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j.image.2017.10.003

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Accepted Manuscript
Visible watermark removal scheme based on reversible data hiding and
image inpainting
Chuan Qin, Zhihong He, Heng Yao, Fang Cao, Liping Gao
PII:
DOI:
Reference:
S0923-5965(17)30186-8
https://doi.org/10.1016/j.image.2017.10.003
IMAGE 15289
To appear in:
Signal Processing: Image Communication
Received date : 7 March 2017
Revised date : 26 June 2017
Accepted date : 9 October 2017
Please cite this article as: C. Qin, Z. He, H. Yao, F. Cao, L. Gao, Visible watermark removal
scheme based on reversible data hiding and image inpainting, Signal Processing: Image
Communication (2017), https://doi.org/10.1016/j.image.2017.10.003
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Visible Watermark Removal Scheme Based on Reversible
Data Hiding and Image Inpainting
Chuan Qin1,2, Zhihong He1, Heng Yao1, Fang Cao3, and Liping Gao1,2
1
Shanghai Key Lab of Modern Optical System, and Engineering Research Center of Optical
Instrument and System, Ministry of Education,
University of Shanghai for Science and Technology, Shanghai 200093, China
E-mail: qin@usst.edu.cn, 2607527101@qq.com, hyao@usst.edu.cn
2
Shanghai Key Laboratory of Data Science,
Fudan University, Shanghai 200433, China
E-mail: lipinggao@fudan.edu.cn
3
College of Information Engineering,
Shanghai Maritime University, Shanghai 200135, China
E-mail: fangcao@shmtu.edu.cn
Correspondence Address:
Dr. Chuan Qin, Associate Professor,
School of Optical-Electrical and Computer Engineering,
University of Shanghai for Science and Technology,
No. 516 Jungong Road, Shanghai 200093, China.
E-mail: qin@usst.edu.cn
TEL: 86-21-55272562
FAX: 86-21-55272982
1
Visible Watermark Removal Scheme Based on Reversible
Data Hiding and Image Inpainting
Chuan Qin, Zhihong He, Heng Yao, Fang Cao, and Liping Gao
Abstract: In this paper, we propose two schemes for visible-watermark removal and reversible
image recovery. In the first scheme, we consider the scenario for the image generated by a specific
visible (not completely reversible) watermarking algorithm [29]. A run-length coding based
method is utilized to compress the difference between the preliminary recovered image and
original image. After embedding the difference information invisibly and reversibly, the final
embedded image can be exactly recovered to its original version after visible-watermark removal,
which avoids the problem of overflow and underflow in [29]. In the second scheme, the scenario of
visible-watermark removal for the image generated by any visible watermarking algorithms (no
matter the sender and the receiver know the algorithms or not) is considered. The scheme can
perfectly remove the embedded visible watermark and can also exactly recover original image with
the assist of image inpainting technique. In addition, for both two proposed schemes, the invalid
user without the knowledge of secret key cannot achieve reversible recovery for original image.
Experimental results demonstrate the effectiveness and superiority of our schemes.
Keywords: visible watermarking, watermark removal, reversible recovery, data compression,
inpainting.
1. Introduction
In recent years, many scholars have paid great attention to the research of multimedia information
security, especially for digital images in military and medical applications [1-6]. As an effective
technique that embeds information into images for copyright protection, image watermarking has
been widely studied. According to whether the stego image can be exactly recovered to its
original version or not, watermarking schemes can be categorized as reversible watermarking
[7-10] and irreversible watermarking [11, 12].
Currently, most of reversible watermarking schemes were studied to embed the watermark
information into cover image in a imperceptible way. That is to say, the embedded watermark for
image tagging or labeling is invisible. The existing, invisible and reversible watermarking
schemes are usually based on three mechanisms, i.e., lossless compression [13, 14], difference
expansion (DE) [15-19] and histogram shifting (HS) [20-25]. The DE based algorithm was first
proposed by Tian et al. in [15], which splitted the host image into a series of pixel pairs and the
2
difference of each pixel pair can be inserted with one-bit information. Ni et al. proposed a HS
based algorithm [20], which utilized the peak point and zero point in the histogram to embed the
watermark information. The invisible and reversible watermarking schemes aim to achieve larger
hiding capacity and better visual quality of stego image under the condition of reversibility.
Another kind of watermarking scheme that adds the watermark logo on the cover image
visibly, i.e., visible watermarking, is more intuitive and convenient to identify the ownership
information or indicate image labeling compared with invisible watermarking, because it can be
directly recognized by human eyes rather than a watermark decoder. However, former visible
watermarking schemes are often irreversible, which means the original image can not be reversed
due to the modifications caused by the inserted visible watermark. Therefore, the visible and
reversible watermarking scheme deserves in-depth investigation [26-34].
In [26], Hu et al. proposed a visible and reversible watermarking scheme, which modified
the remarkable bitplane in the original image and compressed the modified bitplane into the
non-watermarked region. But, the watermarked image in this scheme was somewhat blurred. Yip
et al. proposed lossless visible watermarking methods that rotated the successive pixels of
watermark image to insert a visible bit [27]. In the scheme [28], the pixels of the original image
were mapped into a certain range in order to visualize the watermark. For the sake of recovering
the original image correctly, a reconstructed packet was embedded into the watermarked image.
Both the two schemes [27] and [28] required the original watermark during the procedure of
image recovery. Based on the scaling factors of human visual system (HVS), Yang et al.
transparently revealed the watermark image by overlapping it on a user-specified area of the
original image through adaptively adjusting the pixel values beneath the watermark [30]. In order
to achieve the reversibility, an encoded packet of reconstruction/recovery data was reversibly
embedded into the non-visibly-watermarked area. In [31], a generic visible image watermarking
with the capability of lossless recovery was presented, which was based on the deterministic
one-to-one compound mappings of pixel values for overlaying a variety of visible watermarks
with different sizes on original images. Various types of visible watermarks, such as opaque
monochrome and translucent full color ones, can be embedded through this scheme. Tsai and
Chang proposed a secure reversible visible watermarking scheme based on a pixel mapping
function in [32]. The scheme added an integer sequence to the intermediate watermarked image
to prevent invalid users from obtaining original pixels in the watermarked area, and an almost
3
inverse function was used to produce recovery data that were hidden by reversible data
embedding. Although the schemes in [30-32] can achieve reversible image recovery for the
embedded visible-watermark, however, the recovery methods of these schemes can only be
suitable to their own corresponding embedding methods. In other words, if an image marked with
the unknown visible-watermark embedding methods is given, the schemes [30-32] may fail to
conduct watermark removal and reversible image recovery. In [33], Lin et al. proposed a
contrast-adaptive removable visible watermarking mechanism through adopting the subsampling
technique, which allowed the resource provider to adjust the strength of the embedded watermark
according to the contrast between original image and watermark logo and led to more satisfactory
transparency of visibly-watermarked image. But, the recovery of this scheme cannot realize the
complete reversibility, and the peak signal-to-noise ratio (PSNR) of recovered image with respect
to original image was less than 58 dB. A reversible visible watermarking scheme for encrypted
images was presented in [34]. The original image in this scheme was encrypted with a bitwise
exclusive-or operation, and a portion of encrypted data corresponding to the black pixels of the
binary watermark logo was modified to embed the visible watermark. The receiver, who had the
encryption and data-hiding keys, can conduct data-extraction, image-decryption, and content
recovery to retrieve the original image. However, the visual quality of visibly-watermarked image
after decryption was not satisfactory.
In this work, two schemes for visible-watermark removal and reversible image recovery are
proposed. In the first proposed scheme, we consider the scenario of the image generated by a
specific visible and irreversible watermarking algorithm of [29]. A preliminary embedded image
is first generated after initially embedding visible watermark into the original image, and a
preliminary recovered image can be acquired after removing the visible watermark from the
preliminary embedded image. Then, the residual between the preliminary recovered image and
the original image is compressed through a run-length coding based method and invisibly
inserted into the preliminary embedded image to produce the final embedded image. During the
watermark embedding, our method can effectively avoid the overflow and underflow problems in
[29], thus, original image can be exactly recovered. In the second proposed scheme, we consider
the scenario of visible-watermark removal for the image generated by any visible watermarking
algorithms (no matter the image sender and the receiver know the algorithms or not). The second
scheme can perfectly remove the embedded visible watermark and can also exactly recover the
4
original image with the assist of image inpainting technique. In addition, for both two proposed
schemes, the invalid user or the attacker without the knowledge of secret key can not achieve the
reversible recovery for the original image.
The remaining parts of the paper are organized as follows. Section 2 reviews the related
work [29]. Section 3 describes the first proposed scheme of visible and reversible watermarking
detailedly in the scenario knowing the algorithm of visible watermarking. Section 4 introduces
the second proposed scheme of visible watermark removal in the scenario without knowing the
algorithm of visible watermarking. Section 5 provides experimental results and comparisons to
evaluate the effectiveness and superiority of our schemes. Section 6 concludes the paper.
2. Related Work
In this section, a recently, reported scheme of visible image watermarking in [29] is detailedly
reviewed, including embedding and recovery procedures.
2.1 Embedding Procedure of [29]
The original image Io sized Ro  Co is first divided into non-overlapping k  k blocks, and 2  k 
min{Ro/Rw, Co/Cw}. The binary watermark image W to be embedded is sized Rw  Cw. The
parameter k can be 2, 3 or 4. Each block B of Io can be embedded with one binary watermark bit.
As shown in Table 1, each k  k block B can be partitioned into two sets (i.e., 1 and 2) and two
pixels (i.e., x and y). The set 1 contains (k21)/2 pixels and the set 2 contains (k21)/2  1
pixels. In the procedure of embedding, a parameter v is used to improve the visual effect. The
details of embedding procedure are described as follow.
First, calculate the mean value of the assigned visible-watermark region in original image Io:
kRw 1 kCw 1
avgw 
 I
m0
n0
o
(m  1 , n  2 )
(k  Rw )  (k  Cw )
(1)
,
where (1, 2) denotes the left-top pixel coordinate of the watermark image W embedded in Io,
and the size of the region for watermark embedding is (kRw)  (kCw).
Table 1 Division mode for each block B sized k  k in Io
k
k  k block B
1
2
x
y
5
B(1, 1)
B(1, 2)
B(2, 1)
B(2, 2)
2
3
B(1, 1)
B(1, 2)
B(1, 3)
B(2, 1)
B(2, 2)
B(2, 3)
B(3, 1)
B(3, 2)
B(3, 3)
B(1, 1)
B(1, 2)
B(1, 3)
B(1, 4)
B(2, 1)
B(2, 2)
B(2, 3)
B(2, 4)
B(3, 1)
B(3, 2)
B(3, 3)
B(3, 4)
B(4, 1)
B(4, 2)
B(4, 3)
B(4, 4)
4
B(1, 1)

B(2, 2)
B(1, 2)
B(1, 2)
B(2, 1)
B(2, 3)
B(3, 2)
B(1, 3)
B(2, 2)
B(3, 1)
B(1, 1)
B(3, 3)
B(1, 2)
B(1, 4)
B(2, 1)
B(2, 3)
B(3, 4)
B(4, 1)
B(4, 3)
B(1, 1)
B(1, 3)
B(2, 2)
B(2, 4)
B(4, 2)
B(4, 4)
B(3, 3)
B(3, 2)
Then, according to the mean value avgw, the threshold Tw is calculated:
 avg w  30, if avg w  128,
Tw  
 avg w  30, if avg w  128.
(2)
Also, the mean value of each k  k block B is calculated:
avg B 
1
k2
k
k
 B(i, j ) .
(3)
j 1 i 1
After that, the current watermark bit w from W can be embedded into one corresponding k  k
block B visibly through Eq. (4), which also keeps the average of block B tending to 128 as much
as possible:
B (i , j )  w  v , if avg B  Tw ,
B' ( i , j )  
 B (i , j )  w  v , if avg B  Tw .
(4)
According to the parameters 1, 2, x, and y, the difference values d1 and d2 are calculated for
each k  k block:
d1 
 B' (i, j )   B' (i, j )  x,
B' ( i , j )1
B' ( i , j ) 2
(5)
6
d2 
 B' (i, j )   B' (i, j )  y.
B' ( i , j )1
B' ( i , j ) 2
(6)
Then, the pixel x is modified to x’ by Eq. (7), which is used to better recover the original image
and extract w in the following steps.


B' ( i , j ) 


B' ( i , j ){ 1  2 }
.
x'  2  d 1  w  
  k 2  1 
 2 
 1
  2  
(7)
Similarly, the pixel y is modified to y’ according to the difference value d2 when the watermark
bit w is equal to 1:



B ( i , j ) 




 B' ( i , j ){1  2 } 
2  d 2  0    k 2  1   , if avg B  Tw ,

 2 
  1

  2  
y'  



( i , j ) 
B



 2  d 2  1   B' ( i , j ){1  2 }  , if avg B  Tw .
  k 2  1 

 2 
 1

  2  

(8)
After implementing the steps mentioned above for all bits in W, an image Iw embedded with
visible watermark W can be obtained.
2.2 Recovery Procedure of [29]
On the receiver side, the visible watermark on Iw can be removed and the original image Io can be
recovered.
The watermarked image Iw is divided into non-overlapped k  k blocks in the same manner
with the embedding procedure, and each block can also be partitioned into two sets (i.e., 1’ and
2’) and two pixels (i.e., x’ and y’). Based on 1’, 2’, x’, and y’, the difference values d1’ and d2’
can be calculated for each k  k watermarked block B’:


B ( i , j ) 


B  ( i , j ){ 1 '   2 '}
,
d 1'  x   

 k 2  1 
 2 
 1 
 2  

(9)
7


B ( i , j ) 


B  ( i , j ){ 1'  2' }
.
d 2'  y'  
  k 2  1 
 2 
 1 
  2  
(10)
The binary watermark bit w’ embedded in each block can be extracted and the original
difference values d1 and d2 can be re-calculated, respectively:
w'  mod( d 1' , 2 ),
(11)
d ' 
d i   i  , i  1, 2.
2
(12)
Then, the modified pixel x’ can be recovered to x’’ in block B’:
x'' 
 B ( i , j )   B ( i , j )  d .
B' ( i , j )1'
1
B' ( i , j ) 2'
(13)
Also, the modified pixel y’ can be recovered to y’’ when the bit w’ is equal to 1:
y'' 
 B ( i , j )   B ( i , j )  d
B' ( i , j )1'
B' ( i , j ) 2'
2
, if w'  1.
(14)
According to the parameter v, the pixels in each k  k block B’ of Iw can be recovered, see Eqs.
(15-16).
B (i , j )  w'  v , if   0,
B (i , j )  
 B (i , j )  w'  v , if   1,
(15)
  mod( d 2' , 2).
(16)
The recovered image Ir can be acquired after all blocks are conducted with above steps.
3. Proposed Visible and Reversible Watermarking Scheme
Although the scheme in [29] can efficiently achieve visible watermark embedding and removing,
however, it has one potential problem that the preliminary recovered image Ir is not exactly the
same as the original image Io in some scenarios due to overflow and underflow pixels. In other
words, the scheme in [29] is not totally reversible even though Ir is visually similar with Io.
Therefore, in this Section, we propose a new visible and reversible watermarking scheme and
8
solve the potential problem
p
in [29] effecttively. Figu
ure 1 gives the flowchhart of watermarking
embeddinng procedurre for the pro
oposed scheeme, and th
he details aree presented in the follo
owing.
Figgure 1 Flow
wchart of waatermarkingg embedding
g proceduree for the prooposed scheeme
3.1 Comp
pression forr Differencce Image
The origiinal image and waterm
mark imagee to be emb
bedded are also repreesented as Io and W,
respectiveely. Iw and Ir denote the
t preliminnary embed
dded imagee and the ppreliminary recovered
image gennerated by the
t methodss mentionedd in Section
n 2.1 and Section 2.2, reespectively.
In orrder to solvee the probleem of incom
mplete reverrsible recovery in [29], we first calculate the
differencee between thhe original image Io annd the prelim
minary recovered imagee Ir of [29]::
I d  Io  Ir .
(17)
The differrence imagee Id should be embeddded into Iw to
t guaranteee the reversiibility of ou
ur scheme.
However,, if we directly converrt each valuue of Id into
o binary bits, totally (log2+2)
 (kRw) 
(kCw) biits are generrated, wheree  is the m
maximum for the absolu
ute values oof differencee image Id,
k  k is thhe size of thhe divided non-overlappping block
ks for the im
mage, and R w  Cw is the
t size of
the binaryy watermarrk image W to be em
mbedded. Ob
bviously, it is infeasibble to directly embed
these bitss into Iw, beecause the embedding
e
ccapacity off preliminary
y embeddedd image Iw is limited.
Even if alll the (log2+2) (k
Rw)(kCw ) bits of Id are embedd
ded, the visuual quality of Iw may
be severely influenceed. Thereforre, in our sccheme, we propose
p
a method
m
to efffectively co
ompress Id
that has a lot of elem
ments equal to
t zero.
We ttransplant thhe idea of JPEG
J
codinng in our co
ompression method forr Id. In JPE
EG coding,
AC coeffficients are encoded in
n the form of (VLC, VLI)s.
V
The (VLC, VL
LI) is an inttermediate
symbol thhat is encodded by run length enccoding (RLE). In our scheme, wee analogizee the pixel
values of Id as the AC
C coefficien
nts in JPEG , and encod
de Id through
h the RLE m
method.
9
First, the pixels of the difference image Id are rearranged into a one-dimensional sequence in
the raster-scanning order. Then, each non-zero pixel in the rearranged, one-dimensional sequence
is transformed into an intermediate symbol (VLC, VLI), where VLC denotes the number of the
zero pixels in front of the current non-zero pixel and VLI indicates the value of non-zero pixel.
For example, (2, 3) indicates that there are two pixels of zeros in front of current pixel, and the
value of current pixel is three. It should be noted that there are two special symbols of (VLC,
VLI), i.e., (0, 0) and (15, 0), in the encoding process. (0, 0) denotes the end-of-block (EOB),
which means the remaining pixels are all zeros. (15, 0) means the zero-run-length (ZRL) and
denotes sixteen zeros. Thus, Id can be converted into a series of (VLC, VLI)s. Finally, these
intermediate symbols, i.e., (VLC, VLI)s, of all pixels in Id are encoded into a bit stream S by
Huffman coding. A part of Huffman coding table is listed in Table 2 and the details can be
referred in [35]. The advantage of Huffman coding is that the intermediate symbols with higher
occurrence frequency can be represented with the codewords with shorter lengths for the sake of
space reduction.
Table 2 A part of Huffman coding table
(VLC, VLI)
(0, 0)
(0, 1)
(0, 2)
…
(1, 1)
(1, 2)
(1, 3)
…
(2, 1)
(2, 2)
(2, 3)
…
Code length
4
2
2
…
4
5
7
…
5
8
10
…
Codeword
1010
00
01
…
1100
11011
1111001
…
11100
11111001
1111110111
…
For the better understanding of this compression for Id, an example is illustrated in Figure 2,
in which subfigure (a) is a 8  8 matrix representing the whole difference image Id, subfigure (b)
is the sorted pixel sequence in one dimension, subfigure (c) shows (VLC, VLI)s generated from
the pixel sequence, subfigure (d) is the encoded bits of corresponding (VLC, VLI)s by Huffman
coding, and subfigure (e) is the final compression result of all concatenated, encoded bits.
10
Figure 2 Illustration of the comppression pro
ocedure for the differennce image
3.2 Embeedding Procedure
On the seender side, the
t originall image Io i s first visib
bly embeddeed with the watermark
k image W
through thhe embeddiing method in [29] to pproduce thee preliminarry embeddeed image Iw. Then, by
the recovvery methodd in [29], th
he preliminnary recoverred image Ir can be obbtained from
m Iw. The
differencee image Id is calculatted and com
mpressed in
nto a binarry sequencee S with th
he method
proposed in Sectionn 3.1. Next, how to innvisibly emb
bed the com
mpressed seequence S into Iw to
e
image Iw’ is describeed. Note th
hat, the seqquence S should be
generate the final embedded
b
emb edding into
o I w.
scrambledd through a secret key before
Motiivated by thhe difference expansionn (DE) meth
hod [15], the pixels in I w are segm
mented into
a series oof pairs, andd each pixeel pair can bbe embeddeed with onee bit from SS. First, callculate the
differencee dc and the mean avgc of each pixxel pair:
d c    ,
(18)
   
avgg c  
,
 2 
(19)
where (, ) denotess one of thee pixel pairss from Iw. Then,
T
the current bit s from S is embedded
into the ddifference dc of (, ) an
nd the pixell pair (, ) is modified
d to (’, ’)) correspond
dingly:
11
d c'  2  d c  s ,
 d c'  1 
,
 2 
'  aavg c  
d ' 
'  avg c   c  .
 2 
(20)
(21)
(22)
After all bbits of S arre embedded
d, the final embedded image Iw’ is
i acquired,, which con
ntains both
the visiblle informatiion W and the invisib le informattion S. It sh
hould be nooted that, alll possible
underflow
w and overfflow pixel pairs
p
(, ) in Iw with Eqs. (18-22) are discaarded durin
ng the data
embeddinng, and theiir position informationn (i.e., pixeel coordinattes) are recoorded and embedded
into Iw toggether with S for the co
orrectness oof data extraaction and im
mage recovvery.
3.3 Recovvery Proced
dure
On the reeceiver sidee, the embed
dded, invisiible inform
mation S is first
f
extractted from thee received
Iw’, and Iw’ is recoveered to Iw. Through
T
thee recovery method
m
in [29],
[
Iw cann be then reccovered to
Ir with prreliminarilyy removing visible wattermark W. After decrypting withh the same secret key
on the seender side, S is decom
mpressed too Id, and the
t originall image Io can then be
b exactly
recoveredd by adding Id to Ir. Fig
gure 2 givess the flowch
hart of reco
overy proceddure for thee proposed
scheme, aand the detaails are desccribed in thee following.
Figurre 3 Flowch
hart of recovvery proced
dure for the proposed
p
sccheme
First,, Iw’ is alsoo segmented
d to a seriess of pixel paairs (’, ’)) by the sam
me way mentioned in
Section 3.2. Then, thhe differencee dc’ and thee mean avg
gc’ of each pixel
p
pair aree calculated
d:
d c'  '  ' ,
(23)
12
 '  ' 
avg c'  
,
 2 
(24)
where (’, ’) is the current pixel pair in Iw’. Next, each bit s of the embedded, invisible
information S can be extracted:
s  mod(d c' , 2) .
(25)
Finally, each modified pixel pair (’, ’) can be recovered to (, ):
d ' 
dc   c  ,
 2 
(26)
 d c  1
,
 2 
(27)
 dc 
.
2
(28)
  avg c'  
  avg c'  
Thus, the preliminary embedded image Iw and the invisible information S can be obtained.
According to the method [29] mentioned in Section 2.2, we can easily remove the visible
watermark W on Iw and then acquire the preliminary recovered image Ir from Iw by Eqs. (9-16).
Meanwhile, the extracted bit stream S should be decompressed into the difference image Id.
Detailedly, by searching the Huffman coding table of AC coefficients in Table 2, S can be first
decompressed to a series of intermediate symbols (VLC, VLI)s with entropy decoding. Definition
of (VLC, VLI)s can be found in Section 3.1. All intermediate symbols (VLC, VLI)s are then
decoded to a one-dimensional sequence of pixel values, which can be easily rearranged into the
difference image Id in the raster-scanning order. After obtaining the preliminary recovered image
Ir and the difference image Id, the original image Io can be exactly recovered by Eq. (29), i.e., Ir’
= Io .
I r'  I r  I d .
(29)
4. General Visible Watermark Removal Scheme
In this Section, we propose a general visible watermark removal scheme based on image
13
inpaintingg that can be appliccable to anny visible watermarkiing algorithhm no maatter it is
irreversibble or reverssible and kn
nown or unnknown to the
t user. Th
he legal recceiver can effectively
e
remove thhe visible watermark and exactlly recover the originaal image. T
The flowchaart of the
proposed general vissible waterm
mark removaal scheme iss given in Figure
F
4.
Figure 4 Flowchart of the proposeed general visible
v
watermark remooval schemee
4.1 Pre-p
processing with
w Imagee Inpaintingg
Suppose the sender owns the original
o
imaage Io and its visibly watermarkeed version Iw that is
embeddedd with a vissible waterm
mark W. T
The correspo
onding visib
ble watermaarking algo
orithm can
be unknoown to bothh the senderr and the reeceiver. In order
o
to rem
move the viisible waterrmark and
exactly reecover the original
o
imaage on the reeceiver sidee, the senderr first conduucts image inpainting
i
on Iw. In our work, image
i
inpaiinting basedd on the fast marching method (FM
MM) [36] is
i utilized.
Because the sender has the watermark
w
iimage W and
a
knows its embeddded positio
on on Iw,
therefore,, W can be preliminariily removedd from Iw with
w the assiist of imagee inpainting
g, which is
detailedlyy described as follows.
As shhown in Figgure 5(a),  denotes thhe region in Iw that is em
mbedded w
with visible watermark
w
W and is required foor removal, 
 denotess the boundaary of the reegion . Thhe point p denotes
d
the
current piixel that dissplays visib
ble watermaark and neeeds to be reecovered. A small neig
ghborhood
(p), in which all pixels
p
are kn
nown ( is tthe radius of
o the small region), is chosen to calculate
c
a
p) of the pix
xel p, see Eq
q. (30). Theen, the inpaiinted pixel
new valuee It(p) for reeplacing thee value Iw(p
p is removed from ,
 and both  and its booundary 
 are updateed.
14
It (p) 
 (p, q)[I
q ( p)
w
(q)  Iw (q), (p  q) ]
,
 (p, q)
(30)
q (p )
where ,  representts inner pro
oduct, Iw(q) is one of pixels
p
in thee neighborhoood (p) of
o pixel p,
and Iw(q) denotes the gradien
nt at the piixel q, see Figure 5(b)). Note (pp, q) is an integrated
weight fuunction that assigns the contributioon weights to
t all pixels in (p) duuring recoveering p:
 (p, q)  1 (p , q)   2 (p, q)   3 (p, q),
1 ( p , q ) 
(p  q ), N (p )
p q
 2 (p , q ) 
 3 (p , q ) 
 02
p q
2
(31)
,
(32)
,
0
1   (p )   (q )
(33)
,
(34)
where N((p) denotes the normal vector at thhe point p, 1(p, q) is the directioonal factor that
t
makes
the pixelss of (p) in the norrmal directtion contrib
bute more to
t the pixeel p, 2(p, q) is the
geometricc distance factor
f
that resist the eeffect of pixels far frrom p, 3(pp, q) is thee level-set
distance ffactor that guarantees
g
the
t influencce of the pix
xels near by
y p more thhan the oness far away
from p, () is the distance
d
maap to the booundary 
, and 0 an
nd 0 are thhe two paraameters of
geometricc distance and
a level-set distancee, respectiveely (Both of
o them cann be set to
o 1 in the
experimennts.).
(p)

q
p
N

I
 w(q)
p

(a)
N
(b)
Figure 5 An illustraation of FM
MM based iimage inpaiinting. (a) The regionn to be inpaainted, (b)
Inpaintingg through neighboring pixels.
15
After all pixels in  finish above processing of image inpainting, the embedded visible
watermark W can be preliminarily removed from Iw to produce a preliminary recovered image It.
Then, similar with the procedures in Sections 3.1 and 3.2, the difference image Id’ between the
original image Io and It is compressed into the bit stream S’ by the proposed method in Section
3.1, and S’ is then scrambled with secret key and invisibly embedded into Iw with the DE method
to generate the final embedded image Iw’’.
4.2 Visible Watermark Removal Procedure
On the receiver side, the compressed bit stream S’ is first extracted from the received image Iw’’,
and Iw can be obtained. Next, the receiver also conducts the FMM based image inpainting on Iw
to produce a preliminary recovered image It. Then, after decrypting with the same secret key on
the sender side, the extracted bit stream S’ is decompressed and rearranged into the difference
image Id’. By adding Id’ to It, the final recovered image It’ can be generated without any
embedded visible and invisible watermark, which is exactly the same as the original image Io, i.e.,
I t’ = I o .
5. Experimental Results and Comparisons
In order to evaluate the effectiveness and superiority of the proposed schemes, a number of
experiments were conducted on different original images and watermark images with various
sizes. In the experiments, PSNR was utilized to measure the visual quality of the modified images
with respect to the original image Io, see Eqs. (35-36).
PSNR  10  log10
MSE 
1
Ro  C o
Ro C o
[I
i 1 j 1
m
2552
,
MSE
(i , j )  I o (i , j )]2 ,
(35)
(36)
where MSE denotes the mean square error between the original image Io and its corresponding
modified version Im (Im can be the preliminary embedded image Iw, the preliminary recovered
image Ir or It, the final embedded image Iw’ or Iw’’, or the final recovered image Ir’ or It’), and
Io(i, j) and Im(i, j) are the pixel values of original image and its modified version at coordinate (i,
j), respectively.
16
5.1 Exam
mples of thee Proposed Scheme
Figure 6 show the original im
mage Bird ssized 512  512 and the waterm
mark images W with
lustrate the results for
different sizes of 32  32, 64  64, and 1228  128, reespectively. We first illu
the propoosed schemee of Section
n 4 in Figuures 7-9, wh
hich show the results under the watermark
w
images W with diffeerent sizes, i.e.,
i 32  322, 64  64, and
a 128  128,
1 respecttively. The subfigures
(a-d) of F
Figures 7-9 are the prelliminary em
mbedded im
mage Iw, the preliminaryy recovered
d image It,
the final embedded image Iw’’
’ , and the final recov
vered image It’. It caan be found
d that the
embeddedd visible waatermark caan be effectiively remov
ved. The paarameter k inn the experiment was
set as 2, thhus, the waatermark imaages were eexpanded do
oubly in wid
dth and heigght after em
mbedding.
(aa)
(b)
(cc)
(d)
Figure 6 Original im
mage and watermark
w
iimages. (a) Original im
mage Bird sized 512  512, (b)
mage W sizeed 64  64, (d) Waterm
mark image
Watermarrk image W sized 32  32, (c) Waatermark im
W sized 1128  128.
17
(a)
(b)
(c)
(d)
Figure 7 Results of the proposed scheme in Section 4 for watermark image W sized 32  32. (a)
Preliminary embedded image Iw, (b) Preliminary recovered image It, (c) Final embedded image
Iw’’, (d) Final recovered image It’.
(a)
(b)
18
(c)
(d)
Figure 8 Results of the proposed scheme in Section 4 for watermark image W sized 64  64. (a)
Preliminary embedded image Iw, (b) Preliminary recovered image It, (c) Final embedded image
Iw’’, (d) Final recovered image It’.
(a)
(b)
(c)
(d)
Figure 9 Results of the proposed scheme in Section 4 for watermark image W sized 128 128. (a)
Preliminary embedded image Iw, (b) Preliminary recovered image It, (c) Final embedded image
Iw’’, (d) Final recovered image It’.
19
5.2 Perfoormances off the Propo
osed Schem
me in Sectio
on 3
Tables 3-55 show the PSNR valu
ues of Iw, Ir, Iw’, and Ir’ (i.e., PSNR
Rw, PSNRr, PSNRw’, an
nd PSNRr’)
for the prroposed schheme in Secction 3 undder six stand
dard imagess (Crowd, M
Milk, Bridg
ge, Tiffany,
Airplane, and Man, see
s Figure 10)
1 sized 5112  512 an
nd watermarrk images W (see Figu
ure 6) with
w
different sizes of 400  40, 60  60, and 880  80. It is obvious that, largeer sizes of watermark
ues of Iw, Ir and Iw’ with respect to
t original iimage Io aree. We also
images W are, lowerr PSNR valu
evaluatedd the perform
mance of th
he compresssion method
d used in Seection 3.1. D
Denote maax and min
as the maaximum andd the minim
mum of the pixels in th
he difference image (Id or Id’), resspectively.
Denote Nd and Ns as the bit num
mbers of thee differencee image (Id or Id’) withhout compreession and
the corressponding coompressed stream
s
(S oor S’) with our
o method
d, respectiveely. Compreession rate
R for the difference image
i
(Id orr Id’) can bee calculated:
R
N d k  Rw  k  Cw  
,

Ns
Ns
(37)
  log2 (maax{ max ,  min })  2 ,
(38)
ge W, respeectively. Ob
bviously, R
where Rw and Cw dennotes the heeight and wiidth of wateermark imag
is no smaaller than 1. As mention
ned in Sectiion 5.1, the parameter k was set as 2. Tables 6-8
6 present
the resultts of compression for the differeence imagee Id under different
d
siz
izes of W. It can be
observed from Tablees 6-8 that, the RLE-baased comprression meth
hod proposeed in Sectio
on 3.1 has
satisfactory performaance for thee compressioon of difference image Id.
(a)
(b)
20
(c)
(d)
(e)
(f)
Figure 100 Six standaard test images. (a) Croowd, (b) Miilk, (c) Brid
dge, (d) Tiff
ffany, (e) Aiirplane, (f)
Man.
v
of Iw, Ir, Iw’, andd Ir’ under watermark
w
image W sizzed 40  40
0 (dB)
Tablee 3 PSNR values
Images
PSNRw of Iw
PSNRr of Ir
PSNR
Rw’ of Iw’
PSNRr’ off Ir’
Crowd
48.3
38
60.07
45
5.25
+
Milk
49.3
36
60.60
49
9.06
+
Bridge
48.3
32
57.26
43
3.25
+
Tiffany
51.6
68
61.11
50
0.40
+
A
Airplane
49.6
67
54.87
46
6.85
+
Man
48.8
86
58.85
47
7.33
+
21
Table 4 PSNR values of Iw, Ir, Iw’, and Ir’ under watermark image W sized 60  60 (dB)
Images
PSNRw of Iw
PSNRr of Ir
PSNRw’ of Iw’
PSNRr’ of Ir’
Crowd
44.71
56.98
42.24
+
Milk
45.08
59.07
44.69
+
Bridge
44.07
54.72
39.93
+
Tiffany
47.34
56.17
44.99
+
Airplane
46.14
52.30
43.15
+
Man
45.14
55.02
42.61
+
Table 5 PSNR values of Iw, Ir, Iw’, and Ir’ under watermark image W sized 80  80 (dB)
Images
PSNRw of Iw
PSNRr of Ir
PSNRw’ of Iw’
PSNRr’ of Ir’
Crowd
42.30
54.09
39.63
+
Milk
43.08
57.10
42.54
+
Bridge
41.97
53.41
37.89
+
Tiffany
44.06
54.17
41.61
+
Airplane
44.26
50.19
40.84
+
Man
42.92
54.14
40.07
+
Table 6 Compression Result for difference image Id under watermark image W sized 40  40
Images
max
min
Nd
Ns
R
Crowd
129
111
57600
7431
7.751
Milk
194
107
57600
6262
9.198
Bridge
139
164
57600
11126
5.177
Tiffany
155
143
57600
4082
14.111
Airplane
183
132
57600
10888
5.290
Man
178
149
57600
7369
7.817
Table 7 Compression Result for difference image Id under watermark image W sized 60  60
Images
max
min
Nd
Ns
R
Crowd
153
193
129600
16303
7.949
22
Milk
126
134
129600
13137
9.865
Bridge
139
164
129600
21941
5.907
Tiffany
171
246
129600
15721
8.244
Airplane
183
149
129600
22248
5.825
Man
173
192
129600
18090
7.164
Table 8 Compression Result for difference image Id under watermark image W sized 80  80
Images
max
min
Nd
Ns
R
Crowd
175
176
230400
29933
7.697
Milk
213
122
230400
22283
10.334
Bridge
139
227
230400
35786
6.438
Tiffany
171
246
230400
27368
8.419
Airplane
183
185
230400
36332
6.342
Man
168
183
230400
28730
8.019
5.3 Performances of the Proposed Scheme in Section 4
Tables 9-11 show the PSNR values of Iw, It, Iw’’, and It’ (i.e., PSNRw, PSNRt, PSNRw’’, and
PSNRt’) for the proposed scheme in Section 4 under six standard images (Crowd, Milk, Bridge,
Tiffany, Airplane, and Man in Figure 10) sized 512  512 and watermark images W (see Figure 6)
with different sizes of 40  40, 60  60, and 80  80. Similarly, we also evaluated the
compression performance of the method in Section 3.1 for the proposed scheme in Section 4.
Tables 12-14 list the values of compression rates R for the difference image Id’ under different
sizes of watermark image W by Eqs. (37-38).
Table 9 PSNR values of Iw, It, Iw’’, and It’ under watermark image W sized 40  40 (dB)
Images
PSNRw of Iw
PSNRt of It
PSNRw’’ of Iw’’
PSNRt’ of It’
Crowd
48.38
51.13
42.58
+
Milk
49.36
52.51
47.37
+
Bridge
48.32
49.93
39.98
+
Tiffany
51.68
51.61
44.63
+
23
Airplane
49.67
50.01
43.20
+
Man
48.86
51.01
42.50
+
Table 10 PSNR values of Iw, It, Iw’’, and It’ under watermark image W sized 60  60 (dB)
Images
PSNRw of Iw
PSNRt of It
PSNRw’’ of Iw’’
PSNRt’ of It’
Crowd
44.71
47.29
38.77
+
Milk
45.08
49.19
42.49
+
Bridge
44.07
45.85
36.08
+
Tiffany
47.34
47.20
39.66
+
Airplane
46.14
46.61
39.58
+
Man
45.14
47.24
38.41
+
Table 11 PSNR values of Iw, It, Iw’’, and It’ under watermark image W sized 80  80 (dB)
Images
PSNRw of Iw
PSNRt of It
PSNRw’’ of Iw’’
PSNRt’ of It’
Crowd
42.30
44.73
36.32
+
Milk
43.08
46.79
39.78
+
Bridge
41.97
43.55
32.93
+
Tiffany
44.06
44.02
36.81
+
Airplane
44.26
44.97
37.14
+
Man
42.92
44.76
36.58
+
Table 12 Compression Result for difference image Id’ under watermark image W sized 40  40
Images
max
min
Nd
Ns
R
Crowd
212
193
57600
25441
2.264
Milk
222
148
57600
23862
2.414
Bridge
235
215
57600
30638
1.880
Tiffany
188
231
57600
25790
2.233
Airplane
213
205
57600
30554
1.885
Man
225
216
57600
27294
2.110
24
Table 13 Compression Result for difference image Id’ under watermark image W sized 60  60
Images
max
min
Nd
Ns
R
Crowd
206
193
129600
60662
2.136
Milk
222
148
129600
52448
2.471
Bridge
235
223
129600
69900
1.854
Tiffany
189
255
129600
64149
2.020
Airplane
213
212
129600
67486
1.920
Man
225
216
129600
64055
2.023
Table 14 Compression Result for difference image Id’ under watermark image W sized 80  80
Images
max
min
Nd
Ns
R
Crowd
225
195
230400
108699
2.120
Milk
231
148
230400
92992
2.478
Bridge
247
223
230400
123073
1.872
Tiffany
192
255
230400
114309
2.016
Airplane
213
218
230400
114758
2.008
Man
225
216
230400
111544
2.066
It can be observed from Sections 5.2 and 5.3 that, both PSNRr’ and PSNRt’ for the final
recovered images Ir’ and It’ are positive infinity under different sizes of W, which means our two
proposed schemes can achieve reversible image recovery. PSNR values of the final embedded
images Iw’ and Iw’’ (PSNRw’ and PSNRw’’) are approximately equal to that of the preliminary
embedded image Iw (PSNRw), which means that the embedded invisible watermark (S or S’) of
difference image (Id or Id’) doesn’t significantly degrade the visual quality of the final embedded
image (Iw’ or Iw’’). In addition, obviously, the smaller the size of watermark image W has, the
better quality of the images Iw, Ir, It, Iw’, and Iw’’ achieves.
We also compared compression rates R of the difference images Id and Id’ for the two
proposed schemes in Section 3 and Section 4, see Table 15 (Schemes I and II correspond to the
two proposed schemes in Sections 3 and 4, respectively). We can find from Table 15 that, the first
proposed scheme in Section 3 (i.e, Scheme I) has higher compression rates than the second
proposed scheme in Section 4 (i.e., Scheme II), because the preliminary recovered image Ir of
25
Scheme I with known visible-watermark embedding algorithm has better visual quality than It of
Scheme II without knowing visible-watermark embedding algorithm. Thus, the difference image
Id between original image Io and preliminary recovered image Ir for Scheme I has more zeros and
smaller values than the difference image Id’ between original image Io and preliminary recovered
image It for Scheme II, and obviously, more zeros and smaller values can be compressed into less
bit number of Ns through the RLE-based compression method proposed in Section 3.1, which
makes the compression rate R of Id for Scheme I be greater than that of Id’ for Scheme II.
Table 15 Comparison of compression rates R of difference images for the two proposed schemes
in Sections 3 and 4
Size of watermark image W
Images
Scheme
40  40
60  60
80  80
Scheme I
7.751
7.949
7.697
Scheme II
2.264
2.136
2.120
Scheme I
9.198
9.865
10.334
Scheme II
2.414
2.471
2.478
Scheme I
5.177
5.907
6.438
Scheme II
1.880
1.854
1.872
Scheme I
14.111
8.244
8.419
Scheme II
2.233
2.020
2.016
Scheme I
5.290
5.825
6.342
Scheme II
1.885
1.920
2.008
Scheme I
7.817
7.164
8.019
Scheme II
2.110
2.023
2.066
Crowd
Milk
Bridge
Tiffany
Airplane
Man
5.4 Comparisons with the Scheme in [29]
Due to the problem of overflow and underflow during watermark embedding, the final recovered
image in [29] is not exactly same as the original image, which causes the incomplete recovery
and undesirable reversibility. Both the two schemes proposed in Sections 3 and 4 can effectively
solve this problem and achieve the reversible recovery. The scheme in Section 3 can be seen as an
improved version of [29], and the scheme in Section 4 can be seen as a general visible-watermark
26
removal scheme for any visible watermarking algorithms. Table 16 gives the comparison results
of final recovered image quality for the scheme [29] and the proposed schemes under different
sizes of watermark image. It can be found from Table 16 that, our schemes achieve better
performance of the final recovered image quality than the scheme [29].
Table 16 PSNR values of final recovered image quality for our schemes and [29] (dB)
Size of watermark image W
Images
Scheme
32  32
64  64
128  128
[29]
58.50
52.51
47.09
Proposed
+
+
+
[29]
57.48
51.79
46.92
Proposed
+
+
+
[29]
59.86
54.80
48.52
Proposed
+
+
+
[29]
61.76
54.87
46.69
Proposed
+
+
+
Sailboat
Airplane
Lake
Pentagon
6. Conclusions
Exact image recovery after visible-watermark removal is very useful and important especially for
medical and military images. In this work, we study two typical scenarios for visible-watermark
removal and reversible image recovery. In the scenario of the first proposed scheme, a specific,
visible and irreversible watermarking algorithm in [29] is considered. We utilize a run-length
coding based method to compress the difference between the original image and the preliminary
recovered image, and then, after invisibly and reversibly embedding the compressed difference
information, the visible watermark can be removed and the image can be reversibly recovered to
its original version, which successfully avoids the overflow and underflow problems. In the
scenario of the second proposed scheme, no specific visible-watermark algorithm is considered.
The scheme can also exactly recover the original image after removing the embedded visible
watermark with the assist of image inpainting technique, which is suitable to any irreversible or
reversible visible-watermarking algorithms. Experimental results show the proposed schemes can
27
achieve better performances of recovered images than the compared scheme.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (61672354), the
Open Project Program of the National Laboratory of Pattern Recognition (201600003), the Open
Project Program of Shenzhen Key Laboratory of Media Security, the Open Project Program of
Shanghai Key Laboratory of Data Science (201609060003), Shanghai Key Science and
Technology Project in Information Technology Field (14511107902), Natural Science
Foundation of Shanghai (17ZR1419100), Shanghai Leading Academic Discipline Project
(XTKX2012), Shanghai Engineering Center Project of Massive Internet of Things Technology
for Smart Home (GCZX14014), Hujiang Foundation of China (C14001, C14002), the PAPD
Fund, and the CICAEET Fund.
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31
Biograp
phy
Chuan Qin
Q receivedd the B.S. degree
d
in eleectronic enggineering an
nd the M.S.
degree in
n signal annd informattion processsing from Hefei Uniiversity of
Technolo
ogy, Anhui, China, in 2002
2
and 2005, respecctively, and the Ph.D.
degree in
n signal annd informattion processsing from Shanghai University,
U
Shanghaii, China, in 2008. Sincce 2008, he has been w
with the facu
ulty of the
School of
o Optical-E
Electrical and
a
Compu
uter Engineeering, University of
Shanghaii for Sciencce and Tech
hnology, wh
here he is cuurrently an Associate
Professorr. He was w
with Feng Chia
C
Univerrsity at Taiw
wan as a Po
ostdoctoral
Researcheer and Adjunct Assisttant Professsor from Ju
uly 2010 to
o July 201 2. Dr. Qin is also a
visiting rresearcher with
w
Shenzzhen Key L
Laboratory of Media Security, SShenzhen University,
U
Shenzhenn 518060, China. Hiss research interests in
nclude imaage processsing and multimedia
m
security. H
He has publlished moree than 90 pap
apers in thesse research areas.
a
Zhihong He receiveed B.S. deg
gree in Electronic infoormation en
ngineering
from Lu
udong Univversity, Yan
ntai, Shand
dong, Chinna, in 2015
5. She is
currently pursuing tthe M.S. deegree in sig
gnal and infformation processing
p
niversity off Shanghai for Sciencce and Techhnology, China.
C
Her
from Un
research interests incclude imagee watermark
king and revversible data hiding.
H
Unive
versity of Teechnology,
Heng Yao received the B.S. deegree from Hefei
China, in 2004, the M
M.S. degreee from Shan
nghai Norm
mal Universiity, China,
in 2008, and the Ph .D. degree from Shang
ghai Univerrsity, Chinaa, in 2012.
y, he is w
with Scho
ool of Optical-Electrrical and Computer
Currently
Engineeriing, Univerrsity of Shaanghai for Science
S
andd Technolog
gy, China.
His research intereests includ
de digital forensics, data hidin
ng. image
processin
ng, and patteern recognittion.
32
Fang Cao received thhe B.S. deg
gree in app
plied electroonics from Shanghai
Normal Un
niversity, Shhanghai, Ch
hina, in 2002, the M.S.. degree in signal and
information
n processingg from Shan
nghai Maritime Univerrsity, Shanghai, China,
in 2004, an
nd the Ph.D
D. degree in
i commun
nication andd informatio
on system
from Shang
ghai Univeersity, Shang
ghai, Chinaa, in 2013. Since 2005
5, she has
been with the
t faculty of the Colllege of Info
ormation Enngineering, Shanghai
Maritime University,
U
w
where she iss currently a Lecturer. H
Her research interests
include im
mage processsing, comp
puter vision and multim
media securiity.
Liping Gao
G
graduuated from Fudan University, Chhina with a PhD in
Computeer Science iin 2009. Sh
he received
d her BSc aand master degree in
Computeer Science ffrom Shand
dong Normaal University
ty, China in
n 2002 and
2005 resspectively. She is do
oing her reesearch woork in Univ
versity of
Shanghaii for Sciennce and Teechnology as an assiistant profeessor. Her
current research
r
innterests incllude CSCW
W, heterogeeneous colllaboration,
consisten
ncy maintennance and co
ollaborativee engineerinng.
33
Highlights
> Two schemes for visible-watermark removal and reversible image recovery are proposed.
> Incomplete recovery is avoided by embedding the RLE-compressed difference image.
> Our general scheme with inpainting is applicable to any visible-watermark methods.
> Invalid users without knowing secret key cannot achieve reversible image recovery.
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