Reversible data hiding in encrypted images based on pixel prediction and multi-MSB planes rearrangement
RReversible data hiding in encrypted images based on pixel prediction and multi-MSBplanes rearrangement
Zhaoxia Yin a , Xiaomeng She a , Jin Tang a, ∗ , Bin Luo a a Anhui Province Key Laboratory of Multimodal Cognitive Computation, School of Computer Science and Technology, Anhui University, 230601, P.R.China
Abstract
Great concern has arisen in the field of reversible data hiding in encrypted images (RDHEI) due to the development of cloud storageand privacy protection. RDHEI is an e ff ective technology that can embed additional data after image encryption, extract additionaldata without any errors and reconstruct original images losslessly. In this paper, a high-capacity and fully reversible data hiding inencrypted images method based on pixel prediction and multi-MSB (most significant bit) planes rearrangement is proposed. First,we use the median edge detector (MED) predictor to calculate the predicted value. Next, unlike previous methods, in our proposedmethod, signs of prediction errors (PEs) are represented by one bit plane and absolute value of PEs are represented by other bitplanes. Then, we divide bit planes into uniform blocks and non-uniform blocks, and rearrange these blocks. Finally, according todi ff erent pixel prediction schemes, we embed di ff erent number of additional data adaptively. The experimental results prove thatour method has higher embedding capacity compared with state-of-the-art RDHEI methods. Keywords:
Reversible data hiding, encrypted images, privacy protection, prediction error
1. Introduction
Data hiding is a technique that can embed data into multi-media and extract the data without any error. The shortcomingof this technology is that after extracting the embedded data,the original cover medium will be slightly distorted. Thus, inorder to protect the original cover medium, reversible data hid-ing (RDH) is proposed [1]. RDH is a very useful technologywhich can reconstruct the original cover medium losslessly. Inthe past several decades, RDH has attracted more and more at-tention, and has been applied in many fields, such as militarycommunication, medical diagnosis, judicial evidence obtainingand so on.A major current focus in RDH is how to ensure low distor-tion of original images after embedding data, therefore, visualquality of marked images is the key metric of RDH methods.To achieve better visual quality, many RDH methods have beenproposed in the past several decades [2–11]. These methods aremainly divided into three categories: lossless compression [2–4], histogram shifting [5–7] and di ff erence expansion [8–10].The first category, lossless compression, is used in many RDHmethods to vacate room for data embedding. To achieve betterperformance, lots of RDH methods based on histogram shiftinghave been proposed. The central idea of these methods is touse the peak points and minimum points of the histogram of animage, and embed additional data by modifying the grayscalevalues. The third category is based on di ff erence expansion,which embeds data by expanding the di ff erence between twopixels. ∗ Corresponding author
Email address: [email protected] (Jin Tang)
Although RDH methods can successfully embed additionaldata, the risk of exposing the content of original images stillexists. Therefore, with the ever-increasing demand for privacyprotection, reversible data hiding in encrypted images (RDHEI) [12,13] have attracted wide concern over the past years. As shownin Fig. 1, there are three end users of a RDHEI method: thecontent-owner, data-hider and receiver. In short, the content-owner can preprocess and encrypt the original image. Afterreceiving the encrypted image, the data-hider can embed ad-ditional data into it, but cannot access the content of originalimage. Finally, the receiver can restore the original image andextract the embedded data. However, since the content of origi-nal images cannot be obtained after encryption, the visual qual-ity of marked images don’t need to be compared. Therefore,embedding capacity (EC) is the key metric of RDHEI ratherthan visual quality.According to the encryption order, the existing RDHEI meth-ods can be divided into two categories, Vacating Room AfterEncryption (VRAE) and Reserving Room Before Encryption(RRBE), as shown in Fig. 1. In VRAE methods [14–17], datahiders embed additional data by modifying encrypted pixel val-ues. However, the redundancy of the encrypted image is lowerthan that of the original image, which leads to the EC beingunsatisfactory. To further improve EC, many RRBE methodshave been proposed in the past few years [18–24]. Di ff erentfrom VRAE methods, these methods improve EC based on thespatial correlation of original images. In this paper, we focuson RRBE methods.In [18], Ma et al. first proposed the RRBE scheme. The keyidea of their scheme is to reserve room by embedding the leastsignificant bit (LSB) of some original pixels into other origi- Preprint submitted to Journal of L A TEX Templates July 9, 2020 a r X i v : . [ c s . MM ] J u l eserving roomEncryption key Content-owner
Encrypted image
Data hidingData hiding key Additional data Data extractionImage recovery
Original image
Secret data
Data-hider
Receiver
Marked encrypted image
Encryption
Encryption key
Data hiding key
Original
Image (a)
Encryption
Encryption key
Content-owner
Encrypted image
Data hidingData hiding key Additional data Data extractionImage recovery
Original image
Secret data
Data-hider
Receiver
Marked encrypted image
Reserving room
Encryption key
Data hiding key Original
Image (b)Figure 1: Two categorized frameworks of RDHEI schemes: (a) VRAE and (b) RRBE. nal pixels. Then generate an encrypted image and embed addi-tional data into the reserved room. In comparison with previousVRAE schemes, this scheme increase the size of EC, and hencemake RRBE scheme viable. Yi et al. [19] suggested embeddingthe lower bit planes of original images into the higher bit planesof original images so that the room of lower bit planes can beused to embedding data. In the early work, most of ways to in-crease EC of RDHEI was to research regarding the LSB substi-tution, and little attention was paid to the substitution of MSB.To further improve EC, Puteaux et al. [20] proposed a new RD-HEI scheme based on MSB substitution instead of LSB. Theydesigned a MSB prediction scheme, and generated a label mapfrom which data can be embedded. However, one point of thisscheme can be improved is that only one-MSB can be used.Based on [20], Puyang et al. [21] proposed an extension schemeusing two-MSB prediction, which is more e ffi cient and the per-formance is improved. Later, Yin et al. [22] also proposed animproved scheme based on [21]. During thier reserving embed-dable room phase, multi-MSB of original pixels are predictedadaptively and marked by Hu ff man coding. According to theirresults, the EC is higher than previous methods. In [23], Wu etal. suggested taking advantage of the spatial correlation of orig-inal images and using parametric binary tree labeling to markimage pixels in two di ff erent categories. By using this scheme,original images can be recovered without loss and EC can alsobe improved. Previous schemes introduced above have some drawbacks,such as low EC or high EC without reversibility. For example,since Puteaux et al.’s method [20] is limited to MSB, the sizeof EC is far from satisfaction. Then, although Yin et al. [22]take into account multiple MSBs, for each bit plane, the embed-dable space is still not maximized, which also leads to their ECbeing unsatisfactory. Moreover, spatial correlation isn’t fullyutilized in Wu et al.’s scheme [23]. Considering the similaritybetween bit planes of gray images and binary images, that is,both bit planes and binary images are only composed of twotypes of values, we pay attention to Ren et al.’s scheme [24].This scheme introduced a reversible data hiding in encryptedbinary images based on pixel prediction scheme, and accordingto its results, EC is higher than previous schemes of binary im-ages. However, Ren et al.’s scheme [24] was directly appliedto grayscale images by us, the EC is not satisfactory when thisapplication is reversible. In other words, low redundancy oforiginal grayscale images and too much auxiliary data for eachbit plane lead to a poor EC. To achieve better performance, inthis paper, we proposed a new method which e ff ectively reducesthese drawbacks.The main contributions of our method can be summarizedas follows:1) We successfully extend the pixel prediction scheme of bi-nary image to bit planes of grayscale image, and solve the prob-lem that high EC and reversibility cannot coexist. In a word,2 ncryptionEncryption key Content-owner
Encrypted image
OriginalImage
Data hidingData hiding key Secret data Data extractionImage recovery
Original image
Secret data
Data-hider Receiver
Marked encrypted image PE calculation Multi-MSB planes rearrangement
Reserving room e K d K d K e K e I ew I I Figure 2: The framework of the proposed method. after we improve the EC, our method is still reversible.2) We make full use of the correlation of adjacent pixels andcompress auxiliary data via arithmetic coding, which makesmore embeddable positions in the bit plane. Experimental re-sults also prove that we have achieved a higher EC comparedwith the most advanced RDHEI method.3) Furthermore, we have successfully used the median edgepredictor (MED), and the distribution range of prediction error(PE) values becomes smaller relative to the distribution rangeof original pixel values, which makes the redundancy of imagehigher and the available embedded room larger.The rest of this paper is organized as follows: The proposedmethod is described in detail in Section 2, and Section 3 in-troduces the experimental results and analysis of our method.Finally, this paper is concluded in Section 4.
2. Proposed method
In this section, we propose a high-capacity and fully re-versible RDHEI method based on pixel prediction and multi-MSB planes rearrangement. As shown in Fig. 2, the proposedmethod can be divided into three parts: 1) Embeddable roomreservation and encryption are done by content-owner, 2) Dataembedding is done by data-hider, 3) Data extraction and im-age recovery are done by receiver. In this section, the proposedmethod is introduced in detail. First, Section 2.1 describes theprocess of reserving embeddable room. Next, in Section 2.2,procedures of image encryption are given. Then, Section 2.3presents the process of additional data embedding. In the lastSection 2.4, data extraction and image recovery are describedin detail.
The procedures of this section are divided into three parts:Calculation of predicted errors, generation of bit planes and re-arrangement of bit planes.
For an original image I sized M × N , we calculate predictedvalue px by the MED predictor [25]. As shown in Fig. 3, px iscalculated based on the three pixels around the current pixel x . In particular, the pixels of first row and first column will bethe reference pixels to recover original image, so we will notchange the values of reference pixels. x x xx Figure 3: The context of the current pixel by MED predictor.
The detailed calculation formula of predicted values is asfollows: px = max ( x , x ) , x ≤ min ( x , x ) min ( x , x ) , x ≥ max ( x , x ) x + x − x , otherwise . (1)Then, the PE e ( i , j ) can be obtained as follows: e ( i , j ) = (cid:40) x ( i , j ) , i = or j = x ( i . j ) − px ( i , j ) , otherwise , (2)where 1 ≤ i ≤ M , ≤ j ≤ N .Finally, we define e ( i , j ) greater than 64 or less than -64as overflow pixels, and use Eq. (3) to change the value of thesepixels. The reason for this operation will be explained later. Af-ter the calculation, the distribution of prediction errors is moreconcentrated than that of the original pixel values, which meansthat there are more identical values in bit planes and the embed-ding capacity will be improved. e ( i , j ) = x ( i , j ) , e ( i , j ) < − or e ( i , j ) > . (3) After calculating the prediction error, the prediction errorbit plane is generated. If only traditional method, Eq. (4), isused to calculate bit planes, the proposed scheme will not bereversible. Since the original positions of bit planes are shuf-fled in the subsequent embedding operation, whether the PE ispositive or negative during the image recovery step cannot bedetermined. Based on this problem, we propose an adaptivemethod to calculate PE bit-planes. The method is introduced in3etail as follows: First, considering the range of pixel values ofgrayscale images, we convert the PEs of reference pixels into8-bit binary sequences by Eq. (4), where i = j = (cid:98)∗(cid:99) isthe floor operations. e k ( i , j ) = (cid:36) e ( i , j ) mod 2 − k − k (cid:37) , k = , , . . . , . (4)Next, other PEs are converted into 7-bit binary sequencesby Eq. (5). Whats more, because there are some overflow PEs,we use Eq. (6) to calculate the eighth binary bit of PEs in di ff er-ent situations. Specifically, signs of non-overflow PEs are rep-resented by one bit plane and absolute values of non-overflowPEs are represented by other bit planes. However, althoughPEs are converted into 7-bit binary sequences, the final recon-structed image is still lossless, because only a few PE values areoverflow values (the PE values less than - 64 or greater than 64are overflow PEs). The calculation formulas for this step are asfollows: e k ( i , j ) = (cid:36) e ( i , j ) mod 2 − k − k (cid:37) , k = , , . . . , , (5) e ( i , j ) = (cid:40) − sign e ( i , j ) , − ≤ e ( i , j ) ≤ e ( i , j ) mod 2 , otherwise . (6)Finally, because we use di ff erent formulas to convert PEs,a PE label map must be generated to identify each PE. Thus,we set the tag 1 for overflow PEs and 0 for other PEs. In thisway, a label map L with a large number of 0 and a fairly smallnumber of 1 is generated. Besides, arithmetic coding is used tocompress L losslessly. Particularly, the compressed auxiliarydata only occupies a very small room. For better understanding,as shown in Fig. 4, an example is given to describe our method. reference pixeloverflow PEnon-overflow PE
00 0 1 Figure 4: The label map of PE image.
First, as shown in Fig. 5, the bit planes obtained by theabove steps are divided into several non-overlapping blocks sized k × k . All values are the same for uniform blocks (UB), other-wise they are non-uniform blocks (NUB). Next, we set the tag 1for NUBs and 0 for UBs. Because of the high redundancy of thepreprocessed image, we can also get a label map L with a largenumber of 0 and a small number of 1. In the same way, arith-metic coding can be used to compress L , and the length of thelabel map is expressed in a 16-bit binary sequence. Then, theprocessed bit planes are traversed in order, the NUBs of each bit plane are arranged in order in the upper order, and the UBsin the lower order, as shown in Fig. 6. Meanwhile,all of NUBsneed to be marked, and the NUB that can be embedded into ad-ditional data is marked with 0, otherwise 1. The specific basisfor judging whether NUB can be embedded will be mentionedlater.
11 1 11 1 1 1
010 00
00 0 0 Figure 5: An example of original blocks labeling of bit planes.
00 0 0 NUB UBUBUB
Figure 6: Rearrangement of bit planes.
Lastly, we embed all the auxiliary data into UBs of the cor-responding bit plane, and the last value of each UB is usedas the predicted value without auxiliary data. Moreover, sincesome bit planes are not enough to accommodate auxiliary data,an 8-bit binary sequence is finally generated to indicate whetherthe current bit plane can be embedded.
After reserving the embeddable room, the next step is toencrypt the image. First, the image is divided into eight bitplanes, and the auxiliary data is extracted sequentially in thelower right of each bit plane in order to locate the encryptedposition. Next, a pseudo-random matrix H of size M × N isgenerated by an encryption key K e , and then the values of thismatrix are converted into 8-bit binary sequences by Eq. (7), H k ( i , j ) = (cid:36) H ( i , j ) mod − k − k (cid:37) , k = , , . . . , , (7)where 1 ≤ i ≤ M , ≤ j ≤ N . At last, for the original PE e k ( i , j )of each bit plane that can be encrypted, we use the Eq. (8)to perform encryption operations and ⊕ denotes exclusive-or(XOR) operation: e ke ( i , j ) = e k ( i , j ) ⊕ H k ( i , j ) , k = , , . . . , . (8)In this way, we can calculate the encrypted PE e ke ( i , j ) of k th bitplane and finally get the encrypted image I e .4 d K PorBLR or PorBLR
NUB sized 4*4 ?yes1 01 0 0100101 0 11 0 0Predicted valueEmbed additional data
Figure 7: An example of embedding data into NUB.
Considering the similarity between bit planes and binaryimages, we use the pixel prediction scheme when embeddingadditional data into the processed prediction error bit planes,which is proposed by Ren et al. [24]. As mentioned before, eachprocessed bit plane is divided into UBs and NUBs. For di ff er-ent blocks, di ff erent methods are used to embed additional data.Besides, to improve the security of our method, the data hidingkey K d is used to encrypt additional data before embedding.After completing these steps, embedding steps are described indetail below.First, we embed additional data into NUBs. Auxiliary datain the lower right corner of the MSB plane needs to be extractedfirst to determine whether each bit plane can be embedded andthe embedded coordinates. It can be seen from pixel correlationthat the probability of adjacent pixels being identical is veryhigh. However, values of bit planes are only 0 and 1, whichmeans that the probability of three adjacent values around eachvalue being identical is very high. For each NUB, if the value ofmiddle position is 0, the sum of three neighboring values maybe 0 or 1 (that is, the probability of neighboring values being 0is higher than 1). Similarly, if the middle value is 1, the sum ofthree neighboring values may be 2 or 3. Based on this feature,we judge each NUB, if current NUB satisfies the feature, it isan embeddable block. Conversely, additional data cannot beembedded. As shown in Fig. 7 is an example of embeddingdata into NUB. Each NUB is divided into four parts, and eachpart is composed of four values, where P is the middle positionof each part that can be embedded, and L , B , R are the threeadjacent predicted values around P .Then, we embed data into UBs. According to the extractedauxiliary data, the embeddable coordinates in UB can be easilylocated. As shown in Fig. 8, for each UB, the values of oneblock are identical. This means that, for a UB, we only need tokeep one of value in the block not being changed, and then we can recover all values in the block after taking the unchangedvalue as the prediction value. Based on this characteristic, weembed additional data into UBs except the position of predictedvalue. To facilitate understanding, here is an example of em-bedding data into a UB. As shown in Fig. 8 is a UB that eachvalue is 1. After we embed data, only the last value 1 remainsunchanged. Finally, after embedding additional data into NUBsand UBs, we have generated the marked encrypted image I ew . d K predicted valueembed additional data Figure 8: An example of embedding data into UB.
Whether the receiver obtains the lossless data or the originalimage depends on which key the receiver has. So we give threecases according to di ff erent keys that the receiver has:1) If the receiver has the data hiding key K d , the embeddeddata can be obtained without errors. First, the legal receiver di-vides the marked encrypted image into eight bit planes accord-ing to the auxiliary data in the lower right corner of the MSBplane. If the current bit plane is an embeddable bit plane, locatethe position where the secret data is embedded, and then extractauxiliary data of remaining embeddable bit planes in sequence.To express our method more vividly, Figure. 9 shows di ff er-ent regions of embeddable bit planes. Then, for each NUB, ifthe auxiliary data of this NUB is 0, secret data can be extractedin this NUB. For each UB, except for the prediction pixel ofthe last position, the additional data of other positions is ex-tracted in order. Finally, all embedded secret data can be ex-tracted without errors and decrypted with the data hiding key5 a) (b) (c) (d) (e)Figure 9: Test images: (a) Lena ; (b)
Baboon ; (c)
Jetplane ; (d)
Man ; (e)
Ti f f any .(a) (b) (c) (d)Figure 10: Results of applying our method to
Lena image when k =
4: (a) Original image I ; (b) Encrypted image I e ; (c) Marked encrypted image I ew , with netpayload ER = bpp ; (d) Reconstructed image I . Histogram PEH -100 -50 0 50 10000.511.522.53 10 Figure 11: Original image histogram and prediction error histogram (PEH). K d . However, because the receiver doesnt have encryption key K e , the original image cannot be recovered.2) If the receiver has the encryption key K e , the originalimage can be reconstructed losslessly. First, the legal receiverdecrypts the marked encrypted image with the encryption key K e , and then extracts auxiliary data in the lower right cornerof the MSB plane to determine whether each bit plane is rear-ranged. Then, the auxiliary data of remaining bit planes is se-quentially extracted. According to the prediction scheme men-tioned above, all of NUBs and UBs in embeddable bit planescan be restored. Finally, according to the extracted label map L
2, the receiver can reconstruct the original image.3) If the receiver has both the data hiding key K d and theencryption key K e , then the receiver can extract data and restoreimages without errors. However, the detailed steps are the sameas above.
3. Experimental results and analysis
To clearly evaluate the performance of our proposed scheme,experimental results are detailed in this section. First, as wediscussed earlier, the size of EC is a key metric of RDHEI.Hence Section 3.1 gives performance analysis in terms of EC,and we use the embedding rate (ER) as the evaluation indexof EC. As shown in Fig. 9, we use test images that commonlyused: Lena, Baboon, Jetplane, Man and Ti ff any. Furthermore,we also realize tests on three public datasets: BOSSbase [26],BOWS-2 [27] and UCID [28]. Then, in Section 3.2, we intro-duce performance analysis of reversibility of our method. Fi-nally, Section 3.3 compares the proposed method with recentstate-of-the-art methods. In the proposed method, we divided bit planes into severalnon-overlapping blocks sized k × k and k is a variable. There-6 LenaBaboon JetplaneMan Tiffany
Figure 12: the ERs of di ff erent test images when block size k is di ff erent.Table 1: The percentage of the number of overflow pixels and the total numberof original pixels in di ff erent images. Test image Percentage(%)
Lena 0.04Baboon 1.42Jetplane 0.16Man 0.09Ti ff any 0.02fore, we give the experimental results when block sizes are dif-ferent. Fig. 12 shows the ERs of di ff erent test images whenblock size k is di ff erent, and as shown in Fig. 13, when blocksize k is 4, the ERs of Lena are 2.87 bpp , 1.321 bpp , 3.232 bpp ,2.490 bpp and 2.943 bpp , which is the highest ER comparedto other block sizes. Finally, as shown in Table. 2, we set blocksize k being 4 and list average ERs on three public datasets.In the proposed method, considering the low redundancyof original images, we use the MED predictor to calculate pre-dicted values. After the calculation, as shown in Fig. 11, thedistribution of prediction errors is more concentrated than thatof original pixel values. In other words, it makes more valuesin bit planes being identical and means that more data can beembedded into UBs. So the ER of our method will be higher.Moreover, Table. 1 illustrates the percentage of the number ofoverflow pixels and the total number of pixels in di ff erent im-ages, and we can see clearly that the proportion of overflow pix-els is very low. However, it also directly proves that our methodof calculating bit planes is feasible, specifically, it doesnt gener-ate too much auxiliary data to occupy many embeddable room.It is also worth mentioning that most existing algorithms willgenerate a lot of auxiliary data. Unlike these methods, the aux-iliary data generated by our method is a binary sequence withmany 0 and very few 1. This sequence can be perfectly com-pressed, and we use arithmetic coding to compress it. Aftercompression, there is more room in bit planes to embed addi-tional data, which further improves the ER of our method. To show the performance of our method in more detail, acommonly metric MSE (Mean square error) is used to test the
Table 2: Experimental results on three image databases.
Database MSE Average ER( bpp ) BOSSbase 0 3.498BOWS-2 0 3.393UCID 0 2.797reversibility of our proposed method. As shown in Table. 2,we give the results on three datasets BOSSbase [26], BOWS-2 [27] and UCID [28]. The MSE of each reconstructed imageis 0, which means that each reconstructed image and the cor-responding original image are exactly the same. At the sametime, although we selectively encrypt embeddable bit planes,our method has good visual security. Fig. 10 shows the resultsof applying our method to Lena image when k =
4. When weillegally obtain the encrypted image (b) and marked encryptedimage (c), the content of original images cannot be obtained atall.
The key indicator of RDHEI is the size of EC, in otherwords, the ER. In order to better demonstrate the ER of ourproposed method, this section compares ER with three lateststate-of-the-art RDHEI methods [20, 22, 23]. As shown in Fig-ure. 13, we tested five images using these methods. Puteauxet al. [20] only embedded data into the MSB, so the ER oftheir method is very low. For example, when using Puteauxet al.s method [20], the ER of Lena image is only 0.977 bpp .Compared with [20], Wu et al. [23] considered that spatial cor-relation can be used to increase the ER, and finally the em-bedding rate of Lena image is 2.645 bpp . In addition, Yin etal. [22] uses multiple MSBs, but still doesnt make use of theembeddable room of each bit plane. When using the methodof Yin et al. [22], the embedding rate of Lena image is 2.583 bpp . Finally, to better prove the performance of our method,we directly apply the binary image method of Ren et al. [24]to grayscale images. Taking the Lena image as an example, asshown in Figure. 13, the embedding rate is only 1.712 bpp . Itis worth mentioning that the ER of
Lena image when using ourmethod is 2.87 bpp . We also compared ER with these state-of-the-art methods on three datasets: BOSSbase [26], BOWS-2 [27] and UCID [28]. As shown in Figure. 14, it is obviousthat the proposed method has a higher ER on these datasetsthan other methods.
4. Conclusions
This paper proposes a new method of reversible data hidingin encrypted images based on pixel prediction scheme, whichachieves a higher EC compared with previous methods. It isworth noting that compared with previous methods, we canmake better use of the correlation of adjacent pixels. The ex-perimental results show that our method not only has a signifi-cantly increase in net payload, but also has reversibility. Its alsoworth mentioning that our method achieves higher embedding7 .
977 0 .
838 0 .
983 0 .
981 0 . .
712 0 .
456 2 .
097 1 .
577 2 . .
645 0 .
969 2 .
673 2 .
479 2 . .
583 1 .
006 3 .
03 2 .
349 2 . .
87 1 .
321 3 .
232 2 .
49 2 . E R ( bpp ) Puteaux et al.,2018 [20] Ren et al.,2019 [24] Wu et al.,2019 [23] Yin et al.,2019 [22] Proposed
Figure 13: Comparison of ER ( bpp ) on five test images. .
966 0 .
968 0 . .
561 2 .
519 2 . .
361 3 .
246 2 . .
498 3 .
393 2 . A v e r a g e E R ( bpp ) Puteaux et al.,2018 [20] Wu et al.,2019 [23] Yin et al., 2019 [22] Proposed
Figure 14: Average ER ( bpp ) comparison in di ff erent datasets BOSSBase [26], BOWS-2 [27], and UCID [28]. rate than using pixel prediction scheme directly on grayscaleimage. Main reasons for better performance are: First, the dis- tribution of prediction errors is more concentrated than that oforiginal pixel values, and more embeddable positions of the bit8lane can be used to embed data. Next, we mark the auxil-iary data more e ff ectively. According to the characteristics ofthe mark, we can compress it e ff ectively by arithmetic coding,which makes more space available.In the future work, we will continue to work on improvingthe performance of our algorithm. For example, we can reducethe number of auxiliary data as much as possible, and use moreaccurate prediction schemes to improve embedding rate. In ad-dition, we hope that this paper will enable readers to understandthe possibility of applying binary image algorithm to grayscaleimages, and the idea of improving performance during applica-tion. In the future, it is very practical to explore more generalalgorithms based on binary images and grayscale images. Acknowledgments
This research work is partly supported by National Nat-ural Science Foundation of China (61872003, U1636206 and61860206004).
References [1] J. M. Barton, Method and apparatus for embedding authentication infor-mation within digital data, uS Patent 5,646,997 (1997).[2] M. U. Celik, G. Sharma, A. M. Tekalp, E. Saber, Lossless generalized-lsbdata embedding, IEEE transactions on image processing 14 (2) (2005)253–266.[3] M. U. Celik, G. Sharma, A. M. Tekalp, Lossless watermarking for imageauthentication: a new framework and an implementation, IEEE Transac-tions on Image Processing 15 (4) (2006) 1042–1049.[4] W. Zhang, X. Hu, X. Li, N. Yu, Recursive histogram modification: es-tablishing equivalency between reversible data hiding and lossless datacompression, IEEE transactions on image processing 22 (7) (2013) 2775–2785.[5] Z. Ni, Y.-Q. Shi, N. Ansari, W. Su, Reversible data hiding, IEEE Transac-tions on circuits and systems for video technology 16 (3) (2006) 354–362.[6] X. Li, B. Li, B. Yang, T. Zeng, General framework to histogram-shifting-based reversible data hiding, IEEE Transactions on image processing22 (6) (2013) 2181–2191.[7] Y. Jia, Z. Yin, X. Zhang, Y. Luo, Reversible data hiding based on reduc-ing invalid shifting of pixels in histogram shifting, Signal Processing 163(2019) 238–246.[8] J. Tian, Reversible data embedding using a di ff erence expansion, IEEEtransactions on circuits and systems for video technology 13 (8) (2003)890–896.[9] A. M. Alattar, Reversible watermark using the di ff erence expansion ofa generalized integer transform, IEEE transactions on image processing13 (8) (2004) 1147–1156.[10] H. J. Kim, V. Sachnev, Y. Q. Shi, J. Nam, H.-G. Choo, A novel di ff erenceexpansion transform for reversible data embedding, IEEE Transactionson Information Forensics and Security 3 (3) (2008) 456–465.[11] Y.-Q. Shi, X. Li, X. Zhang, H.-T. Wu, B. Ma, Reversible data hiding:advances in the past two decades, IEEE access 4 (2016) 3210–3237.[12] W. Puech, M. Chaumont, O. Strauss, A reversible data hiding methodfor encrypted images, in: Security, Forensics, Steganography, and Water-marking of Multimedia Contents X, Vol. 6819, International Society forOptics and Photonics, 2008, p. 68191E.[13] W. Zhang, K. Ma, N. Yu, Reversibility improved data hiding in encryptedimages, Signal Processing 94 (2014) 118–127.[14] X. Zhang, Reversible data hiding in encrypted image, IEEE signal pro-cessing letters 18 (4) (2011) 255–258.[15] X. Zhang, Separable reversible data hiding in encrypted image, IEEEtransactions on information forensics and security 7 (2) (2011) 826–832.[16] W. Hong, T.-S. Chen, H.-Y. Wu, An improved reversible data hiding inencrypted images using side match, IEEE Signal Processing Letters 19 (4)(2012) 199–202. [17] X. Wu, W. Sun, High-capacity reversible data hiding in encrypted imagesby prediction error, Signal processing 104 (2014) 387–400.[18] K. Ma, W. Zhang, X. Zhao, N. Yu, F. Li, Reversible data hiding in en-crypted images by reserving room before encryption, IEEE Transactionson information forensics and security 8 (3) (2013) 553–562.[19] S. Yi, Y. Zhou, Binary-block embedding for reversible data hiding in en-crypted images, Signal Processing 133 (2017) 40–51.[20] P. Puteaux, W. Puech, An e ffi cient msb prediction-based method for high-capacity reversible data hiding in encrypted images, IEEE Transactionson Information Forensics and Security 13 (7) (2018) 1670–1681.[21] Y. Puyang, Z. Yin, Z. Qian, Reversible data hiding in encrypted imageswith two-msb prediction, in: 2018 IEEE International Workshop on In-formation Forensics and Security (WIFS), IEEE, 2018, pp. 1–7.[22] Z. Yin, Y. Xiang, X. Zhang, Reversible data hiding in encrypted imagesbased on multi-msb prediction and hu ff man coding, IEEE Transactionson Multimedia 22 (4) (2019) 874–884.[23] Y. Wu, Y. Xiang, Y. Guo, J. Tang, Z. Yin, An improved reversible datahiding in encrypted images using parametric binary tree labeling, IEEETransactions on Multimedia (2019) 1–10.[24] H. Ren, W. Lu, B. Chen, Reversible data hiding in encrypted binary im-ages by pixel prediction, Signal Processing 165 (2019) 268–277.[25] M. J. Weinberger, G. Seroussi, G. Sapiro, The loco-i lossless image com-pression algorithm: Principles and standardization into jpeg-ls, IEEETransactions on Image processing 9 (8) (2000) 1309–1324.[26] P. Bas, T. Filler, T. Pevn`y, break our steganographic system: the insand outs of organizing boss, in: International workshop on informationhiding, Springer, 2011, pp. 59–70.[27] P. Bas, T. Furon, Image database of bows-2, Accessed: Jun 20.[28] G. Schaefer, M. Stich, Ucid: An uncompressed color image database, in:Storage and Retrieval Methods and Applications for Multimedia 2004,Vol. 5307, International Society for Optics and Photonics, 2003, pp. 472–480.man coding, IEEE Transactionson Multimedia 22 (4) (2019) 874–884.[23] Y. Wu, Y. Xiang, Y. Guo, J. Tang, Z. Yin, An improved reversible datahiding in encrypted images using parametric binary tree labeling, IEEETransactions on Multimedia (2019) 1–10.[24] H. Ren, W. Lu, B. Chen, Reversible data hiding in encrypted binary im-ages by pixel prediction, Signal Processing 165 (2019) 268–277.[25] M. J. Weinberger, G. Seroussi, G. Sapiro, The loco-i lossless image com-pression algorithm: Principles and standardization into jpeg-ls, IEEETransactions on Image processing 9 (8) (2000) 1309–1324.[26] P. Bas, T. Filler, T. Pevn`y, break our steganographic system: the insand outs of organizing boss, in: International workshop on informationhiding, Springer, 2011, pp. 59–70.[27] P. Bas, T. Furon, Image database of bows-2, Accessed: Jun 20.[28] G. Schaefer, M. Stich, Ucid: An uncompressed color image database, in:Storage and Retrieval Methods and Applications for Multimedia 2004,Vol. 5307, International Society for Optics and Photonics, 2003, pp. 472–480.