=Paper=
{{Paper
|id=Vol-2665/paper36
|storemode=property
|title=Semi-fragile watermarking for HGI image compression
|pdfUrl=https://ceur-ws.org/Vol-2665/paper36.pdf
|volume=Vol-2665
|authors=Alina Bavrina,Victor Fedoseev
}}
==Semi-fragile watermarking for HGI image compression ==
https://ceur-ws.org/Vol-2665/paper36.pdf
Semi-fragile watermarking for HGI image
compression
Alina Bavrina Victor Fedoseev
Samara National Research University; Samara National Research University;
Image Processing Systems Institute of RAS - Branch of the FSRC Image Processing Systems Institute of RAS - Branch of the FSRC
"Crystallography and Photonics" RAS "Crystallography and Photonics" RAS
Samara, Russia Samara, Russia
bavrina@mail.ru vicanfed@gmail.com
Abstract—A novel semi-fragile watermarking system should be extracted with high accuracy from compressed
adopted for the HGI image compression algorithm is proposed. data.
The watermarking method exploits the hierarchical structure
of the image when embedding and replaces post-interpolation In this paper, we consider a hierarchical grid interpolation
residual quantization inside HGI compression with a special (HGI) compression method, which shows high performance
quantizer based on quantization index modulation. As a result, for still images and especially for remote sensing data [9,
the protected image became robust to HGI compression with a 10]. This method has two main advantages: the ability to
tunable quality parameter. Several experiments have shown control the compression error and the ability of hierarchical
the ability of the proposed watermarking system to protect access to data. These properties make the method attractive
images with high quality in terms of PSNR. We also investigate for applications in areas where the accuracy of image
the accuracy of local distortion detection. As a result, a trade- restoration after compression is important, for example, in
off between image quality and forgery detection accuracy has remote sensing or when processing medical images.
been found.
There are some examples of semi-fragile watermarking
Keywords—digital image processing, digital watermarks, systems adopted for different compression formats. More
image compression, hierarchical grid interpolation method than two dozens were developed for JPEG ([11, 12], many
algorithms are compared in the review paper [7]). We can
I. INTRODUCTION also mention papers [13, 14, 15]. Paper [15] contains an
Nowadays, the problem of image (and more specifically, overview of existing watermarking systems for the H.264
remote sensing image) protection against malicious video. However, we did not find any example of a
distortions plays an important role. watermarking system adopted for HGI. This fact could be
explained by a limited HGI usage by the academic
Satellite and drone images are increasingly used in community. However, both its importance in practice for
various fields of industry, agriculture, in the prevention of remote sensing data storage and its closeness to some other
natural disasters, in the military sphere, and in the media [1]. hierarchical compression methods based on wavelets or
Modern image processing tools, which include not only quadtrees (such as [17-21]) make it actual the study of HGI
raster editors but also artificial intelligence tools such as watermarking.
generative adversarial neural networks, allow users to create
fake images or their fragments that are practically The paper proposes a semi-fragile watermarking system
indistinguishable from real ones [2, 3]. Distribution of such based on the QIM (Quantization Index Modulation)
fake images can have serious economic and political technique [22, 23], consistent with the HGI compression
consequences [4, 5]. algorithm. The idea is to use the hierarchical structure of the
image when embedding and to replace an HGI quantizer
One way to protect an image from tampering is to embed with a QIM-based quantizer.
a fragile or semi-fragile digital watermark [6, 7]. Fragile
watermarks are destroyed after any modifications of The parameters of the proposed system make it possible
protected data. Therefore, if there is a set of allowable to find the compromise between the watermarking
modifications (such as compression, or cropping, or color distortions and the robustness to certain attacks (the paper
correction, etc.), it is better to use semi-fragile watermarks. considers two attacks of image compression and local
They are resistant to the allowable transformations and are alteration).
destroyed by any others [8]. The difference between the The rest of the paper is organized as follows. Section 2
embedded watermarks and those extracted at the describes the HGI compression method, necessary for a
authentication stage could evidence illegal changes in the better understanding of the proposed watermarking system,
protected image. which is described in Section 3. The next section contains
Remote sensing images usually have high spatial and/or some numerical experiments to study the characteristics of
spectral resolution. Therefore they are usually stored and the proposed system. Finally, conclusion and future work
transmitted in a compressed form. Consequently, the follow in Section 5.
“allowable” transformations often include distortions arising
from compression. A watermarking system (we use this term II. THE HGI COMPRESSION METHOD
to determine a set of algorithms for watermark embedding The HGI compression method is based on the
and extraction [8]) designed for compressed image protection representation of an image I ( m , n ) as a union of hierarchical
must be resistant to distortions caused by a corresponding levels:
compression algorithm. That is, the embedded watermark
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0)
Image Processing and Earth Remote Sensing
L 1
1, B ( k ) 0
I (m , n ) I l ( m , n ) ,
l0 W ( m , n ) F ( B ) 0 , n o e m b e d d in g in to ( m , n )
where I L 1 ( m , n ) are the highest level samples taken in a
1, B ( k ) 1
distance of 2 L 1 at both coordinates. The following equation The mapping takes into account the hierarchical structure
specifies the lower levels: of the image used in HGI, and also uses a pseudo-random
secret key, known both at the embedding and extraction side.
I l { I l ( m , n )} \ { I l 1 ( m , n )} .
During compression, at first, samples of the current level A. Interpolation
are interpolated by higher-level samples. The following L 1
Iˆl ( m , n ) PQ IM (
W
stages of the compression procedure are quantization of the { I k ( m , n )}) ,
k l 1
interpolation errors, reconstruction of samples (for use at
lower levels), statistical coding of post-interpolation where PQ I M ( ...) is the interpolation function.
residuals, and their storage in an archive. Samples of the
B. Calculation of post-interpolation residuals
highest level are stored in the archive unchanged.
R ( m , n ) I l ( m , n ) Iˆl ( m , n ) .
Let us consider these stages in more detail. Let l be a
current level. C. Quantization-based watermarking
A. Interpolation R
Q IM
( m , n ) Q Q IM ( R , W , Q IM ) ,
Interpolation of samples at level l is based on samples of where Q Q I M is a quantizer based on QIM watermarking [22-
higher levels that have already passed the quantization and
reconstruction procedure: 23], and Q I M is half of the QIM quantization step. This
L 1
parameter determines the robustness of the watermark to
Iˆl ( m , n ) PH G I ( { I k ( m , n )}) ,
additive white noise and the amount of distortion introduced
k l 1
by embedding.
where PH G I (...) is an interpolation function. D. Calculation of reconstructed sample values
1
B. Calculation of post-interpolation residuals R ( m , n ) Q Q IM ( R , Q IM ) ,
Q IM Q IM
Calculation of the differences between true sample values ( m , n ) Iˆl ( m , n ) R
W
Il ( m , n ) .
and those obtained by the interpolation: q im
When extracting the watermark from a received and
R ( m , n ) I l ( m , n ) Iˆl ( m , n ) . possibly changed image I W ( m , n ) , the same steps are
C. Quantization of post-interpolation residuals: performed, but watermark values W ( m , n ) are restored at the
R ( m , n ) Q H G I ( R , H G I ) ,
quantization stage.
HGI
where Q H G I is a quantizer that guarantees the preservation of IV. EXPERIMENTAL INVESTIGATION OF THE PROPOSED
the recovery error H G I (either maximal or root mean WATERMARKING SYSTEM
square). When conducting the research, we held the following
scheme. Suppose I be the source image, W be the watermark.
D. Calculation of reconstructed sample values Embedding W into I with parameter Q I M is done according
Based on the quantized post-interpolation residuals, the to Section 3. Distortions introduced by watermark
calculation of differential values is done, followed by the embedding are estimated using the PSNR criterion, which
calculation of reconstructed sample values: indicates Peak Signal to Noise Ratio between the source
R
1
(m , n ) Q HGI ( R , H G I ) , image I and the watermarked image I W .
HGI HGI
I l ( m , n ) Iˆl ( m , n ) R
W
( m , n ) . I can be subjected to any attacks, so on the receiver
HGI
side, we have an image I W that may differ from I W . The
E. Statistical encoding watermark W is extracted from I W and compared with
The quantized post-interpolation residuals undergo a initial watermark W. The paper considers two types of
statistical encoding procedure. attacks: compression and local editing.
III. SEMI-FRAGILE WATERMARKING FOR HGI COMPRESSION To carry out numerical experiments, ten images from the
Waterloo Grayscale Set 1 and 2 [24] were chosen. Fragments
The proposed watermarking system uses a hierarchical
of M N 2 5 7 size were extracted from each image. The
image representation and the HGI compression scheme with
a changed quantizer. matrix W was formed as follows: zero values for the samples
of level l L 1 and the equally probable values 1 and -1
Let I ( m , n ) [ 0 , 2 5 5 ] be the source image, or cover for other samples.
image, B ( k ) {0 ,1} be a binary sequence acting as a A. Specification of HGI and QIM parameters
watermark. The correspondence between source image The following parameter values were used.
samples and the watermark is set by a certain mapping. As a
result of this mapping, we obtain the following matrix: Bilinear interpolation functions as PH G I (...) and
PQ I M ( ...) .
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 158
Image Processing and Earth Remote Sensing
HGI quantizer to ensure maximum recovery error levels ( l m in 0 , l m a x 7 ) and the maximum for embedding
HGI :
m ax
only in the highest hierarchical level ( l m in l m a x 7 ).
R
) , HGI 2 HGI ,
m ax
Q HGI ( R , HGI ) HGI R ound ( TABLE I. PSNR VALUES IN THE CASE OF WATERMARK EMBEDDING
HGI IN HIERARCHICAL LEVELS FROM l m in TO l m a x FOR Q IM 2 0
(MINIMAL
1
Q HGI ( R , HGI ) R . AND MAXIMAL VALUES ARE GIVEN IN BOLD).
HGI HGI
As a QIM quantizer, the simplest QIM family lmax
quantization function is used [23]: lmin 0 1 2 3 4 5 6 7
0 27.65 27.05 26.91 26.87 26.87 26.87 26.86 26.85
1 30.95 30.59 30.50 30.47 30.48 30.48 30.47
R 2 32.65 32.47 32.44 32.42 32.43 32.43
2 Q IM R o u n d ( ) , W { 0 , 1}
2 3 33.33 33.26 33.25 33.22 33.23
Q IM
4 33.54 33.52 33.52 33.53
R 5
Q Q IM ( R , W , Q IM ) 2 Q IM R o u n d ( ) 6
33.61 33.60 33.59
2 Q IM 33.63 33.63
7 33.63
R
Q I M s ig n ( R R o u n d ( )), W 1
2 Q IM
One more parameter that affects the degree of the
1
Q Q IM ( R , Q IM ) R , distortion is the percentage of embedding into each
Q IM Q IM
hierarchical level θ. Fig. 2 represents the dependence of
Watermark extraction: PSNR on θ value for the fixed Q IM 2 0 . Again, the more
R samples are used for embedding, the lower PSNR value is.
W (m , n ) 2 m od( R ound ( ), 2 ) 1
Q IM
Q IM So, we can make the conclusion that the degree of cover
HGI parameters setting the embedding rate: l m in , l m a x image distortions, resulting from watermark embedding, can
be regulated by changing Q IM , l m in , l m a x , and θ.
and θ. Parameters l m in and l m a x are the minimal and
maximal hierarchical levels correspondingly, in Fig. 3 allows us to estimate visually the distortions
which the embedding is performed. Parameter θ sets introduced by watermark embedding. Fig. 4 shows
the percentage of current hierarchical level samples histograms of the original and the watermarked images. One
that undergo the watermark embedding. can see there are no elements in the watermarked image
histogram that are may indicate the watermark existence to a
B. Distortions introduced by watermarking
third party (like regular "teeth" or "dips").
This subsection is aimed to investigate image distortions
introduced by watermark embedding. Fig. 1 represents the
dependence of P S N R ( I , I W ) on the value Q IM (the values
were averaged for ten investigated images). The value L 7
of the maximum number of hierarchical levels was used. The
figure shows that the PSNR value decreases with increasing
Q IM .
Fig. 2. Dependence of PSNR on the embedding percentage θ
(for Q IM 2 0 ).
C. Watermark restoration after a compression attack
In this experiment, the watermarked image I W is
subjected to HGI compression with H G I , and I W is the
compressed image. Denote W the extracted watermark
Fig. 1. Dependence of PSNR(I,IW) on ɛQIM value. (using the parameter Q IM ). In this subsection, we are
The next part of the investigation is concerned with the interested in how the ratio of HGI and QIM parameters
question of how the embedding applied to a subset of affects the restoration of the watermark, as well as what
hierarchical levels effects on distortions of the source image. distortions the embedding and compression introduce into
Table 1 gives the PSNR values for different combinations of the cover image.
l m in and l m a x parameters values (averaged for investigated
For W and W comparison, the BER (Bit Error Rate)
images). The table shows that the more samples undergo the criterion was used. Fig. 5 shows the dependence of
watermarking, the lower PSNR value is. PSNR value has
B E R (W , W ) and maximal deviation m a x on H G I under the
achieved the minimum for embedding in all hierarchical
fixed value Q IM (averaged щмук ten investigated images).
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 159
Image Processing and Earth Remote Sensing
Investigations show that BER is zero for values When H G I Q I M , the watermark is extracted without
Q IM
HGI , as well as for H G I Q IM . When errors, since after the embedding, all interpolation residuals
2
are multiple Q IM , and their re-quantization in HGI on the
H G I Q IM
BER undergoes a sharp jump and is set at a
same value makes no changes.
value of about 0.5 (which indicates the destruction of the
watermark).
(a) (b) (c)
Fig. 3. Visual distortions introduced by watermark embedding: (a) source image "Lena"; (b) embeding with Q IM 1 0 ; (c) embeding with Q IM 2 0 .
(a) (b) (c)
Fig. 4. Histogram of container and watermarked image: (a) Cover image "Lena"; (b) embeding with Q IM 1 0 ; (c) embeding with Q IM 2 0 .
(a) (b)
Fig. 5. Investigation on watermark fragility: (a) Dependence of B E R (W , W ) on H G I when Q IM 8 (b) Dependence of maximal deviation m a x
on H G I at Q IM 8 .
The maximum deviation between initial cover image and and θ). The difference between W and W is not equal to D
the image reconstructed after embedding and compression (because watermark bits are correctly extracted from
equals approximately half of the distorted samples randomly) (see
Fig. 6).
Q IM , H G I is d iv id e r o f Q IM ,
m ax m a x I I
W
Semi-fragile watermarking is always a compromise
Q IM 0 , 5 H G I , o th e r w is e .
between the watermark robustness and imperceptibility. In
D. Reconstruction of local distortions area the case of watermark embedding in selective hierarchical
levels and with 1 0 0 % we have got a sparse structure of
In this subsection we analyze the accuracy of local
distortion area estimation. To model local distortions, for nonzero difference between W and W . The following
simplicity, we replaced samples within a predefined mask by algorithm is suggested for local distortions area
random samples, as shown in Fig. 6. Such processing makes reconstruction D .
it easy to estimate the mask of distortions without using a
In the first step, going down from the samples of the
watermark, but we have not used any information on the type
of distortions in the investigation. We will denote the highest hierarchical level to l m in , when W ( m , n ) W ( m , n )
resulting image as I W . and W ( m , n ) 0 we fill with "1" its neighborhood
D ( m ( 2 1), n ( 2 1)) 1 , where l is a current level. This
l l
On the receiving side W is extracted from I W and is
compared with W that is generated using the same secret key area can "suffer" from the distortion of sample (m,n) at the
sequential reconstruction of samples.
as on the embedding side (with the same values l m in , l m a x ,
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 160
Image Processing and Earth Remote Sensing
(a) (b) (c) (d)
Fig. 6. Local distortions of a watermarked image: (a) watermarked image ( Q IM 2 0 , l m in 0 , l m a x 7 , 1 0 0 % ); (b) local distortions area D;
(c) distorted watermarked image; (d) difference between initial and reconsructed watermarks.
In the second step, we process D with two sequential Fig. 8 shows curves for q, q01, q10 depending on θ for
local morphological filters (max-min) with window size l m in l m a x 1
and l m in 1 , l m a x 2 for a fixed value
1
w in 2 2 1 .
l
Q IM 2 0 . The comparison can be done as follows. Suppose
m in
To investigate the quality of the proposed algorithm, we we are interested in the value of the relative quantity of
use the following criteria: q01, the relative quantity of false omissions q 1 0 0 .0 5 , we can find the intersection with q10
positive detections of local distortion area, q10, the relative curve and get θ and q values (see green dashed line and
quantity of omissions, their sum q: values). So, we get that for l m in l m a x 1 the criterion value
{ D 0 , D 1} { D 1, D 0} q=0.2, and for l m in 1 , l m a x 2 the criterion value q=0.3.
q 01 q 1 0 Therefore, values l m in l m a x 1 and θ=70..100% can be
{ D 1} { D 1}
where ǀ ǀ is cardinality of a set. We define denominator as the recommended for the embedding in the case of local
size of local distortions area to make criteria values distortion attack.
comparable for big and small areas. Fig. 9-10 represent some results of the proposed
The next part of the current subsection is aimed to algorithm of local distortions area reconstruction for
investigate how criteria values change for different values of parameter values, highlighted in Fig. 8 (see green circle).
The comparison shows better results for Fig. 9 than for Fig.
l m in , l m a x , and θ. In this part, we use only the "Lena" image,
10.
and all presented numerical values have been averaged over
100 observations. V. CONCLUSIONS
Fig. 7 presents the dependence of P S N R ( I , I ) on θ for W In this paper, we have proposed a semi-fragile
watermarking system adopted for the HGI compression
different combinations of l m in , l m a x and fixed value algorithm. Its main idea is to utilize the HGI scheme in the
Q IM 2 0 . The figure shows that for l m in l m a x 0 , the watermarking procedure and to replace the quantization of
curve lies too low (cover image distortions are too evident). interpolation residuals with watermark embedding using a
Watermark embedding in the second hierarchical level QIM-based method. This approach makes it possible to
provides better PSNR, but q is too high. So, the cases obtain the robustness against HGI compression in a
predefined range of quality factors.
l m in l m a x 1 and l m in 1 , l m a x 2 should be analyzed.
The parameters of the proposed algorithm allow us to
find the compromise between distortions, contributed by the
embedding, and robustness to certain attacks.
The conducted experiments have shown the ability of the
proposed watermarking system to protect images with high
quality in terms of PSNR. We also investigated the accuracy
of local distortion detection. As a result, a trade-off between
image quality and forgery detection accuracy has been found.
Future work may include the investigation of some other
QIM family quantizers, including those providing fewer
distortions (like DC-QIM, distortion compensated QIM [22])
and more protected ones (like IM-QIM, statistically immune
QIM [23]).
Fig. 7. Dependence of PSNR on the θ for diffenent lmin and lmax ACKNOWLEDGMENT
(PSNR00 corresponds to l m in l m a x 0 , PSNR11 - l m in l m a x 1 ,
The work was funded by the RSF grant #18-71-00052 (in
PSNR22 - l m in l m a x 2 , PSNR12 - l m in 1 l m a x 2 ).
parts of watermarking system construction and
investigation), and by the RFBR grant #19-29-09045(in part
of application and parameters adaptation to protect remote
sensing data and local distortion estimation).
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 161
Image Processing and Earth Remote Sensing
(a) l m in l m a x 1 , green circle corresponds to q=0.2, q10=0.05, q01=0.15, (b) l m in 1 , l m a x 2 , green circle corresponds to q=0.3, q10=0.05,
θ=68%, PSNR=31.65 q01=0.25, θ=47%, PSNR=31.85
Fig. 8. Dependence of relative quantity of incorrect reconstruction of local distortions area q on embedding percentage θ.
(a) (b) (c) (d)
Fig. 9. Results of local distortions area reconstruction algorithm for l m in l m a x 1 , θ=68%: (a) difference between W and W ; (b) result after the
step 1 of proposed algorithm; (c) result of proposed algorithm (after the step 2); (d) incorrect reconstruction of local distortions area ( D D ).
(a) (b) (c) (d)
Fig. 10. Results of local distortions area reconstruction algorithm for l m in 1 , l m a x 2 , θ=47%: (a) difference between W and W ; (b) result after the
step 1 of proposed algorithm; (c) result of proposed algorithm (after the step 2); (d) incorrect reconstruction of local distortions area ( D D ).
REFERENCES [7] A.A. Egorova and V.A. Fedoseev, “A classification of semi-fragile
watermarking systems for JPEG images,” Computer Optics, vol. 43,
[1] E. Chuvieco, “Fundamentals of Satellite Remote Sensing: An no. 3, pp. 419-433, 2019. DOI: 10.18287/2412-6179-2019-43-3-419-
Environmental Approach,” Boca Raton: CRC Press, 2016. 433.
[2] X. Xuan, B. Peng, W. Wang and J. Dong, “On the Generalization of [8] M. Barni and F. Bartolini, “Watermarking Systems Engineering,”
GAN Image Forensics,” Biometric Recognition, Cham, pp. 134-141, New-York, USA: Marcel Dekker, Inc., 2004.
2019. DOI: 10.1007/978-3-030-31456-9_15. [9] M.V. Gashnikov, N.I. Glumov and V.V. Sergeev, “A hierarchical
[3] M. Westerlund, “The emergence of deepfake technology: A review,” compression method for space images,” Automation and Remote
Technology Innovation Management Review, vol. 9, no. 11, pp. 39- Control, vol. 71, no. 3, pp. 501-513, 2010. DOI: 10.1134/
52, 2019. S0005117910030112.
[4] A. Piva, “An Overview on Image Forensics,” ISRN Signal [10] M.V. Gashnikov, N.I. Glumov, A.V. Kuznetsov, V.A. Mitekin, V.V.
Processing, vol. 2013, pp. 1-22, 2013. DOI: 10.1155/2013/496701. Myasnikov and V.V. Sergeev, “Hyperspectral remote sensing data
[5] A. Rocha, W. Scheirer, T. Boult and S. Goldenstein, “Vision of the compression and protection,” Computer Optics, vol. 40, no. 5, pp.
Unseen: Current Trends and Challenges in Digital Image and Video 689-712, 2016. DOI: 10.18287/2412-6179-2016-40-5-689-712.
Forensics,” ACM Comput. Surv., vol. 43, no. 4, pp. 26:1-26:42, 2011. [11] C.Y. Lin and S.F. Chang, “Semifragile watermarking for
DOI: 10.1145/1978802.1978805. authenticating JPEG visual content,” Electronic Imaging, pp. 140-
[6] I.J. Cox, M.L. Miller, J.A. Bloom, J. Fridrich and T. Kalker, “Digital 151, 2000.
Watermarking and Steganography,” USA: Elsevier, 2008, 587 p.
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 162
Image Processing and Earth Remote Sensing
[12] H. Wang, A. Ho and X. Zhao, “Novel fast self-restoration semi- Transmission of Multiview Images,” IEEE International Conference
fragile watermarking algorithm for image content authentication on Image Processing, vol. 5, p. V-105-V-108, 2007. DOI: 10.1109/
resistant to JPEG compression,” Journal of Electronic Imaging, vol. ICIP.2007.4379776.
17, no 3, pp. 72-85, 2011. [19] M. Rabbani and R. Joshi, “An overview of the JPEG 2000 still image
[13] K. Maeno, Q. Sun, S.-F. Chang and M. Suto, “New semi-fragile compression standard,” Signal Processing: Image Communication,
image authentication watermarking techniques using random bias and vol. 17, no. 1, pp. 3-48, 2002. DOI: 10.1016/S0923-5965(01)00024-8.
nonuniform quantization,” IEEE Transactions on Multimedia, vol. 8, [20] A. Munteanu, J. Cornelis, G. Van Der Auwera and P. Cristea,
no. 1, pp. 32-45, 2006. DOI: 10.1109/TMM.2005.861293. “Wavelet image compression - the quadtree coding approach,” IEEE
[14] Q. Sun, S.-F. Chang, M. Kurato and M. Suto, “A quantitative semi- Transactions on Information Technology in Biomedicine, vol. 3, no.
fragile JPEG2000 image authentication system,” Proceedings. 3, pp. 176-185, 1999. DOI: 10.1109/4233.788579.
International Conference on Image Processing, vol. 2, p. II-II, 2002. [21] J. Andrew, “A simple and efficient hierarchical image coder,”
DOI: 10.1109/ICIP.2002.1040102. Proceedings of International Conference on Image Processing, vol. 3,
[15] V. Fedoseev and T. Androsova, “Watermarking algorithms for JPEG pp. 658-661, 1997. DOI: 10.1109/ICIP.1997.632207.
2000 lossy compressed images,” CEUR Workshop Proceedings, vol. [22] B. Chen and G. Wornell, “Quantization index modulation: a class of
2391, pp. 366-370, 2019. provably good methods for digital watermarking and information
[16] Y. Tew and K. Wong, “An overview of information hiding in embedding,” IEEE Transaction on Information Theory, vol. 47, no. 4,
H.264/AVC compressed video,” IEEE Transactions on Circuits and pp. 1423-1443, 2001.
Systems for Video Technology, vol. 24, no. 2. pp. 305-319, 2014. [23] V.A. Mitekin and V.A. Fedoseev, “New secure qim-based
[17] R K. Senapati, U.C. Pati and K.K. Mahapatra, “Low bit rate image information hiding algorithms,” Computer Optics, vol. 42, no. 1, pp.
compression using hierarchical listless block-tree dtt algorithm,” Int. 118-127, 2018. DOI: 10.18287/2412-6179-2018-42-1-118-127.
J. Image Grap., vol. 13, no. 01, p. 1350005, 2013. DOI: [24] The Waterloo Image Repository [Online]. URL:
10.1142/S0219467813500058. http://links.uwaterloo.ca/Repository.html, (10.05.2020).
[18] Y. Morvan, D. Farin and P.H.N. de With, “Depth-Image Compression
Based on an R-D Optimized Quadtree Decomposition for the
VI International Conference on "Information Technology and Nanotechnology" (ITNT-2020) 163