A proposed assessment metrics for image steganography

International Journal on Cryptography and Information Security (IJCIS), Vol. 4, No. 1, March 2014
DOI:10.5121/ijcis.2014.4101 1
A Proposed Assessment Metrics for Image
Steganography
Mazhar Tayel, Hamed Shawky
Department of Electrical Engineering, Faculty of Engineering, Alexandria University,
Egypt
ABSTRACT
Data security has become an important problem in the communication systems. Steganography is used to
hide existence of a secret-message. In this article a modified Steganography algorithm will be proposed
depending on decomposition principle of both secret-message and cover-image. A fuzzification is
performed in the secret message to optimize the decomposed coefficients before embedding in the cover-
image to get a Stego Image. The well known metrics (Cor., MSE, PSNR, and Entropy) were used to
evaluate the modified algorithm. Also, a trade-off factor was introduced to determine an optimum value for
the embedding strength factor to get an acceptable degradation. Moreover to evaluate and assess the
modified algorithm and any Steganography algorithms, a new histogram metrics are proposed which
represents the relative frequency occurrence of the various images.
KEYWORDS
Steganography, Cover- image, Secret-message, Decomposition, Fuzzy set, Histogram Deviation.
1. INTRODUCTION
In digital world, Steganography and Cryptography are synonymous used to protect information
from unauthorised users (third party). Steganography can be used for different formats in digital
media like, bmp, .gif, .jpeg, .mp3, .txt, and .wav. One of the most important and valuable tools to
analyse image is the histogram. So what exactly is a histogram? A histogram is a graph that
shows the colour range of image. A histogram shows how much of it is currently pure white, and
how much of it falls somewhere between black and white images [1— 7].
2. Objective
This paper introduces a new Steganography metric able to evaluate effectiveness of any
Steganography algorithm, applying this metric in the proposed algorithm which introduced in the
previous paper.
3. THE PROPOSED ALGORITHM
The aim of this algorithm is to hide secret-message coefficients in a cover image without
perceptible degrading of cover-image quality and to provide better resistance against steganalysis
process. The proposed algorithm is composed of two channels namely: cover-image channel and
secret-message channel that are used to embed the decomposed coefficients together.

2
(i)- Fuzzy Optimization.
Using nine triangular MF to compress the secret-image from (0 — 255) to (0 — 30) image color
range. Then embeding into the cover image to obtain a uniformly diffused distribution of message
pixels all over the cover image.
(ii) - Image decomposition
The fuzzified secret-message and the cover-image are decomposed and then embed the
coefficients of the fuzzified message in the cover-image. When data is embedded in the frequency
domain, the security of the secret data resides in more robust areas, spread across the entire
image, to provide better resistance against statistical attacks, high capacity, high imperciptability
and robustness.
The DCT is used to decompose image into spectral sub-bands, working from left to right, top to
bottom. The embedding function resultant matrix, obtained by addition of the DCT coefficients of
the cover-image and the fuzzified secret-message, is given by [10 —14]:
S(j, k) = β C(j, k) + α M′(j, k) (1)
where:
β + α = 1 (2)
S(j, k) is the modified DCT coefficients of the stego-image, C(j, k) is the cover-image DCT
coefficients and M'(j, k) is the modified secret-message coefficients. Beta and alpha are two
complementary ESF. Alpha is chosen to obtain a stego-image without perceptible degrading of
the image quality and to provide better resistance against steganalysis process. Then apply inverse
IDCT on this modified embedded coefficients to get the stego-image. Figure (1) shows the
proposed embedding algorithm. This proposed system can take a decision for the Stego image, is
it acceptable or not. Figure (2) shows the block diagram of the proposed message reconstruction
algorithm to recovere the secret-message.
3.1 Steganography assessment
To assess the performance of the Steganography algorithm, three evaluation statistical metrics are
used. The first is the well known statistical metrics (MSE, PSNR, Cor, and Entropy), the others
are two proposed methods. There used three messages (Cameraman, House, and Baboon) to be
embedded in a cover-image (Barbara) to obtained three different stego-images which will be
under evaluation. These evaluation metrics will be described in the following [8,9, 10].

3
Fig.(2): The Block diagram of the reconstruction algorithm.
Fig. (1): The Block diagram of the introduced embedding algorithm.
n = 1 +0.1 α = α
To channel
Inverse Decomposition
Stego Image
Yes
No
Statistical Evaluations
=
= +0.1 +0.1 α =
∆TO = TO − TO +0.1 α = α
= + 1 +0.1 α =
Stego-image +0.1 α =
∆T > 0
= 1/2 +0.1 α =
Decomposition
Strength
factor α
Strength
factor β
= 0.1 , TO = 0
Cover Image
Fuzzy
Optimization
Embedding Process
Decomposition
Secret messege
Stego Image
DCT
Scaling 1/
Reconstructed
Secret messege
IDCT
Defuzzification
DCT
+
-
1 −
Cover-image

4
Reconstructed messageStego image
Alp
ha
0.1
0.2
0.3
0.4
0.6
0.8
0.9
Fig. 3. Barbara as a Stego- image and different reconstructed secret messages for different values of alpha.

5
A. Common Metric Methods
1) Mean Square Error (MSE): The distortion in an image can
be measured using the following equation:
MSE =
(C(j, k) − S(j, k))
M ∗ N
(3)
where: M, N is the size of the image.
2) Peak Signal to Noise Ratio (PSNR): The percentage of noise present in the stego-image, is to
be computed using the equation:
PSNR = 10 log
( )
(4)
3) Cross Correlation coefficient: which is given by:
COR =
∑ ( ( , ) )( ( , ) )
∑ ( ( , ) ∑ ( ( , )
(5)
It is used to comparing the similarity between the cover-image and the Stego-image. Where
m1 & m2 are the mean value of cover and Stego-image respectively.
4) Entropy: It is a statistical measure of randomness that can be used to characterize the texture of
the input image,
it is given by:
Entropy = − Pj Log Pj (6)
Figures (3) show the obtained Stego-images of the three secret-messages (Cameraman, Baboon,
House) using Barbara as a cover-image with different ESF (α). From these figures it is worth to
note that the Steg-image is drastically depending on the ESF (α) value. As the ESF (α) increases
the visual Steg-image degrades.
From figures it is worth to note that the Stego-image for < is accepted, while for >
the Stego-image is highly distorted.
Figure (4 - a, b, c & d) shows the statistical results of the proposed steganography algorithm for
the Stego-image of the House, Baboon, and the Cameraman using the common metrics (MSE,
PSNR, Cor and Entropy).
From this figure it is seen that as the ESF ( ) increases the MSE and entropy are increas, the
PSNR decreases and the Corr. is very slowly decreasing up to ESF ≅ 0.7, then rapidly
decreasing. Considering the mentioned above results, it is necessary to find some measurable
metric parameter to determine to which limit the ESF is to be applied.

6
(a): MSE of the three images under test.
(b): PSNR of the three images under test.
(c): Corr. of the three images under test.
(d): Entropy of the three images under test.
Fig. 4. The common assessment metrics against ESF.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
A lp ha
MSE
Barbara / House
Barbara / C ameraman
Barbara / Baboon
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
50
55
60
65
70
75
A lp ha
PSNR
Barbara / Baboon
Barbara / C ameraman
Barbara / House
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Alpha
Correlation
Barbara / House
Barbara / Cameraman
Barbara / Baboon
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Alpha
Entropy
Barbara / House
Barbara / Cameraman
Barbara / Baboon

7
B. A Proposed Trade-Off Evaluation Metric
A proposed Trade-Off (TO) combining between the MSE and correlation to satisfy the most
suitable value for ESF (α) is introduced, as follows
TO =
MSE
max
.
Corr
max
(7)
Figure (5) shows the Trade-Off between the correlation (Cor.) and the MSE for the three secret
messages under evaluation. The proposed TO was iterated for ESF range (α = 0.1 — 0.9) to
evaluate the Stego image. The iteration runs to determine the optimum value of alpha ( =
), see figure (1).
(a): Cameraman.
(b): House.
(c): Baboon.
Fig. 5. The Trade-Off Corr. and MSE for the tested images.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Alpha
MSE/Cor/TO
MSE
Cor
TO
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Alpha
MSE/Cor/TO
MSE
Cor
TO
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Alpha
MSE/Cor/TO
MSE
Cor
TO

8
C. Visual Acceptance of Stego-image
From the visual inspection of figure (3) it is seen that acceptable value of the ESF (α) for the
Stego-image must satisfy the condition:
=
1
2
(8)
where is the visual acceptable Stego-image.
Fig. 6. The Stego and reconstructed images for the visual acceptance value.
Figure (6) shows the Stego-images for the House, Baboon, and Cameraman with their
reconstructed secret-messages for the visual acceptance values ( = / 2 ). Thus the
proposed algorithm enables to reconstruct the original message with degradation depending on
the visual acceptance of the ESF ( ). In order to improve the degradation of the reconstructed
image a scaling factor (1/ ) is proposed as in [9].
D. A Proposed Histogram Deviation metric
Deviation histograms for the coefficients of the cover, fuzzified secret-message and Stego-image
are introduced as follows:
i- Stego-Message Histogram Deviation (SMD)
It is given as
∆ = | − | (9)
where:

9
SIC is the Stego-Image Coefficients, and MC is the Message Coefficients and its percentage
deviation is
∆SMD% =
∆
∗ 100 (10)
where
CC is the cover coefficient
ii- Stego-Cover Histogram Deviation (SCD)
It is given as
∆SCD = |SIC − CC| (11)
and its percentage deviation is
∆SCD% =
∆
∗ 100 (12)
iii- Stego-Image Variance Deviation (∆ ),
It is given as
var(x) = Σ(Xi, j − μ) /N (13)
where: μ Is the mean value, (Xi, j) is the image pixels, N is
number of pixel. The variance deviation (∆ ) is given as
∆var = |var(SIC) − var(CC)| (14)
and its percentage deviation is
∆var% =
∆
( )
∗ 100 (15)
3.2 EXPEREMINTAL RESULTS
Figures (7) and (8), show the proposed histogram deviation metric at = , for (a) the
histogram of Barbara as a cover image, (b) the histogram of Cameraman as a secret message, (c)
the histogram of Cameraman after fuzzification as a secret message, (d) the histogram of Stego-
image, (e) is the reconstructed secret message, (f) and (g) are the histograms for ∆ , ∆
compared with the histograms of (c) and (d) respectively, and (h) is the variance deviation.
(d) Stego-message(c) Fuzzified secret
message
(b): Cameraman as a secret
(a):Barbara as a cover
0
100
200
300
400
500
600
700
800
900
Stego-Image
0 50 100 150 200 250
0
500
1000
1500
2000
2500
3000
Secret messageafter fuzzification
0 50 100 150 200 250
0
200
400
600
800
1000
Cameramanas aSecret message
0 50 100 150 200 250
0
100
200
300
400
500
600
700
Barbara as a Cover Image
0 50 100 150 200 250

10
(h): ∆(g) :SCD(f) : SMD(e) :Reconstructed message
Fig.7. Histogram metric for the Barbara and Cameraman.
(d) Stego-message(c) Fuzzified secret
message
(b): Cameraman as a secret.
(a):Barbara as a cover
(h): ∆(g) :SCD(f) : SMD(e) :Reconstructed message
Fig.8. Histogram metric for the Barbara and House.
From this figures it is concluded that the stego-image is very close to the cover-image. This
shows that the proposed algorithm is more secure. Also, it is worth to note that deviations are
message dependent.
4. CONCLUSION
Steganography is used to transfer secret message over open channel. The human visual system
will be unable to perceive any difference in a Stego image. So the proposed metrics analyze the
Stego image to evaluate performance of the Steganography algorithm. In this paper a new
assessment metrics are proposed to evaluate security of any Steganography algorithm.
REFERENCES
[1] D. Lee Fugal "conceptual wavelet in digital signal processing" 2009 Space & Signals Technologies
LLC, www.ConceptualWavelets.com.
[2] Ivan W. Selesnick Polytechnic University Brooklyn, NY "Wavelet Transforms A Quick Study"
September 27, 2007.
[3] Eric Cole Ronald D. Krutz, Consulting Editor "Hiding in Plain Sight: Steganography and the Art of
Covert Communication" Published by Wiley Publishing, Inc., Indiana Published simultaneously in
Canada 2003.
[4] H S Manjunatha Reddy, N Sathisha, Annu Kumad, K B Raja," Secure Steganography using Hybrid
Domain Technique" ICCCNT'12, July 2012, Coimbatore, India.
0 10 20 30 40 50 60
0
0.5
1
1.5
2
2.5
3
-60 -40 -20 0 20 40 60
0
1
2
3
4
5
6
7
8
Stego-Cover Deviation (SCD)
-200 -150 -100 -50 0 50 100 150
0
1
2
3
4
5
6
7
8
Stego-Message Deviation (SMD)
0
500
1000
1500
2000
2500
3000
Reconstructedsecret message
0 50 100 150 200 250
0
100
200
300
400
500
Stego-Image
0 50 100 150 200 250
0
200
400
600
800
1000
1200
1400
Secret message after fuzzification
0 50 100 150 200 250
0
100
200
300
400
500
House as a Secret message
0 50 100 150 200 250
0
100
200
300
400
500
600
700
Barbara as a Cover Image
0 50 100 150 200 250
0 10 20 30 40 50 60
0
0.5
1
1.5
2
2.5
3
-80 -60 -40 -20 0 20 40 60 80 100
0
1
2
3
4
5
6
7
Stego-Message Deviation SMD
-60 -40 -20 0 20 40 60
0
1
2
3
4
5
6
7
8
9
Stego-Cover Deviation SMD
0
200
400
600
800
1000
1200
1400
Reconstructed secret message
0 50 100 150 200 250

11
[5] Mehdi Kharrazi, Husrev T. Sencar, "Image Steganography: Concepts and Practice" Lecture Notes
Series: April, 2004.
[6] L LAWSON and J. ZHU "Image compression using wavelet and a jpeg: tutorial" electronics and
communication engineering journal, June 2002.
[7] Elham Ghasemi, Jamshid Shanbeh zadeh, Nima Fassihi "High Capacity Image Steganography using
Wavelet Transform and Genetic Algorithm" proceeding of International Multi Conference of
Engineers and computer scientists 2011, Hong Kong.
[8] H S Manjunatha Reddy, K B Raja " Steganography based on Adaptive Embedding of Encrypted
Payload in Wavelet domain " International Journal of Scientific & Engineering Research, Volume 3,
Issue 8, August-2012.
[9] Souvik Bhattacharyya and Gautam Sanyal " Data Hiding in Images in Discrete Wavelet Domain
Using PMM" World Academy of Science, Engineering and Technology 2010.
[10] Vladimír BÁNOCI, Gabriel BUGÁR, Dušan LEVICKÝ " A Novel Method of Image Steganography
in DWT Domain" IEEE, 2011.
[11] Saurabh V. Joshi, Ajinkya A. Bokil, Nikhil A. Jain,and Deepali Koshti " Image Steganography
Combination of Spatial and Frequency Domain" International Journal of Computer Applications
Volume 53– No.5, September 2012.
[12] DEE - Politecnico di Bari," Steganography Effects in Various Formats of Images. A Preliminary
Study" International Workshop on Intelligent Data Acquisition and Advanced Computing Systems:
Technology and Applications -4 Foros Ukraine, July 2001.
[13] Vijay Kumar, Dinesh Kumar "Performance Evaluation of DWT Based Image Steganography" IEEE,
6/10/2010.
[14] Haiying Gao, Xiaolong Zheng," Image Information Hiding Algorithm Based on DWT with Alterable
Parameters" IEEE, 7/10/2010.
Author
Mazhar Basyouni Tayel is professor in Faulty of Engineering, Alexandria University,
Alexandria, Egypt. He holds B.Sc. in Electronics and Communications from Faculty of
Engineering, Alexandria University, He also holds M.Sc. and Ph.D. in Electrical
Engineering from Faculty of Engineering, Alexandria University. He tought many
technical courses in Electrical and Electronic (Analog and Digit al) system design and
Implementation, works as System Engineer for more than 20 years, teach up to 30 undergraduate,
postgraduate subjects, supervising more than 75 thesis, publish more than 150 papers in different
international conferencse, Forums and Journals.
Hamed Shawky Zied is a Post Graduate Student (Ph.D.), Alexandria University,
Alexandria, Egypt and became a Member of IEEE in 2012. He was born in Minoufia,
Egypt in 1973. He holds B.Sc. in Electronics and Communications from Faculty of
Engineering, Alexandria University, M.Sc. in Electrical Engineering from Faculty of
Engineering, Alexandria University. He received many technical courses in electronic
engineering design and Implementation.

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