authenticator watermark generation and embedding are described in Table I. (42) Since the embeddability of a coefﬁcient is invariant in the Noticeably, an embedder in DPC is chosen based on a random watermark embedding process, the same steps as that in thekey, whereas it is chosen to minimize the distortion for each watermark embedding process can be carried out to generateﬂipping in DPDC. As illustrated in Fig. 6, by using DPC or the hash values, i.e., , of , where is theDPDC, ﬂipping a candidate pixel (coarse signal) of the sub- intermediate image of . Extract the watermarksidiary blocks (e.g., pixel “A” in the OOB, here by computing and obtain ) results in changes in the corresponding diagonal detail coeff-cient of the main processing blocks (e.g., EEB). (46) (41)
YANG et al.: ORTHOGONAL DATA EMBEDDING FOR BINARY IMAGES IN MORPHOLOGICAL TRANSFORM DOMAIN-A HIGH-CAPACITY APPROACH 345 TABLE I STRATEGIES OF WATERMARK GENERATION AND EMBEDDING USING IMBWTwhere is the odd-even feature of the of . The minimizing distortion based on an asymmetric distortion tableextracted payload watermark is given by makes it difﬁcult to locate the same suitable candidates for the watermarked image. A symmetric distortion table can thus be employed to solve this problem. (47) To address the security concerns, e.g., the oracle attacks , we propose to generate the authenticator watermark inwhere is the public key of owner, Table I by encrypting the XORed value of the replicated hash and is the retrieved, replicated hash value of the binary images and the payload watermarkvalue of . Authenticity and integrity of are determined by [see (44)]. To compute the hash value, the image is dividedcomparing the extracted with the original . Noticeably, into two parts: 1) that contains main contents of the imageboth ﬂippable candidates should be cleared out to generate is used to compute the hash value and 2) that consists ofthe intermediate image using DPDC for a in which edge portions is used to embed the authentication data. Anyboth candidates are ﬂippable. This is due to the reason that tampering conducted to will render the computed replicated
346 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 10, NO. 3, APRIL 2008hash value of the watermarked image vary signiﬁcantlyfrom the retrieved replicated hash value of the original image , due to the sensitivity of the hash function to changes.Hence, reveal the tampering. On the other hand, any tamperingconducted to will results in changes in either or or both of them. Changes in eventually lead tochange [see (47)]. Thus, the tampering can be easily detectedupon comparison of with . Employing the secure hashfunction helps detect any changes made to the watermarkeddocument.B. Redundancy Elimination Let’s look at the ﬂippability condition for the odd-oddprocessing case given in (33), in which four coefﬁcients,i.e., , , and , need to be computed and six “XOR” and onelogical “AND” operations are required. The redundancy lies Fig. 8. Example to illustrate 1-D PUMBWT: (a) forward transform and (b) in- verse transform.in that the center pixel has been XORed four times in thecoefﬁcients calculation, which can be eliminated when theﬂippability condition is expressed in pixel values [see (37)]. where . The 1-D PUMBWT can be classiﬁed intoMotivated by this observation, we design a transform called the even and odd processing cases depending on the coordinatesprediction and update lifting MBWT (PUMBWT) to eliminate of the coarse signal. The even PUMBWT, i.e., even processingthe redundancy in IMBWT. case [see (48) and (49)], for a 1-D signal is deﬁned such that the 1) Forward and Inverse PUMBWT for 1-D Signal: Let coarse signal takes the even-indexed sample and is updated byand be the prediction and update operators. The prediction the difference of its two neighboring odd-indexed samples. Theand update lifting scheme for the even processing case consists detail signal is the difference of the two odd-indexed samplesof the following steps. that surround the even-indexed sample. For the odd processing • Split the signal into odd-indexed and even-indexed sets, de- case, left-padding one sample before the ﬁrst sample is required noted as and , respectively, such that (48) and (49) can be applied to the new data set. The where . appended sample should be discarded after the processing. • Predict the odd sets from the even sets, using the prediction 2) Forward and Inverse PUMBWT for 2-D Signal: We now error, , to update the current deﬁne a non-separable 2-D PUMBWT. Each processing case of prediction, i.e., PUMBWT is equivalent to the corresponding transform, e.g., , where . even-even processing case corresponds to even-even transform. • The coarse approximation of the signal is the even sets of Take for example, the 2-D PUMBWT even-even processing case samples, denoted by which is updated by the predic- is deﬁned such that the coarse signal takes the even-indexed tion error , i.e., . samples from both row and column directions and is updated • Reverse the same prediction and update steps, the original by the difference of its horizontal and vertical detail signals. The signal can be perfectly reconstructed, i.e., horizontal detail signal is the difference of the two odd-indexed and samples that surround the coarse signal vertically. The vertical , where . detail signal is the difference of the two odd-indexed samplesThe 1-D PUMBWT is illustrated in Fig. 8. Let and be that surround the coarse signal horizontally, whereas the diag-the operators, where the superscript “ ” denotes “prediction and onal detail signal is the difference of the four samples that areupdate lifting” for 1-D signal. Using the index notation, the for- 8-connected to the coarse signal from its diagonal and anti-di-ward transform for 1-D signal is given by agonal directions. The prediction and update lifting strategy is based on a 3 3 block shown in Fig. 9 for the even-even pro- (48) cessing case. Let , , and be the operators for (49) the coarse signal, horizontal, vertical and diagonal detail signals, respectively. The superscript “ ” denotes “prediction and up-where . The prediction operation is designed to date lifting” for a 2-D signal. The signals obtained by applyingkeep track of the transitions among every three consecutive the analysis operators are given byneighboring pixels such as , and . The (52)inverse transform for a 1-D signal is given by (53) (50) (54) (51) (55)
YANG et al.: ORTHOGONAL DATA EMBEDDING FOR BINARY IMAGES IN MORPHOLOGICAL TRANSFORM DOMAIN-A HIGH-CAPACITY APPROACH 347 Fig. 9. Designations of samples in a 3 2 3 block. Fig. 10. Coefﬁcients comparison. (a) Original image. (b)–(m) Coarsewhere the indices of the signal are , [(b),(f),(j)], horizontal detail [(c),(g),(k)], vertical detail [(d),(h),(l)], and diag- onal detail [(e),(i),(m)] signals obtained from: IMBWT even-even transform ; and (b)–(e), IMBWT odd-odd transform (f)–(i), and PUMBWT even-even transformthe subscript “ ” represents the “even-even” transform. The (j)–(m).boundary conditions for (52)–(55) are given by (56), as shownat the bottom of the page. The signals at level are reconstructedby applying the synthesis operators to yield data, respectively. In applying PUMBWT for data hiding, up- dating the coarse signal is not necessary so that the watermark can be embedded in the coarse signal directly. The vertical and (57) horizontal detail signals obtained from (52) and (53) can be employed to determine the “ﬂippability” of the coarse signal [obtained from (55) without term]. It is noteworthy that (58) the images are still processed in 2 2 blocks despite the fact that PUMBWT is deﬁned based on 3 3 blocks. When DPC or (59) DPDC is chosen using PUMBWT and an embeddable location is in the subsidiary blocks, the diagonal detail coefﬁcients of the four main processing blocks being affected can be used to embed the data, i.e., swap embedding. (60) IV. EXPERIMENTAL RESULTSThe boundary conditions for (57)–(60) are given by A. Coefﬁcients Comparison when Comparisons of the coefﬁcients obtained from PUMBWT (without updating the coarse signal) and a pair case of IMBWT when are made with the result for letter “a” is shown in Fig. 10. The entropy-based cost function  is employed to measure the when compactness of the signal representation, which is given by (62) (61) where is the ratio of the number of foreground pixels, e.g., The same set of equations [i.e., (52)–(55)] can be applied black pixels, versus the total number of pixels within an image.to compute odd-even, even-odd and odd-odd PUMBWT by ap- To compare the entropy of the coefﬁcients obtained frompending one row, one column and both one row and one column computing IMBWT and PUMBWT, 40 images of different when when (56) when and
348 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 10, NO. 3, APRIL 2008 TABLE II ENTROPY COMPARISON OF WAVELET COEFFICIENTS Fig. 11. Capacity increase using DPC or DPDC compared with that of SPC. Fig. 12. Comparisons of average per pixel distortion for DPC and DPDC.types and resolutions are used with the results of 15 imageshown in Table II. It is not difﬁcult to observe from Fig. 10 andTable II that the coefﬁcients of a single transform of IMBWT the achieved is lower than that achieved by employing DPC.and PUMBWT give small entropy values, indicating the large It should be noted that can be high for those images of lowdiscrepancy between the number of foreground and background resolutions such as 150 dpi, as observed for the last several im-pixels. Hence, a more compact signal representation can be ages in Fig. 12. This is due to the fact that few good patternsachieved using both transforms. However, the entropy value exist in images consisting of many thin strokes. The capacityof the detail coefﬁcients obtained from computing PUMBWT and average per pixel distortion mainly depend on the contentsis much larger than that obtained from computing a single of the images, which varies for different types of images. Thetransform of IMBWT, e.g., even-even transform. This demon- richer the contents of the images (more edges exist), the largerstrates that more transition information can be obtained using the capacity. For images of same size and similar contents, inPUMBWT or the interlaced transform. general, text or cartoon images which consist of rich corners and thin strokes may easily cause larger distortion. This is due toB. Capacity, Visual Quality, and Authentication Results the facts that few good patterns exist in corners and thin strokes, To show the capacity increase by employing DPC and DPDC hence, ﬂipping pixels can be easily noticed.compared with that of SPC, 100 images of a variety of sizes Noticeably, with the use of DPC or DPDC, more than oneare used. These images are of different types (e.g., cartoons, ta- pixel may be ﬂipped in each 3 3 block. In this case, the mainbles, handwritten and text in different languages) and resolu- 2 2 block is reconstructed timely once a candidate is pro-tions (e.g., 300 dpi, 200 dpi, and 150 dpi). The visual distor- cessed. The pattern used for distortion evaluation is taken astion table  is used to quantitatively evaluate the visual quality the reconstructed watermarked image (some neighboring can-of the watermarked image, which is deﬁned in . The in- didates possibly have been ﬂipped) with the center pixel takencrease in capacity represented in percentage from SPC to DPC from the original image so that better visual quality of the wa-or DPDC and the average per pixel distortion (denoted as ) termarked images can be preserved. The good visual quality offor DPC and DPDC are shown in Figs. 11 and 12, respectively. the watermarked images obtained by employing SPC, DPC andThe results further reinforce our observations that capacity has DPDC is shown in Fig. 13, in which is 0.5753, 0.5896, andincreased signiﬁcantly using DPC or DPDC versus SPC, e.g., 0.5780, respectively. The results demonstrate that better visualincrease from 56% to 95% for the 100 test images. With appro- quality of the watermarked image can be achieved using DPDCpriate selection of the lower distortion pixel to ﬂip for DPDC, compared with that of DPC. The proposed data-hiding scheme
YANG et al.: ORTHOGONAL DATA EMBEDDING FOR BINARY IMAGES IN MORPHOLOGICAL TRANSFORM DOMAIN-A HIGH-CAPACITY APPROACH 349 2Fig. 13. Hiding Effects. (a) Original image of size 501 300 and 300 dpi. (b) Hide 1274 bits by employing SPC. (c) and (d) Hide 2316 bits by employing (c) DPCand (d) DPDC. (e)–(g) Enlarged difference image of (b), (c), and (d). Black and dark gray dots are the pixels that are ﬂipped from white to black and from blackto white, respectively. 2Fig. 14. Authentication Results. (a) Original text image of size 638 126. (b) Watermarked image with 1793 bits embedded by employing DPDC. (c) Water-marked image that is tampered, “binary” and “transform” in the 1st and 3rd lines are changed to “gray” and “spatial”, respectively. (d) Original logo image of size 280 20. (e) Reconstructed logo image from the watermarked image shown in (b). (f) Reconstructed logo image from the tampered watermarked image shownin (c).can also be applied to halftone images with acceptable visual The capacity achieved by employing different methods andquality. Further improvement in visual quality can be done by the corresponding average per pixel distortion are shown inpreserving the local average intensity and considering the error Tables III and IV, respectively. In the tables, the block sizesdiffusion process in halftoning. for these methods are chosen such that larger capacity is ob- Experiments are conducted by randomly choosing 50 binary tained under the constraints that the watermarked image is ofimages of different resolutions, types and sizes to test effective- acceptable visual quality. It can be noticed from Table III thatness of the hard authenticator watermark using SPC, DPC and with orthogonal embedding, i.e., using DPDC or DPC of ourDPDC. Various tamperings such as erasing, tampering in blank proposed method, the capacity achieved is larger than that ofarea, word substitution, adding noise, ﬁltering are performed Wu et al.’s method, Yang and Kot’s method and Tseng et al.’sto the watermarked image. The results show that all the tam- method (block size of 16 16). For Tseng et al.’s method, weperings can be detected. One example is shown in Fig. 14, in embed data in the non-uniform blocks having edge pixels andwhich a logo image is used as to be XORed with the repli- enforce the element-wise computation of the image, key andcated hash value of the image to visually show the tamperings. weight matrixes to be even for the convenience of watermarkIt can be seen from the results that the logo image can be recon- extraction. As observed from Tables III and IV, employing DPCstructed perfectly when no tampering occurs, whereas it looks or DPDC slightly degrades the average per pixel distortion oflike a random noise pattern when the watermarked image is sub- the watermarked images compared those obtained in Wu etjected to tampering. al.’s approach and Yang and Kot’s approach. However, the gain in capacity is signiﬁcant. Our proposed method achieves betterC. Comparisons average per pixel distortion than Tseng et al.’s approach. The Comparisons of the capacity and visual quality of the number of bits used for authentication varies depending on thewatermarked images obtained using our proposed method security requirements of the application. A message authenti-and that obtained by employing the methods proposed by cation code or cryptographic signature can be incorporated forWu et al. , Tseng et al.  and Yang and Kot  are made. higher security. For example, a capacity as large as 512 bits
350 IEEE TRANSACTIONS ON MULTIMEDIA, VOL. 10, NO. 3, APRIL 2008 TABLE III for Tseng et al.’s method. These compu- CAPACITY FOR DIFFERENT METHODS tations can be time-consuming especially for larger block size. Further, at most logical AND, logical NOT and addi- tion are required using Yang and Kot’s methods, which is higher than that required by our proposed method. The major compu- tations required for DPC or DPDC of our proposed method are assignment and XOR using PUMBWT, whereas assignment and XOR are required using IMBWT. In addition, at most comparison is required for DPDC. Obviously, our proposed method has lower computational com- plexity compared with other approaches. Our proposal of processing an image in 2 2 blocks not only prevents the computational load from getting high for block- based approach with large block size (e.g., in , ), but also improves the efﬁciency of utilization of ﬂippable pixels . No- ticeably, the un-embeddability of the sharing rows, columns and block boundaries in  decreases as illustrated in Fig. 7(a). TABLE IV Generally, and for an interlaced AVERAGE PER PIXEL DISTORTION FOR DIFFERENT METHODS and non-interlaced block of size , respectively. becomes lower with the increase of block size since only one among many ﬂippable pixels is chosen. for each and two pixels can be chosen for each for both DPC and DPDC in our proposed approach, which signiﬁcantly in- creases the probability for a block to be embeddable. In addi- tion, the need to locate the embeddable pixels to incorporate cryptographic signature in  causes decrease in capacity and increase in computational load for block size larger than 3 3, which has been avoided in our present approach. V. CONCLUSIONS In this paper, we present a high-capacity data-hiding scheme for binary images authentication based on the interlaced mor- phological binary wavelet transforms. The relationship between the coefﬁcients obtained from different transforms is utilized to identify the suitable locations for watermark embedding such that blind watermark extraction can be achieved. Two processing cases that are not intersected with each other areis required to incorporate a message authentication code such employed for orthogonal embedding in such a way that notas SHA-2 (e.g., SHA-512), whereas 1024 bits are required to only can the capacity be signiﬁcantly increased, but the visualincorporate a cryptographic signature generated by RSA. Our distortion can also be minimized. Results of comparative ex-proposed scheme with high capacity can better serve for the periments with other methods reinforce the present scheme’sauthentication purpose. In general, the larger the capacity, the superiority in being able to attain larger capacity while main-more the number of bits are to be modiﬁed so that the total taining acceptable visual distortion and low computational cost.distortion will be larger. Our proposed method also has computational complexity ad- REFERENCESvantages. The most time-consuming computation using Wu et  I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking. Sanal.’s method is to ﬁnd the best pattern in each block, which re- Mateo, CA: Morgan Kaufmann, 2001.quires comparisons, where is the  B. Furht and D. Kirovski, Multimedia Security Handbook, B. Furht and D. Kirovski, Eds. Boca Raton, FL: CRC, 2005.determined pixels in each block, and and are the number  Y. Liu, J. Mant, E. Wong, and S. H. Low, “Marking and detection ofof blocks in and directions, respectively. text documents using transform-domain techniques,” in Proc. SPIE,approximates to the size of image for a large block San Jose, CA, 1999, vol. 3657, pp. 317–328.  Q. Mei, E. K. Wong, and N. Memon, “Data hiding in binary text doc-size. While calculation of distance matrix for each pixel is re- ument,” in Proc. SPIE, 2001, vol. 4314, pp. 369–375.quired according to Tseng et al., which needs  Y. C. Tseng and H.-K. Pan, “Data hiding in 2-color images,” IEEEmultiplication and addition. Similarly, com- Trans. Comput., vol. 51, no. 7, pp. 873–878, Jul. 2002.  K.-F. Hwang and C.-C. Chang, “A run-length mechanism for hidingparisons of the distance matrix for any two pixels in each block data into binary images,” in Proc. Paciﬁc Rim Workshop on Digitalrequire comparisons, where Steganography, Kitakyushu, Japan, Jul. 2002, pp. 71–74.
YANG et al.: ORTHOGONAL DATA EMBEDDING FOR BINARY IMAGES IN MORPHOLOGICAL TRANSFORM DOMAIN-A HIGH-CAPACITY APPROACH 351  H. Lu, X. Shi, Y. Q. Shi, A. C. Kot, and L. Chen, “Watermark Alex C. Kot (F’06) has been with Nanyang Tech- embedding in DC components of DCT for binary images,” in Proc., nological University, Singapore, since 1991. He IEEE Workshop on Multimedia Signal Processing, Dec. 9–11, 2002, headed the Division of Information Engineering at pp. 300–303. the School of Electrical and Electronic Engineering  M. Wu and B. Liu, “Data hiding in binary images for authentication for eight years and is currently a Professor and and annotation,” IEEE Trans. Multimedia, vol. 6, no. 4, pp. 528–538, the Associate Chair/Vice Dean (Research) for the Aug. 2004. School of Electrical and Electronic Engineering. He  H. Y. Kim and R. L. de Queiroz, “Alteration-locating authentication has published extensively in the areas of signal pro- watermarking for binary images,” in Proc. Int. Workshop Digital Wa- cessing for communication, biometrics, data-hiding termarking, 2004, pp. 125–136. and authentication.  H. Lu, A. C. Kot, and Y. Q. Shi, “Distance-reciprocal distortion mea- Dr. Kot served as Associate Editor for the IEEE sure for binary document images,” IEEE Signal Process. Lett., vol. 11, TRANSACTIONS ON SIGNAL PROCESSING, the IEEE TRANSACTIONS ON CIRCUITS no. 2, pp. 228–231, Feb. 2004. AND SYSTEMS FOR VIDEO TECHNOLOGY, and the IEEE TRANSACTIONS ON  H. Yang and A. C. Kot, “Pattern-based date hiding for binary images CIRCUITS AND SYSTEMS II. He is currently an Associate Editor for the authentication by connectivity-preserving,” IEEE Trans. Multimedia, EURASIP Journal of Applied Signal Processing, the IEEE TRANSACTIONS ON vol. 9, no. 3, pp. 475–486, Apr. 2007. CIRCUITS AND SYSTEMS I, and the IEEE TRANSACTIONS ON MULTIMEDIA. He  B. B. Zhu, M. D. Swanson, and A. H. Tewﬁk, “When seeing isn’t be- is a member of the Visual Signal Processing and Communication Technical lieving,” IEEE Signal Process. Mag., pp. 40–49, Mar. 2004. Committee and the Image and Multidimensional Signal Processing Technical  P. W. Wong and N. Memon, “Secret and public key image water- Committee. He was the General Co-Chair for the 2004 IEEE International Con- marking schemes for image authentication and ownership veriﬁcation,” ference on Image Processing (ICIP) and has served as an IEEE Distinguished IEEE Trans. Image Process., vol. 10, no. 10, pp. 1593–1601, Oct. 2001. Lecturer. He is a Fellow of IES.  D. Kundur and D. Hatzinakos, “Digital watermarking for telltale tamper prooﬁng and authentication,” Proc. IEEE, vol. 87, no. 7, pp. 1167–1179, Jul. 1999.  C.-Y. Lin and S.-F. Chang, “A robust image authentication method Susanto Rahardja (SM’03) received the B.Eng. de- distinguishing JPEG compression from malicious manipulation,” IEEE gree from the National University of Singapore and Trans. Circuits Syste. Video Technol., vol. 11, no. 2, pp. 153–168, Feb. the M.Eng. and Ph.D. degrees from Nanyang Techno- 2001. logical University (NTU), Singapore, all in electrical  H. J. A. M. Heijmans and J. Goutsias, “Nonlinear multiresolution signal and electronic engineering. decomposition schemes-part II: Morphological wavelets,” IEEE Trans. He is the Director of the Personal 3D Enter- Image Process., vol. 9, no. 11, pp. 1897–1913, Nov. 2000. tainment System program and Head of the Signal  W. Sweldens, “The lifting scheme: A construction of second generation Processing Department at the Institute for Info- wavelets,” SIAM J. Math. Anal., vol. 29, pp. 511–546, 1998. comm Research (I R), Singapore. He is also an  B. Chen and G. W. Wornell, “Quantization index modulation: A Associate Professor at the School of Electrical and class of provably good methods for digital watermarking and infor- Electronic Engineering, NTU. His research interests mation embedding,” IEEE Trans. Inform. Theory, vol. 47, no. 4, pp. are in audio/video signal processing, spread-spectrum and multi-user detection 1423–1443, May 2001. techniques for CDMA applications, digital signal processing algorithms and im-  J. Wu, B. B. Zhu, S. Li, and F. Lin, “Efﬁcient oracle attacks on yeung- plementations, and logic synthesis, of which he has more than 200 publications mintzer and variant authentication schemes,” in Proc. IEEE Int. Conf. in internationally refereed journals and conferences. Since 2002, he has actively Multimedia and Expo., Jun. 27–30, 2004, vol. 2 , pp. 931–934. participated in the international ISO/IEC JTC1/SC29/WG11 Moving Picture  M. D. Swanson and A. H. Tewﬁk, “A binary wavelet decomposition Expert Group (MPEG) where he contributed to the MPEG-4 Scalable Lossless of binary images,” IEEE Trans. Image Process., vol. 5, no. 12, pp. System (SLS) which is incorporated into ISO/IEC 14496–3:2005/Amd.3:2006. 1637–1650, Dec. 1996. He also contributed technology to the MPEG-4 Audio Lossless System (ALS) which is now incorporated into ISO/IEC 14496–3:2005/Amd.2:2006. Dr. Rahardja was awarded the Standards Council Merit Award by SPRING Singapore in 2006 in recognition for his contributions to the national standard- ization program. For his leadership and technical contribution to advancement Huijuan Yang received the B.Sc degree from Jilin of digital audio signal processing and its adoption to the MPEG, he was awarded University, Changchun, China, and the M. Eng. the National Technology Award in 2007. He was also the recipient of the IEE degree from Nanyang Technological University, Hartree Premium Award in 2002 and the prestigious Tan Kah Kee Young Singapore, where she is currently pursuing the Ph.D Inventors’ Gold award in the Open Category, for his contributions on scalable degree. to lossless audio compression technology, in 2003. He has served on several From March 2001 to November 2002, she was boards and advisory and technical committees in various IEEE- and SPIE- a Security Software Engineer with CrimsonLogic related professional activities in the areas of multimedia. He is an elected Pte. Ltd., Singapore. She has been a Research member of the Technical Committee of the Visual Signal Processing and Associate with School of Electrical and Electronic Communications, Circuits and Systems for Communications and Multimedia Engineering, Nanyang Technological University, Systems and Applications of the IEEE Circuits and Systems Society. He since 2002. Her research interests include digital is currently serving as Associate Editor for the IEEE TRANSACTIONS ONmultimedia processing, authentication, and information security. She has AUDIO, SPEECH AND LANGUAGE PROCESSING and the IEEE TRANSACTIONSinvented/co-invented two Singapore patents (granted) on watermarking and ON MULTIMEDIA, as well as the Journal of Visual Communication and Imagecontrol of document distribution and has three pending U.S. patents. Representation.