978-1-5090-4093-3/16/$31.00 ©2016 IEEE 2262
2016 12th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD)
Evolving Distortion Function By Exploiting The
Differences Among Comparable Adaptive
Steganography
Wenbo Zhou
CAS Key Laboratory of
Electro-magnetic Space Information
University of Science
and Technology of China
Hefei, China
Email:welbeckz@mail.ustc.edu.cn
Weiming Zhang
CAS Key Laboratory of
Electro-magnetic Space Information
University of Science
and Technology of China
Hefei, China
Tel.:0551-63600863
Email:zhangwm@ustc.edu.cn
Nenghai Yu
CAS Key Laboratory of
Electro-magnetic Space Information
University of Science
and Technology of China
Hefei, China
Tel.:0551-63600681
Abstract—So far, the most effective model for adaptive
steganography is to minimize a well-defined distortion function,
in which the distortion function determines the modification
probability (MP) of each pixel. We found that the MPs of some
pixels calculated by a group of steganographic methods may be
very different even though these methods have close performances
in resisting the detection of steganalysis. We call such pixels as
controversial pixels, and consider that steganalysis is not sensitive
to such pixels. Therefore we can assign more payloads to the
controversial pixels by increasing MPs on them to generate a
new steganographic distortion function. We call this evolutionary
strategy as the rule of Controversial Pixels Prior (CPP). Taking
the state-of-art methods {WOW, UNIWARD} and {HILL, MVG}
as two pairs of examples, we show that the principle of CPP can
improve the security of state of the art steganographic algorithms
for spatial images.
Index Terms—Steganography, evolutionary, distortion func-
tion, controversial pixels, modification probability, steganalysis
I. INTRODUCTION
Steganography is a technique for covert communication,
which aims to hide secret messages into ordinary digital
media without drawing suspicion [1], [2], [16]. Designing
steganographic algorithms for various cover sources is chal-
lenging due to the fundamental lack of accurate models.
Currently, the most successful approach to design content
adaptive steganography is based on minimizing the distortion
between the cover and the corresponding stego object. The
distortion is obtained by assigning a cost to each modified
cover element (e.g., pixel in spatial domain image), and the
messages are embedded while minimizing the total distortion
which is the sum of costs of all modified elements.
The first method based on the framework of minimizing
distortion is HUGO (highly undetectable stego) [3]. HUGO
defines the pixel’s distortion by the changing amplitude of
steganalyzer’s features caused by modifying the current pix-
el, and pixels that make the feature vectors deviated more
will have higher costs. The features of steganalyzer SPAM
(subtractive pixel adjacency matrix) [4] is used in HUGO.
Steganalyzer’s features are usually generated by exploiting
correlations between the predicted residuals of neighboring
pixels [4], [23]. Because the pixels in smooth areas can be
accurately predicted, the modifications in such areas will be
easily detected by steganalyzers. Therefore the embedding
changes of HUGO will be gathered within textured regions.
However, HUGO can be detected by steganalyzer with higher
dimension of features, such as SRM (spatial rich models) [6].
In SRM, the predicted residuals are generated in various
directions and manners, so the correlations between pixels can
be further exploited. If the pixel can be accurately modeled
in any direction, it should be considered as a smooth point
and assigned larger cost. With this insight, WOW has been
proposed [5], which assigns high costs to pixels that are more
predictable by a bank of directional filters. WOW improves the
security of HUGO under the detection of SRM (spatial rich
models) [6]. UNIWARD (universal wavelet relative distortion)
[7] generalizes the cost function of WOW to make it simpler
and more suitable for embedding in an arbitrary domain,
including spatial domain and DCT domain for JPEG images.
Hence UNIWARD has a similar performance compared to
WOW in spatial domain. Li et al. proposed the method HILL
[8], which improves WOW by spreading the costs with a low-
pass filter. In HILL [8], the local modification probabilities are
evened out and thus the modifications cluster in the complex
areas.
The above methods design cost function in an ad hoc
or empirical manner. Sedighi et al. proposed model-driven
approaches [9], [11], in which Multivariate Gaussian (MG) or
Multivariate Generalized Gaussian (MVG)’s distribution was
used to model noise residuals of pixels by assuming them to
be independent but have varying variances. The models are
established by estimating the variances and then the costs are
computed by minimizing the power of an optimal statistical
test. In fact, small costs will be assigned to residuals modeled
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