A New Approach to Reducing the Distortion of the Digital Image Natural
Model in the DCT Domain When Embedding Information According to
the QIM Method
O.O. Evsutin1,2,3, A.S. Melman3, R.V. Meshcheryakov2, A.O. Ishakova2,3
evsutin.oo@gmail.com | annakokurina94@yandex.ru | mrv@ipu.ru | shumskaya.ao@gmail.com
1
National Research University Higher School of Economics, Moscow, Russia;
2
V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia;
3
Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia
One of the areas of digital image processing is the steganographic embedding of additional information into them. Digital
steganography methods are used to ensure the information confidentiality, as well as to track the distribution of digital content on the
Internet. Main indicators of the steganographic embedding effectiveness are invisibility to the human eye, characterized by the PSNR
metric, and embedding capacity. However, even with full visual stealth of embedding, its presence may produce a distortion of the digital
image natural model in the frequency domain. The article presents a new approach to reducing the distortion of the digital image natural
model in the field of discrete cosine transform (DCT) when embedding information using the classical QIM method. The results of the
experiments show that the proposed approach allows reducing the distortion of the histograms of the distribution of DCT coefficients,
and thereby eliminating the unmasking signs of embedding.
Keywords: information security, steganography, digital images, discrete cosine transform.
1. Introduction 2. The embedding operation
One of the promising areas for solving the problem of Embedding operation, i.e. operation of direct changes in the
ensuring information security of multimedia data is the use of values of frequency coefficients, is based on the QIM method.
digital steganography and digital watermarking (DWM) The idea of the QIM method [7] is to modulate the brightness of
technique, which allow you to hide additional information of the pixels or the values of the frequency coefficients depending
various purposes in digital objects, in particular, in digital on the values of the embedded bits. In this study, the QIM method
images. is used to embed information in DCT coefficients. Images are
The methods for embedding information in digital images are processed in blocks of 8 × 8 pixels. The embedding area consists
divided into methods for embedding in the spatial domain and in of 36 high- and mid-frequency AC-coefficients. The embedding
the frequency domain of digital images. In practice, the use of of information is carried out by the formula
embedding methods in the frequency domain is more effective, c q
since such embedding in the general case provides greater c q b ,
resistance to various destructive influences. However, most of q 2 i
the known frequency embedding algorithms lead to significant where c is the DCT coefficient before embedding, c – is the
distortions of a digital image natural model in the frequency DCT coefficient after embedding, b is the secret message bit,
domain. Such distortions are an unmasking feature that reduces i
the stability of the steganographic algorithm before steganalysis, q is the quantization step.
aimed at identifying the presence of embedded additional The algorithm used in this study is distinguished by the
information in digital objects. Using steganalysis methods, an possibility of error-free extraction of embedded information due
intruder can detect the presence of an embedded message in a to an iterative embedding procedure. Since this feature of the
given stego-image and subsequently compromise or destroy it. algorithm does not affect the distortion of the digital image
In general case, steganalysis of digital images is considered natural model in the frequency domain, typical for the QIM
as a two-class classification problem. Many modern methods of method, we shall omit its description. The authors of this study
steganalysis are the development of a classical study [4], which give more information on the principle of iterative correction of
proposes a set of features for conducting steganalysis. The extraction errors by example of the discrete Fourier transform in
studies presented in articles [5, 8] are aimed at minimizing [3].
distortions of the natural model of digital images by using
various feature spaces. The articles [2, 6] are devoted to 3. Proposed Approach
steganalysis, the improvement of steganographic algorithms to
The application of the QIM method to the DCT domain is
counteract it and the expansion of feature spaces.
associated with the problem of distortion of the digital image
This article proposes a new approach to reducing the
natural model. In the present work, as a digital image natural
distortions of the digital image natural model in the discrete
model in the DCT domain we mean a histogram of distribution
cosine transform (DCT) domain by the steganographic
of the DCT coefficient values. An example of a typical histogram
embedding of information. Embedding is performed according
of DCT-coefficients of the image is shown in Fig. 1 (a).
to an algorithm based on the popular steganographic method of
If we embed a message in the corresponding image using the
quantization index modulation (QIM). The idea of the proposed
QIM method with a predefined quantization step q , the
approach consists in adaptive selection of the quantization step
(the main parameter of the classical QIM method) depending on histogram of the DCT coefficients will take the form shown in
the characteristics of a particular cover image. The aim of the Fig. 1 (b). The obtained histogram is markedly different from the
work is to study the effectiveness of this approach and its specific original. This is due to the fact that the classical QIM method
algorithmic implementations. narrows the number of possible variants of the DCT coefficient
values [7].
One of the solutions to this problem was previously proposed
by the authors of this study in [1], where to redistribute the
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
arising distortions of the histogram, the quantization step was steganography due to the compromise of the fact of the hidden
variable and depended on the ratio of the average values of the transmission of information.
AC-coefficients moduli of the one-dimensional DCT in and out In order to decide how the non-embedding area can be
of the embed area. This approach demonstrated a positive effect interconnected with the value q , it is necessary to pay attention
on the compensation of distortions of the histogram, but the on the nature of the distortions that arise when embedding
problem was not completely solved. The form of the histogram information with a constant quantization step. The histogram in
for a number of images still made it possible to unambiguously Fig. 1 (b) corresponds to the stego-image obtained with q 8 .
determine the presence of a steganographic attachment. Fig. 1 (c) The peaks that appear in the histogram correspond to the values
demonstrates the influence of the approach described in [1] on
the reduction of histogram distortions. 4 , i.e. q 2 . So, a certain predetermined value leads to the
fact that the frequency of occurrence of values equal to q
8000 2
increases. To reduce the probability that some new value of the
6000
quantization step for the next block will coincide with the most
The number of values
frequently occurring value of DCT coefficients, i.e. in order not
to enhance the growth of possible peaks in the histogram, it is
4000 proposed to choose the least frequently encountered value of
a) DCT coefficients from the non-embedding area as the value of
2000
the quantization step. It should be defined more exactly that the
quantization step is a positive integer, while the DCT coefficients
are real values; therefore, to select the next quantization step, the
0 DCT coefficients from the non-embedding area must be taken
-40 -20 0 20 40
The DCT coefficient values modulo and rounded (an example is shown in Fig. 2). To
determine the least common values of DCT coefficients, it is
8000
necessary to construct a histogram of the distribution of their
converted values over the non-embedding area.
6000
The number of values
-16,9 -8,4 -0,6 2,4 5,2 0,4 17 8 1 2 5 0
45,4 28,0 5,1 -3,7 -1,7 -8,3 45 28 5 4 2 8
4000
b) -15,1 -16,8 2,1 -7,4 4,1 15 17 2 7 4
17,4 11,4 -6,3 3,2 17 11 6 3
2000
7,9 3,3 4,1 8 3 4
5,8 0,3 6 0
0 1,8 2
-40 -20 0 20 40
The DCT coefficient values Fig. 2. Transformation of the non-embedding area.
8000
The authors of the study considered two options for choosing
the quantization step based on the obtained histogram of the non-
6000 embedding area:
The number of values
‒ from a group of values with a frequency not exceeding
4000
the set one;
c) ‒ from all values of the non-embedding area.
To implement the first option, it is necessary to pre-set the
2000 threshold for the frequency of occurrence of rounded absolute
values of the DCT coefficients, among which the quantization
step will be selected. Then the values that occur no more often
0
-40 -20 0 20 40 than the quantity of the threshold value will form a group. The
The DCT coefficient values
quantization step will be equal to the smallest value in the group.
Fig. 1. The histogram of the image: a) before the embedding; b) The second option does not require explicitly setting a threshold
after the embedding with a constant quantization step; c) after value. In this case, the smallest of the most rarely found values
the embedding with a variable quantization step from [1]. in the block is selected as the quantization step.
These approaches are somewhat similar, since in both cases
This study proposes to develop the idea of using the ratio of the decision to select the quantization step is made using the
domains within a block to select a quantization step. threshold value of the frequency of occurrence of DCT
Obviously, the embedding area undergoes the most coefficients. However, the fundamental difference between them
significant distortions. At the same time, a change in the non- is that the first option operates on a single threshold value for all
embedding area, i.e. in the other AC-coefficients of the block is image blocks, while the second option uses different threshold
negligible. Therefore, to select the quantization step, it is values for different blocks.
proposed to use the non-embedding area of the corresponding It is empirically found that the choice of a quantization step
block. The invariance of the non-embedding area will allow to of less than three provides a very small capacity, insufficient for
extract embedded data without errors, since the quantization step effective operation, and the selection of a quantization step of
selected over the non-embedding area will be the same for both more than twenty leads to a significant deterioration in the visual
the cover and the stego-images. It does not require knowledge of quality of images, therefore we introduce the condition:
any additional key information. This means that the transmission 3 q 20 .
of the stego-image does not require a preliminary exchange of Fig. 3 shows an example of selecting a quantization step q
keys, the presence of which would contradict the very idea of over the non-embedding area for both variants. In the first case,
the choice of q is made according to a group of values, the
occurrence frequency of which should be no more than two. The capacity in all cases was further set equal to the capacity obtained
smallest among these values is three, therefore q 3 . In the in the case of a selection over a group.
second case, the lowest frequency of occurrence of individual
values should be firstly determined, in this case it is equal to one. 50000
Then from the values encountered only once, the smallest is
selected, and in the end q 7 . 40000
The number of values
4
30000
3 3 3
The number of values
3
a)
Option No. 1
20000
2 2 2
2
10000
1 1 1
1
0
-80 -60 -40 -20 0 20 40 60 80
0 0 0 0 0 0
0 The DCT coefficient values
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
q
50000
q=3
4
40000
The number of values
3 3 3 30000
The number of values
3
Option No. 2
2
2 2 2 b) 20000
1 1 1 10000
1
0 0 0 0 0 0 0
0
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 -80 -60 -40 -20 0 20 40 60 80
q The DCT coefficient values
q=7 50000
Fig. 3. The choice of the quantization step over the non-
embedding area. 40000
The number of values
30000
4. The results of the experiments
To evaluate the effectiveness of the proposed approach and c) 20000
to compare the two options described above, computing
experiments were conducted. For the experiments, 20 classic test 10000
images of 512 × 512 pixels in grayscale were taken from the
“USC-SIPI Image Database”. 0
-80 -60 -40 -20 0 20 40 60 80
When evaluating the effectiveness, such standard The DCT coefficient values
characteristics as capacity is used, i.e. the ratio of the number of
Fig. 4. Histograms for the “Airplane” image: a) container; b)
embedded bits to the size of the container, and the PSNR metric,
stego-image (constant q , maximum capacity); c) stego-image
which is calculated by the formula
(new approach, option No. 2, maximum capacity).
255
PSNR 20 log10 ,
RMSE Fig. 5 and Fig. 6 present the results of comparing the
histograms for the “Airplane” and “Baboon” images obtained for
Pi Q1 2 ,
1 n
RMSE the cover and stego-images with different options for choosing
n i 1
the quantization step. For the “Airplane” test image, the
where n is the total number of pixels, Pi is the pixel value of embedding capacity is 0.29 bit / pixel, for the “Baboon” test
the cover image, Qi is the pixel value of the stego-image. image, it is 0.11 bit / pixel. These images are selected as
examples, as they belong to different types: the “Airplane” image
Since when choosing a quantization step over a group, its
contains many one-colour areas, while the “Baboon” image has
value is on average less than when choosing it over the entire
a high degree of detail.
non-embedding area, the algorithm capacity when using the first
According to Fig. 5 and Fig. 6, the application of the
option is much lower. So, the maximum capacity for the first
proposed approach significantly reduces the distortions that
option is an average of 201 bit/pixel over 20 test images, with the
occur when embedding information. The histograms shown in
corresponding average PSNR of 36.19 dB, while for the second
Fig. 5 (b) and Fig. 6 (b) unambiguously show the presence of a
option, the average capacity is 0.34 bits/pixel with a PSNR of
steganographic embedding in the corresponding images ( q 8 )
35.63 dB. The comparison of the histogram of the container, the
histogram of the stego-image obtained with a constant while histograms corresponding to stego-images obtained with
quantization step q 8 at the maximum capacity, and the the proposed approach conform with the natural form of the
histograms of cover images. So we can conclude that the
histogram of the stego-image obtained using the second option at
proposed approach can reduce the distortions of the digital image
the maximum capacity is shown in Fig. 4. The form of the
natural model in the frequency domain, and therefore, increase
histogram of the stego-image obtained using the selection of q
the imperceptibility of embedding.
over the non-embedding area is close to the form of the histogram
of the container. However, for a correct assessment of the
effectiveness of the proposed approach and both its variants, the
50000 quantization step over a group (the first option) demonstrates an
average RMSE value less than for all values (the second option),
40000 but the difference between them is not significant. It is also worth
noting that the second option allows you to provide a larger
The number of values 30000 embedding capacity, so the first option is preferable with a small
embedment volume, but you should use the second option if you
a) 20000 need to embed a larger message.
The analysis of the presented histograms showed that, on the
10000 one hand, they do not contain characteristic peaks, and, on the
other hand, the proposed approach allows us to restore exactly
0 the natural form of the initial histograms and does not lead to
-80 -60 -40 -20 0 20 40 60 80
The DCT coefficient values
excessive “uniformity”, which could also become an unmasking
sign.
50000
17500
40000
15000
The number of values
30000
The number of values
12500
b) 10000
20000
a) 7500
10000
5000
0 2500
-80 -60 -40 -20 0 20 40 60 80
The DCT coefficient values 0
-80 -60 -40 -20 0 20 40 60 80
50000 The DCT coefficient values
17500
40000
15000
The number of values
30000
The number of values
12500
c) 20000
10000
b) 7500
10000
5000
0 2500
-80 -60 -40 -20 0 20 40 60 80
The DCT coefficient values 0
-80 -60 -40 -20 0 20 40 60 80
50000 The DCT coefficient values
17500
40000
15000
The number of values
The number of values
30000 12500
10000
d) 20000
c) 7500
10000 5000
2500
0
-80 -60 -40 -20 0 20 40 60 80
0
The DCT coefficient values -80 -60 -40 -20 0 20 40 60 80
Fig. 5. Histograms for the “Airplane” image: a) container; b) The DCT coefficient values
stego-image (constant q ); c) stego-image (new approach, 17500
option No. 1); d) stego-image (new approach, option No. 2). 15000
The number of values
12500
To evaluate the differences of the histograms numerically,
the value of the RMSE metric between the histograms of the 10000
cover images and the corresponding stego-images was 7500
d)
calculated. On average, for 20 test images, the RMSE value
between the histograms of cover and stego-images obtained with 5000
a constant q 8 was 1017,80, for the “Airplane” and the 2500
“Baboon” images it was 513,13 and 268,55 respectively. The 0
results for the first option of the variable q : 565.81 on average, -80 -60 -40 -20 0 20 40 60 80
The DCT coefficient values
799.21 for "Airplane", 184.76 for "Baboon". Results for the
second variant of the variable q : 598.06 on average, 680.40 for Fig. 6. Histograms for the “Baboon” image: a) container; b)
the “Airplane”, 288.72 for the “Baboon”. It can be concluded that stego-image (constant q ); c) stego-image (new approach,
the differences between the histograms of cover and stego- option No. 1); d) stego-image (new approach, option No. 2.
images are much smaller when using a variable q. The choice of
5. Conclusion
The article presented and investigated a new approach to
reducing the distortions of a digital image natural model in the
DCT domain when embedding information using the QIM
method. As it can be seen from the results of the experiments, the
application of this approach has a positive effect on reducing the
unmasking signs of the embedding in the frequency domain. In
the future, it is planned to continue work to reduce the distortions
of the natural model of images in the frequency domain by
adapting the embedding parameters to a specific container.
6. Acknowledgments
This work was financially supported by a grant from the
Russian Foundation for Basic Research and the Tomsk Region
in the framework of project No. 19-47-703003 and financially
supported by a grant from the Russian Foundation for Basic
Research in the framework of project No. 18-29-22104.
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