reversible image watermarking algorithm based on...

Research ArticleReversible Image Watermarking Algorithm Based onQuadratic Difference Expansion

Zhengwei Zhang 12 Mingjian Zhang2 and Liuyang Wang1

1Faculty of Computer and Software Engineering Huaiyin Institute of Technology Huairsquoan Jiangsu 223003 China2Hunan Provincial Key Laboratory of Network Investigational Technology Hunan Police Academy ChangshaHunan 410138 China

Correspondence should be addressed to Zhengwei Zhang zzw49010650sinacom

Received 9 July 2019 Revised 9 September 2019 Accepted 26 November 2019 Published 9 January 2020

Academic Editor Simone Bianco

Copyright copy 2020 Zhengwei Zhang et al +is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

To improve the visual quality and embedding rate of existing reversible image watermarking algorithms a reversible imagewatermarking algorithm based on quadratic difference expansion is proposed First the pixel points with grayscale values 0 and255 in the original image are removed and then the half-scrambled watermark information is embedded into the original imageusing linear difference expansion Finally the remaining half of the watermark information is embedded into the previouslygenerated watermarked image by the quadratic difference expansion meanwhile the removed pixel points with grayscale values 0and 255 in the image are merged and the final watermarked image is generated accordingly +e experimental results show thatthe algorithm has both a high embedding rate and a high visual quality which can completely recover the original imageCompared with other difference expansion watermarking algorithms it has certain advantages without having to consider thesmoothness of the embedded image region

1 Introduction

Digital watermarking is an important branch of informationhiding technology Information hiding technology studieshow to hide secret information in public information It canbe divided into steganography and digital watermarkingtechnology +e digital watermarking is an important meansof copyright protection Its basic principle is a technology ofembedding identification information directly into digitalmultimedia by using redundant data and randomness whichare ubiquitous in digital multimedia works +e reversiblewatermarking is a special application of digital watermarking

Reversible image watermarking embeds the infor-mation into the carrier image on the premise of ensuringthe visual quality [1] +e purpose is to losslessly re-construct the host image after the watermark is extracted+erefore compared with the traditional watermarkingmethods the amount of embedding information is moredemanding hence it has more extensive research and

application value in the fields of judicial military med-ical and other fields which ask for high-image authen-ticity and integrity +e basic goal of the reversible imagewatermarking algorithms study is to achieve the maxi-mum embedding capacity of effective information withless distortion [2]

+e large-capacity reversible watermarking algorithmbased on the difference expansion of adjacent pixels pro-posed by Tian [3] has caught increasing attention +emethod is to calculate the mean and difference of the se-lected pairs of adjacent pixels +e difference is expandedthrough a pixel pair to embed the watermark On the basisof Tianrsquos algorithm Alattar [4] proposed a generalizedinteger wavelet transform reversible watermarking algo-rithm +e adjacent pixels are selected as a transform unitfor watermark embedding +e capacity of embeddingwatermark information via Alattarrsquos method can be up to15 times that of the Tianrsquos and the embedding capacity islarger

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 1806024 8 pageshttpsdoiorg10115520201806024

For the difference expansion embedding method theoverflow location map is an important factor affectingthe embedding capacity Eliminating the location map isextremely important for improving the performance ofthe algorithm In the literature [5] a reversible water-marking algorithm combining difference expansion andreversible comparison graph was proposed to divide theimage into mutually disjoint 2times2 image blocks In eachimage block the first two pixels were reversible contrastimage pixel pairs and the other two pixels were differenceexpansion pixel pairs both of which were used to embedinformation +e reversible contrast image pixel pairswere mainly used to embed little additional informationto replace the location map and the embedding capacitywas greatly improved However half of the pixel pairsadopted a reversible contrast map transformation andthe image quality was seriously degraded In the litera-ture [6] a reversible embedding method based on dif-ference histogram translation was proposed To avoidpixel overflow the pixel value was adjusted to a certainrange before translation and the position of the ad-justment pixel was recorded in the location map +isembedding method was quite unique in terms of over-flow handle but it still needed to embed a compressedlocation map

+e literature [7] proposed a reversible image water-marking algorithm which combined the difference expan-sion and LSB It achieved a large embedding capacity andgood visual quality Lin et al [8] proposed a reversiblewatermarking algorithm that combined histogram transla-tion and prediction difference to expand the embeddingcapacity and achieved good results

In this paper a reversible image watermarking algo-rithm based on quadratic difference expansion is proposedwhich uses the difference expansion algorithm to embedthe watermark twice without considering the overflowlocation map that may occupy effective space and thesmoothness of the embedded image region accordinglythe embedding capacity is increased and the visual qualityis improved Experimental results indicate that the algo-rithm not only has a high embedding rate but also has ahigh visual quality and completely restores the originalimage

2 Quadratic Difference Expansion Algorithm

+e difference expansion algorithm based on adjacent pixelpairs proposed by Tian [3] performs integer transform onany pixel pair P (x y) in the image to obtain the mean l andthe difference h Accordingly the l and h are inverselytransformed and can losslessly recover the original imagepixel pair values x and y

Positive transform is as follows

l x + y

21113878 1113879

h x minus y

(1)

Inverse transform is as follows

xprime l +hprime + 12

1113892 1113893

yprime l minushprime2

1113892 1113893

(2)

+e obtained h is shifted to the left by 1 bit and thewatermark b is embedded in its least significant bit which isthe difference expansion and its mathematical expression ishprime 2h + b

Using the difference expansion to embed the water-mark information to obtain the pixel value may cause thepixel overflow so the xprime and yprime obtained by the inversetransform should be limited to the range [0 255] oth-erwise it will not be reversible +erefore it is necessary tolimit hprime

hprime1113868111386811138681113868

1113868111386811138681113868lemin(2(255 minus l) 2l + 1) (3)

+e difference expansion watermarking algorithm usesthe difference of pixel pairs to perform watermark em-bedding and its embedding capacity is limited

To improve the watermark embedding capacity and thevisual quality the pixel pair (xprime yprime) generated by the dif-ference transform is used again to perform the quadraticwatermark embedding using difference expansion +especific process is as follows

lprime xprime + yprime

21113892 1113893

hPrime xprime minus yprime

h

hPrime2

1113892 1113893 + b

(4)


xPrime lprime +h + 1

21113892 1113893

yPrime lprime minush

21113892 1113893

(5)

+e watermarked image generated by embedding thewatermark after linear difference expansion may overflowbut after the quadratic difference expansion it returns to theoriginal image

+e specific implementation process of the quadraticdifference expansion watermarking algorithm is as follows

Assuming that the initial pixel pair P (x y) the lineardifference expansion is embedded with a watermark bitvalue of b and the quadratic difference expansion is em-bedded with the watermark bit value of bprime then

2 Mathematical Problems in Engineering

xprime x + y

21113878 1113879 +

2x minus 2y + 1 + b

21113892 1113893

yprime x + y

21113878 1113879 minus

2x minus 2y + b

21113892 1113893

l xprime + yprime

21113892 1113893

(x + y)21113860 1113861 + (2x minus 2y + 1 + b)21113860 1113861 + (x + y)21113860 1113861 minus (2x minus 2y + b)21113860 1113861

21113892 1113893

h xprime minus yprime 2x minus 2y + 1 + b

21113892 1113893 +

2x minus 2y + b

21113892 1113893

hprime (2x minus 2y + 1 + b)21113860 1113861 + (2x minus 2y + b)21113860 1113861

21113892 1113893 + bprime

xPrime (x + y)21113860 1113861 + (2x minus 2y + 1 + b)21113860 1113861 + (x + y)21113860 1113861 minus (2x minus 2y + b)21113860 1113861

21113892 1113893

+( (2x minus 2y + 1 + b)21113860 1113861 + (2x minus 2y + b)21113860 1113861)21113860 1113861 + bprime + 1

21113892 1113893

yPrime (x + y)21113860 1113861 + (2x minus 2y + 1 + b)21113860 1113861 + (x + y)21113860 1113861 minus (2x minus 2y + b)21113860 1113861

21113892 1113893

minus( (2x minus 2y + 1 + b)21113860 1113861 + (2x minus 2y + b)21113860 1113861)21113860 1113861 + bprime

21113892 1113893

(6)

Depending on the watermark embedding value the newimage pixel pair value (xPrimeyPrime) and the original image pixelpair value (x y) are also different

When the embedded watermark information b 1bprime 1

If one of the pixel pair (x y) is odd and the other is even

xPrime x + y

21113878 1113879 +

x minus y

21113878 1113879 + 1 x minus 1 + 1 x

yPrime x + y

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

2minus12

minusx minus y + 1

2 y minus 1

(7)

If in the pixel pair (x y) both are odd or even

xPrime x + y + 1

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y

21113878 1113879 +

x minus y

21113878 1113879 + 1 x + 1

yPrime x + y + 1

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

21113878 1113879 minus

x minus y

21113878 1113879 y

(8)



xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2minus12

+x minus y + 1

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus12

minusx minus y

2+12

y

(9)


xPrime x + y + 1

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y + 1

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(10)



xPrime x + y minus 1

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y minus 1

2+

x minus y minus 12

+ 1 x

yPrime x + y minus 1

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y minus 1

2minus

x minus y + 12

y minus 1

(11)


xPrime x + y

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y

2+

x minus y

2+ 1 x + 1

yPrime x + y

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

2minus

x minus y

2 y

(12)




21113878 1113879 +

x minus y + 12

1113878 1113879 x + y minus 1

2+

x minus y + 12

x


21113878 1113879 minus

x minus y

21113878 1113879

x + y minus 12

minusx minus y minus 1

2 y

(13)

Mathematical Problems in Engineering 3


xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(14)

Regardless of the embedded watermark b and bprime thegenerated new image pixel pair value (xPrime yPrime) and theoriginal image pixel pair value (x y) are equivalent inmost cases but there are very few cases that xPrime is 1 greaterthan x or yPrime is 1 less than y so in this paper whenembedding the watermark using quadratic differenceexpansion in order to avoid overflow it is necessary tofirst remove the pixel points of the original image withpixel values of 0 and 255

3 Watermark Embedding

+e process of watermark embedding is shown in Figure 1and the specific operation process is as follows

(1) Make an Arnold transform on the watermark W toget Wprime +e Wprime is transformed into a one-dimen-sional binary sequenceTo enhance the robustness and security of digitalimage watermarking the traditional Arnold scram-bling transform is improved [9] +is improvedmethod is as follows

xprime

yprime1113888 1113889

1 1

1 21113888 1113889

c 2 1

1 11113888 1113889

dx

y1113888 1113889modM

xprime yprime isin 0 1 2 N minus 1

(15)

where (xprime yprime) is the transformed pixel coordinate(x y) is the original pixel coordinateM is the imagesize and c and d are the scrambling numbers +eArnold transform is one-to-one mapped and theparameters c and d are randomly generated

(2) Remove the pixel points with grayscale values 0 and255 in the original image to avoid overflow when thewatermark is embedded and send the removed pixelpoints with grayscale values 0 and 255 to the receiveras a zero watermark so as not to use whenextracting it

(3) From left to right and from top to bottom take twopixels in order (the number of the selected pixel pairand the half of the watermark to be embedded areequal) Carry out the difference expansion based onthe embedded watermark capacity (the first half ofthe watermark)

(4) For the watermarked image generated after lineardifference expansion the quadratic difference ex-pansion is performed (the quadratic half watermarkis embedded) and the pixel points with values 0 and255 in the original image removed before embeddingare add finally the watermarked image is generated

4 Watermark Extraction

+e watermark extraction first uses the inverse quadraticdifference expansion algorithm to extract the second half ofthe watermark information and restore the watermarkedimage with the embedding watermark using linear differenceexpansion +en the first half of the watermark is extractedby the inverse linear difference expansion algorithm and theoriginal image is restored

(1) Assuming that any pixel pair (xprime yprime) in the water-marked image generated by linear difference ex-pansion embeds the watermark information byquadratic difference expansion and the embeddedwatermark is bprime +e value of the newly generatedpixel pair (xPrimeyPrime) is

xPrime xprime + yprime

21113892 1113893 +

xprime minus yprime( 111385721113860 1113861 + bprime + 12

1113892 1113893

yPrime xprime + yprime

21113892 1113893 minus

xprime minus yprime( 111385721113860 1113861 + bprime2

1113892 1113893

(16)

Suppose xprime 205 yprime 200 and bprime 1 then xPrime 204 andyPrime 201Inverse transform is as follows

lprime xPrime + yPrime

21113892 1113893

2052

1113878 1113879 202

hprime xPrime minus yPrime 3

h 2 times xPrime minus yPrime( 11138571113860 1113861 2 times 3lfloor rfloor 6

xprime xPrime + yPrime

21113892 1113893 +

h + 12

1113892 1113893 202 + 3 205

yprime xPrime + yPrime

21113892 1113893 minus

h

21113892 1113893 202 minus 3 199

(17)

After the inverse transform the hprime value is 3 which isan odd number so the extracted watermark is 1Since the two values xPrime and yPrime are odd and even thevalues obtained are 205 and 199 by the foregoinginverse quadratic difference expansion algorithm+erefore we make the adjustment of the pixel pairgenerated by the quadratic inverse difference ex-pansion When two values xPrime and yPrime are odd andeven and the extracted watermark is 1 the restored xprimeremains invariant and yprime is plus 1 when two valuesxPrime and yPrime are odd and even and the extracted wa-termark is 0 the restored xprime and yprime remain un-changed when xPrime and yPrime values are both odd or evenand the extracted watermark is 1 the restored xprime isminus 1 and yprime remains unchanged when xPrime and yPrimevalues are both odd or even and the extracted wa-termark is 0 the recovered xprime and yprime remain


unchanged An inverse difference expansion isperformed using the newly generated pixel pair (xprimeyprime) to further extract the embedding watermarkinformation

(2) Furthermore extract the watermark informationand restore the original image using the linear in-verse difference expansion for the image recoveredby the quadratic inverse difference expansion

Assume that the watermark information is embedded bylinear difference expansion for any pixel pair (x y) in theoriginal image If the embedded watermark information is 1the newly generated pixel pair (xprime yprime) values are

xprime x + y2

1113878 11138792(x minus y) + 1 + 1

21113892 1113893

x + y2

1113878 1113879 + x minus y + 1

yprime x + y

21113878 1113879 minus

2(x minus y) + 12

1113892 1113893 x + y

21113878 1113879 minus x + y

(18)

+erefore xprime minus yprime 2x minus 2y+ 1+erefore when the embedded one-bit watermark in-

formation is 1 in any pixel pair the obtained new pixel pairdifference is an odd value Similarly if the embedded wa-termark information is 0 the obtained new pixel pair dif-ference is an even value By this method when we restore theoriginal carrier image if the difference of the pixel pair (a b)in the watermarked image is odd the embedded watermarkinformation is 1 otherwise it is 0 By this method thewatermark information embedded by linear difference ex-pansion can be extracted

Watermark extraction is the inverse process of water-mark embedding +e specific operation flow is as follows

(1) Remove the pixel points with grayscale values 0 and255 of the corresponding position in the water-marked image according to the received zerowatermark

(2) According to the pixel points order in the water-marked image from left to right and from top tobottom two pixel points are taken out (the numberof the selected pixel pair and half of the watermarkare equal) to perform quadratic inverse difference

expansion and extract the quadratic embeddingwatermark information

(3) After the quadratic inverse difference expansion thenewly generated pixel pair is adjusted

(4) Perform linear inverse difference expansion on theadjusted pixel pair to recover the original pixel pairsand extract the linear embedding watermarkinformation

(5) Perform inverse Arnold transform on the acquiredwatermark information and finally generate therequired watermark information

(6) +e pixel pairs restored are combined in order andthe removed pixel values 0 and 255 are added torestore the original image

5 Experimental Results and Analysis

+e standard images of size 512times 512 such as Lena and girlare used as original test images as shown in Figure 2 +ewatermark is a binary image of size 32times 32 as shown inFigure 3

+e reversible image watermarking algorithm generallyrequires that the carrier image can be completely recoveredafter the watermark is extracted +erefore the NC (nor-malized correlation) of the original carrier image and thecarrier image recovered after the watermark is extracted canbe used

Table 1 denotes the integrity of the results of the 4different types of watermarked images without any attackbased on this algorithm It shows that the original image canbe recovered completely without any attack +is indicatesthat the algorithm is reversible

+e watermarked images are compared with PSNR andSSIM using this algorithm and the algorithm in the literature[10] as shown in Table 2 (the data are taken as the average of20 tests) +e image shown in Figure 3 is used as embeddedwatermark information in this algorithm and the algorithmin the literature [10]

Compared with the algorithm in the literature [10] thehighest PSNR of the above 4 original carrier images in thisalgorithm can be as 7959 dB +is shows this algorithm hasbetter invisibility At the same time the SSIM is also higherthan the algorithm in the literature [10] From Table 2 it is

Original image

Remove 0 and 255

pixels

WatermarkArnold

scrambling

Selected pixel pairs

Primary difference expansion

Watermarkedimage

Quadratic difference expansion

Final watermarked

image

Figure 1 Flow chart of watermark embedding


easy to note that the proposed algorithm outperforms thealgorithm in the literature [10] in terms of the same payloadcapacity with good SSIM and PSNR values +e resultspresented here demonstrated that the proposed algorithmsignificantly increases the quality of watermarked imagesSpecific effects of visual and extraction are shown inTable 3

From Figures 1ndash3 it is found that our eyes cannot feelthe presence of watermark information in the water-marked images +e watermarked images have bettervisual effect and the corresponding PSNR values indicatethat they have better imperceptibility to different types ofimage algorithms and the average PSNR value is as highas 7817 dB

+e PSNR is utilized in estimating the deformationbetween the original cover image and resulted water-marked image when embedding 10 30 70 90 and 100from the allowed cover image capacity From Table 4 it iseasy to note that the proposed quadratic difference ex-pansion-based reversible watermarking technique out-performs the literature [10] and literature [11] techniquesin terms of payload capacity with good SSIM and PSNRvalues +e results presented here demonstrate that the

proposed quadratic difference expansion-based reversiblewatermarking technique significantly increases the payloadcapacity while still keeping the visual quality of water-marked images

When embedding more watermark information thewatermark embedding may be performed in a round ofquadratic difference expansion to embed more watermarkinformation so two or more rounds of watermark em-bedding may be performed to complete the embedding

In order to estimate the visual quality of the water-marked image this paper analyzes the performance of thealgorithm by performing multiple rounds of watermarkembedding on the original image (multiple rounds of wa-termark shown in Figure 3)

As can be seen fromTable 5 the watermarked images withhigh visual quality can be obtained by embedding watermarkas shown in Figure 3 once When embedding watermark asshown in Figure 3 twice and three times the visual quality isstill high Compared with embedding watermark informationonce the visual quality is not significantly reduced and thewatermark information can be repeatedly embedded On thepremise of guaranteeing certain visual quality more water-mark information can be embedded

In order to further estimate the visual quality of thewatermarked image this paper analyzes the performance ofthe proposed algorithm by performing multiple rounds ofwatermark embedding on the original image (embeddedwatermark with maximum watermark embedding amountper round)

In Table 5 only part of the original image is selectedaccording to the size of the watermark capacity to embed thewatermark information+e embedding capacity is not largeenough In order to further test the performance of thealgorithm the maximum capacity of the image that can beembedded at one time is used as the size of the watermarkembedding capacity As shown in Table 6 when embeddingonce twice and three times respectively it is found that thegenerated watermarked image can still achieve greater visualquality and good SSIM Moreover the PSNR and SSI de-crease little with the increase of embedding times At thesame time after three times of maximum capacity em-bedding the embedding rate approximates as high as 3 andthe visual quality reaches 5056 which shows that the overallperformance of the algorithm is high the invisibility is good

(a) (b) (c) (d)

Figure 2 Original images (a) Lena (b) Baboon (c) Barbara (d) Peppers

Figure 3 Watermark image

Table 1 Integrity assessment form without attack

Images (512times 512) Lena Baboon Barbara PeppersNC 1 1 1 1

Table 2 Comparison of PSNR (dB) and SSIM

Image nameProposedalgorithm

Literature [10]algorithm

PSNR SSIM PSNR SSIMLena 7959 0997 4572 0983Baboon 7687 0995 4737 0985Barbara 7846 0996 4494 0982Peppers 7776 0996 4581 0981


Table 3 Algorithmic experimental visual effect

Image name Original image Watermarked image Original watermark Extracted watermark PSNR

Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776

Table 4 Comparison between this algorithm the method in the literature [10] and the method in the literature [11] in terms of payloadcapacity SSIM and PSNR for original images

Image Method Payload in bytes SSIMPSNR ()

10 30 70 90 100

LenaLiterature [10] 9767 0918 4578 4348 4158 3978 3864Literature [11] 37992 09232 5958 5581 5328 5124 5072+is algorithm 262144 0993 7411 7197 6912 6724 6547

BaboonLiterature [10] 11056 0904 4586 4384 4195 4056 3976Literature [11] 14893 09085 5877 5524 5335 5228 5134+is algorithm 262066 0992 7203 7014 6856 6607 6421

BarbaraLiterature [10] 13232 0893 4566 4289 3954 3710 3665Literature [11] 31423 09011 5962 5708 5376 5187 5132+is algorithm 262144 0992 7339 7087 6816 6650 6498

PeppersLiterature [10] 8562 0936 4624 4477 4182 3954 3826Literature [11] 29372 09393 5889 5543 5185 5094 5007+is algorithm 262096 0992 7267 7012 6801 6591 6435


and the embedding capacity is large On the premise ofguaranteeing a certain visual quality the watermarkinginformation can be embedded repeatedly by using this al-gorithm and the embedding capacity is very large

6 Conclusion

In this paper a reversible image watermarking algorithm basedon quadratic difference expansion is proposed which caneffectively improve watermark embedding capacity and visualquality After extracting the embedding watermark the algo-rithm can losslessly recover the original carrier image +ewatermark is embedded by quadratic difference expansion inthis paper +e quadratic difference expansion algorithm isequivalent to the backup process of the traditional differenceexpansion algorithm +is algorithm is equivalent to performanother difference expansion based on the traditional differ-ence expansion algorithm +e algorithm is equivalent to therepeating difference expansion watermarking algorithm twicebut the second difference expansion is equivalent to a callbackprocess of the first difference expansion algorithm So thisalgorithm effectively improves the embedding capacity andvisual quality +e embedding capacity is doubled and thevisual quality is improved significantly+e proposed reversibleimage watermarking algorithm mainly contributes to im-proving the watermark embedding rate while maintainingbetter visual quality than other algorithms

Data Availability

In this paper all study images were derived from httpsipisucedudatabase+ese images can be used under the publicplatform

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+is work was supported by the National Key RampD Plan (no2018YFB1004904) and National Statistical Science ResearchProject (2018LY12) At the same time this work was alsosupported by the Huaian Natural Science Research Program(no HAB201704) the Open Project Program of the StateKey Lab of CADampCG under Grant A1923 Zhejiang Uni-versity and the Open Research Fund of Hunan ProvincialKey Laboratory of Network Investigational Technologyunder Grant 2018WLZC009

References

[1] Z Zhang L Wu and Y Yan ldquoAdaptive reversible imagewatermarking algorithm based on DErdquo KSII Transactions onInternet and Information Systems vol 11 no 3 pp 1761ndash1784 2017

[2] S Weng and J-S Pan ldquoAdaptive reversible data hiding basedon a local smoothness estimatorrdquo Multimedia Tools andApplications vol 74 no 23 pp 10657ndash10678 2015

[3] J Tian ldquoReversible data embedding using a difference ex-pansionrdquo IEEE Transactions on Circuits and Systems for VideoTechnology vol 13 no 8 pp 890ndash896 2003

[4] A M Alattar ldquoReversible watermark using the differenceexpansion of a generalized integer transformrdquo IEEE Trans-actions on Image Processing vol 13 no 8 pp 1147ndash11562004

[5] K Ma and N Xin-Xin ldquoAn improved reversible water-marking schemerdquo in Proceeding of the of InternationalConference on Signal Processing pp 2229ndash2232 BeijingChina October 2008

[6] Li Zhuo C Xiao-Ping X-Z Pan et al ldquoLossless data hidingscheme based on adjacent pixel differencerdquo in Proceedings ofthe of the 8th International Conference on Computer Engi-neering and Technology pp 588ndash592 IEEE Computer SocietySingapore January 2009

[7] H K Maity and S P Maity ldquoReversible image watermarkingusing modified difference expansionrdquo in Proceedings of the20123ird International Conference on Emerging Applicationsof Information Technology (EAIT) vol 17 no 3 pp 320ndash323IEEE Kolkata India November-December 2012

[8] S L Lin C-F Huang M H Liou et al ldquoImproving histogrambased reversible information hiding by an optimal weight-based prediction schemerdquo Journal of Information Hiding andMultimedia Signal Processing vol 1 no 1 pp 19ndash33 2013

[9] Z Zhang L Wu H Li H Lai and C Zheng ldquoDualwatermarking algorithm for medical imagerdquo Journal ofMedical Imaging and Health Informatics vol 7 no 3pp 607ndash622 2017

[10] H S El-sayed S F El-Zoghdy and O S FaragallahldquoAdaptive difference expansion-based reversible data hidingscheme for digital imagesrdquo Arabian Journal for Science andEngineering vol 41 no 3 pp 1091ndash1107 2016

[11] S Weng J-S Pan and L Zhou ldquoReversible data hiding basedon the local smoothness estimator and optional embeddingstrategy in four prediction modesrdquo Multimedia Tools andApplications vol 76 no 11 pp 13173ndash13195 2017

Table 5 Performance comparison of multiround watermarkingembedding algorithms

Image nameEvaluating indicator

One round Two rounds +ree roundsPSNR SSIM PSNR SSIM PSNR SSIM

Lena 7959 0997 7723 0996 7511 0994Baboon 7687 0995 7492 0994 7303 0993Barbara 7846 0996 7651 0995 7439 0994Peppers 7776 0996 7563 0995 7367 0994






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For the difference expansion embedding method theoverflow location map is an important factor affectingthe embedding capacity Eliminating the location map isextremely important for improving the performance ofthe algorithm In the literature [5] a reversible water-marking algorithm combining difference expansion andreversible comparison graph was proposed to divide theimage into mutually disjoint 2times2 image blocks In eachimage block the first two pixels were reversible contrastimage pixel pairs and the other two pixels were differenceexpansion pixel pairs both of which were used to embedinformation +e reversible contrast image pixel pairswere mainly used to embed little additional informationto replace the location map and the embedding capacitywas greatly improved However half of the pixel pairsadopted a reversible contrast map transformation andthe image quality was seriously degraded In the litera-ture [6] a reversible embedding method based on dif-ference histogram translation was proposed To avoidpixel overflow the pixel value was adjusted to a certainrange before translation and the position of the ad-justment pixel was recorded in the location map +isembedding method was quite unique in terms of over-flow handle but it still needed to embed a compressedlocation map

+e literature [7] proposed a reversible image water-marking algorithm which combined the difference expan-sion and LSB It achieved a large embedding capacity andgood visual quality Lin et al [8] proposed a reversiblewatermarking algorithm that combined histogram transla-tion and prediction difference to expand the embeddingcapacity and achieved good results

In this paper a reversible image watermarking algo-rithm based on quadratic difference expansion is proposedwhich uses the difference expansion algorithm to embedthe watermark twice without considering the overflowlocation map that may occupy effective space and thesmoothness of the embedded image region accordinglythe embedding capacity is increased and the visual qualityis improved Experimental results indicate that the algo-rithm not only has a high embedding rate but also has ahigh visual quality and completely restores the originalimage

2 Quadratic Difference Expansion Algorithm

+e difference expansion algorithm based on adjacent pixelpairs proposed by Tian [3] performs integer transform onany pixel pair P (x y) in the image to obtain the mean l andthe difference h Accordingly the l and h are inverselytransformed and can losslessly recover the original imagepixel pair values x and y

Positive transform is as follows

l x + y

21113878 1113879

h x minus y

(1)


xprime l +hprime + 12

1113892 1113893

yprime l minushprime2

1113892 1113893

(2)

+e obtained h is shifted to the left by 1 bit and thewatermark b is embedded in its least significant bit which isthe difference expansion and its mathematical expression ishprime 2h + b

Using the difference expansion to embed the water-mark information to obtain the pixel value may cause thepixel overflow so the xprime and yprime obtained by the inversetransform should be limited to the range [0 255] oth-erwise it will not be reversible +erefore it is necessary tolimit hprime

hprime1113868111386811138681113868

1113868111386811138681113868lemin(2(255 minus l) 2l + 1) (3)

+e difference expansion watermarking algorithm usesthe difference of pixel pairs to perform watermark em-bedding and its embedding capacity is limited

To improve the watermark embedding capacity and thevisual quality the pixel pair (xprime yprime) generated by the dif-ference transform is used again to perform the quadraticwatermark embedding using difference expansion +especific process is as follows

lprime xprime + yprime

21113892 1113893

hPrime xprime minus yprime

h

hPrime2

1113892 1113893 + b

(4)


xPrime lprime +h + 1

21113892 1113893

yPrime lprime minush

21113892 1113893

(5)

+e watermarked image generated by embedding thewatermark after linear difference expansion may overflowbut after the quadratic difference expansion it returns to theoriginal image

+e specific implementation process of the quadraticdifference expansion watermarking algorithm is as follows

Assuming that the initial pixel pair P (x y) the lineardifference expansion is embedded with a watermark bitvalue of b and the quadratic difference expansion is em-bedded with the watermark bit value of bprime then


xprime x + y

21113878 1113879 +

2x minus 2y + 1 + b

21113892 1113893

yprime x + y

21113878 1113879 minus

2x minus 2y + b

21113892 1113893

l xprime + yprime

21113892 1113893


21113892 1113893


21113892 1113893 +

2x minus 2y + b

21113892 1113893


21113892 1113893 + bprime


21113892 1113893


21113892 1113893


21113892 1113893


21113892 1113893

(6)




xPrime x + y

21113878 1113879 +

x minus y

21113878 1113879 + 1 x minus 1 + 1 x

yPrime x + y

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

2minus12

minusx minus y + 1

2 y minus 1

(7)


xPrime x + y + 1

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y

21113878 1113879 +

x minus y

21113878 1113879 + 1 x + 1

yPrime x + y + 1

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

21113878 1113879 minus

x minus y

21113878 1113879 y

(8)



xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2minus12

+x minus y + 1

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus12

minusx minus y

2+12

y

(9)


xPrime x + y + 1

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y + 1

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(10)




21113878 1113879 +

x minus y + 22

1113878 1113879 x + y minus 1

2+

x minus y minus 12

+ 1 x


21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y minus 1

2minus

x minus y + 12

y minus 1

(11)


xPrime x + y

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y

2+

x minus y

2+ 1 x + 1

yPrime x + y

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

2minus

x minus y

2 y

(12)




21113878 1113879 +

x minus y + 12

1113878 1113879 x + y minus 1

2+

x minus y + 12

x


21113878 1113879 minus

x minus y

21113878 1113879

x + y minus 12


2 y

(13)



xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(14)





xprime

yprime1113888 1113889

1 1

1 21113888 1113889

c 2 1

1 11113888 1113889

dx

y1113888 1113889modM


(15)









21113892 1113893 +


1113892 1113893


21113892 1113893 minus


1113892 1113893

(16)



21113892 1113893

2052

1113878 1113879 202




21113892 1113893 +

h + 12

1113892 1113893 202 + 3 205


21113892 1113893 minus

h

21113892 1113893 202 minus 3 199

(17)






xprime x + y2

1113878 11138792(x minus y) + 1 + 1

21113892 1113893

x + y2

1113878 1113879 + x minus y + 1

yprime x + y

21113878 1113879 minus

2(x minus y) + 12

1113892 1113893 x + y

21113878 1113879 minus x + y

(18)

















Original image

Remove 0 and 255

pixels

WatermarkArnold

scrambling



Watermarkedimage


Final watermarked

image












(a) (b) (c) (d)












Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776



10 30 70 90 100







6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018








xprime x + y

21113878 1113879 +

2x minus 2y + 1 + b

21113892 1113893

yprime x + y

21113878 1113879 minus

2x minus 2y + b

21113892 1113893

l xprime + yprime

21113892 1113893


21113892 1113893


21113892 1113893 +

2x minus 2y + b

21113892 1113893


21113892 1113893 + bprime


21113892 1113893


21113892 1113893


21113892 1113893


21113892 1113893

(6)




xPrime x + y

21113878 1113879 +

x minus y

21113878 1113879 + 1 x minus 1 + 1 x

yPrime x + y

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

2minus12

minusx minus y + 1

2 y minus 1

(7)


xPrime x + y + 1

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y

21113878 1113879 +

x minus y

21113878 1113879 + 1 x + 1

yPrime x + y + 1

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

21113878 1113879 minus

x minus y

21113878 1113879 y

(8)



xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2minus12

+x minus y + 1

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus12

minusx minus y

2+12

y

(9)


xPrime x + y + 1

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y + 1

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(10)




21113878 1113879 +

x minus y + 22

1113878 1113879 x + y minus 1

2+

x minus y minus 12

+ 1 x


21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y minus 1

2minus

x minus y + 12

y minus 1

(11)


xPrime x + y

21113878 1113879 +

x minus y + 22

1113878 1113879 x + y

2+

x minus y

2+ 1 x + 1

yPrime x + y

21113878 1113879 minus

x minus y + 12

1113878 1113879 x + y

2minus

x minus y

2 y

(12)




21113878 1113879 +

x minus y + 12

1113878 1113879 x + y minus 1

2+

x minus y + 12

x


21113878 1113879 minus

x minus y

21113878 1113879

x + y minus 12


2 y

(13)



xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(14)





xprime

yprime1113888 1113889

1 1

1 21113888 1113889

c 2 1

1 11113888 1113889

dx

y1113888 1113889modM


(15)









21113892 1113893 +


1113892 1113893


21113892 1113893 minus


1113892 1113893

(16)



21113892 1113893

2052

1113878 1113879 202




21113892 1113893 +

h + 12

1113892 1113893 202 + 3 205


21113892 1113893 minus

h

21113892 1113893 202 minus 3 199

(17)






xprime x + y2

1113878 11138792(x minus y) + 1 + 1

21113892 1113893

x + y2

1113878 1113879 + x minus y + 1

yprime x + y

21113878 1113879 minus

2(x minus y) + 12

1113892 1113893 x + y

21113878 1113879 minus x + y

(18)

















Original image

Remove 0 and 255

pixels

WatermarkArnold

scrambling



Watermarkedimage


Final watermarked

image












(a) (b) (c) (d)












Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776



10 30 70 90 100







6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018









xPrime x + y

21113878 1113879 +

x minus y + 12

1113878 1113879 x + y

2+

x minus y

2 x

yPrime x + y

21113878 1113879 minus

x minus y

21113878 1113879

x + y

2minus

x minus y

2 y

(14)





xprime

yprime1113888 1113889

1 1

1 21113888 1113889

c 2 1

1 11113888 1113889

dx

y1113888 1113889modM


(15)









21113892 1113893 +


1113892 1113893


21113892 1113893 minus


1113892 1113893

(16)



21113892 1113893

2052

1113878 1113879 202




21113892 1113893 +

h + 12

1113892 1113893 202 + 3 205


21113892 1113893 minus

h

21113892 1113893 202 minus 3 199

(17)






xprime x + y2

1113878 11138792(x minus y) + 1 + 1

21113892 1113893

x + y2

1113878 1113879 + x minus y + 1

yprime x + y

21113878 1113879 minus

2(x minus y) + 12

1113892 1113893 x + y

21113878 1113879 minus x + y

(18)

















Original image

Remove 0 and 255

pixels

WatermarkArnold

scrambling



Watermarkedimage


Final watermarked

image












(a) (b) (c) (d)












Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776



10 30 70 90 100







6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018











xprime x + y2

1113878 11138792(x minus y) + 1 + 1

21113892 1113893

x + y2

1113878 1113879 + x minus y + 1

yprime x + y

21113878 1113879 minus

2(x minus y) + 12

1113892 1113893 x + y

21113878 1113879 minus x + y

(18)

















Original image

Remove 0 and 255

pixels

WatermarkArnold

scrambling



Watermarkedimage


Final watermarked

image












(a) (b) (c) (d)












Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776



10 30 70 90 100







6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018

















(a) (b) (c) (d)












Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776



10 30 70 90 100







6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018










Lena 7959

Baboon 7687

Barbara 7846

Peppers 7776



10 30 70 90 100







6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018









6 Conclusion


Data Availability




Acknowledgments


References




























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








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