Color images steganalysis using rgb channel geometric transformation measures

Abstract

In recent years, information security has received a great deal of attention. To give an example, steganography techniques are used to communicate in a secret and invisible way. Digital color images have become a good medium for digital steganography because of their easy manipulation as carriers via Internet, e-mails, or used on websites. The main goal of steganalysis is to detect the presence of hidden messages in a digital media. The proposed method is a further extension of the authors' previous work: steganalysis based on color feature correlation and machine learning classification. Fusing features with those obtained from color-rich models allows increasing the detectability of hidden messages in the color images. Our new proposition uses two types of features, computed between color image channels. The first type of feature reflects local Euclidean transformations, and the second one reflects mirror transformations. These geometric measures are obtained by the sine and cosine of gradient angles between all the color channels. Features are extracted from co-occurrence correlation matrices of measures. We demonstrate the efficiency of the proposed framework on three steganography algorithms designed to hide messages in images represented in the spatial domain: S-UNIWARD, WOW, and Synch-HILL. For each algorithm, we applied a range of different payload sizes. The efficiency of the proposed method is demonstrated by the comparison with the previous authors work and the spatial color-rich model and color filter array-aware features for steganalysis.

Full text

SECURITY AND COMMUNICATION NETWORKS
Security Comm. Networks 2015; 00:1–12
DOI: 10.1002/sec
RESEARCH ARTICLE
Color Images Steganalysis
Using RGB Channel Geometric Transformation Measures
Hasan ABDULRAHMAN 2,4, Marc CHAUMONT 1,2,3, Philippe MONTESINOS 4
and Baptiste MAGNIER 4
1Nˆ
ımes University, Place Gabriel P ´
eri, 30000 Nˆ
ımes Cedex 1, France.
2Montpellier University, UMR5506-LIRMM, 34095 Montpellier Cedex 5, France.
3CNRS, UMR5506-LIRMM, 34392 Montpellier Cedex 5, France.
4Ecole des Mines d’Al`
es, LGI2P, Parc Scientifique G.Besse, 30035 Nˆ
ımes Cedex 1, France.
ABSTRACT
In recent years, information security has received a great deal of attention. To give an example, steganography techniques
are used to communicate in a secret and invisible way. Digital color images have became a good medium for digital
steganography due to their easy manipulation as carriers via Internet, e-mails, or used on websites. The main goal of
steganalysis is to detect the presence of hidden messages in a digital media. The proposed method is a further extension of
the authors previous work: steganalysis based on color feature correlation and machine learning classification. Fusing
features with those obtained from Color-Rich Models allows increasing the detectability of hidden messages in the
color images. Our new proposition uses two types of features, computed between color image channels. The first type
of feature reflects local Euclidean transformations and the second one reflects mirror transformations. These geometric
measures are obtained by the sine and cosine of gradient angles between all the color channels. Features are extracted
from co-occurrence correlation matrices of measures. We demonstrate the efficiency of the proposed framework on three
steganography algorithms designed to hide messages in images represented in the spatial domain: S-UNIWARD, WOW,
and Synch-HILL. For each algorithm, we applied a range of different payload sizes. The efficiency of the proposed method
is demonstrated by the comparison with the previous authors work and the Spatial Color Rich Model and CFA-Aware
features for steganalysis.
Copyright c
2015 John Wiley & Sons, Ltd.
KEYWORDS
Steganalysis; Color Spatial Rich Model; CFA-aware steganalysis; channel correlation; ensemble classifier; steganography.
Received . . .
1. INTRODUCTION
Steganalysis, the art of detecting hidden information, has
received a great deal of attention in recent years. There
are many researchers working on solutions ensuring the
detection of hidden messages inside digital media. As
a result, there are many techniques and methods that
are currently used in the field of steganography and
steganalysis [1].
Modern information security techniques demonstrate
that cryptography alone is not enough to ensure the
safe communication of a hidden message. Indeed, it is
simple to corrupt, sabotage or delete a file containing
secret/encrypted message, as they may be tracked. In
addition, the presence of encrypted information itself is
valuable information. Additionally, when any person finds
and sees an encrypted message, this makes possible its
decryption. For these reasons, it is common to work with
steganography, encrypting the messages, and then hiding
them in a digital medium. By the way, steganography is
not intended to replace cryptography but supplement it to
make the detectability of the secret messages more and
more difficult [2].
More specifically, steganography is the art of hiding
the presence of a communication, by embedding messages
within a media such as audio, image or video files, in a
way that is hard to detect. The steganographer objective is
thus to hide the fact that there are information, hidden in a
media [3].
Image steganography techniques based on the modifi-
cation are predominantly classified into the spatial and fre-
quency domains [4]. In the spatial domain, pixel values are
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Data Extraction Data Embedding
Secret Message
Stego Image Cover Image
Secret Message
Embedding Process Extraction Process
Figure 1. Basic Steganography Model.
used directly to embed the message bits. In the frequency
domains [5], the frequential coefficients are used to embed
the message. Each domain has several different algorithms.
Generally, steganography is made of two parts, messages
are embedded inside the digital media in the first part (the
embedding) and they are extracted in the second part (the
extraction) [6], as illustrated in Fig.1.
Although the embedded messages inside the digital
medium involves some slight changes in this medium,
these changes modify slight coefficient values of the image
[18]. These changes are difficult to identify by a common
user. On the other hand, steganalysis research aims to
develop some methods, theories and applications that are
effectively able to detect these minor modifications in
order to detect hidden messages in this medium. Although,
the real-world uses significantly more color images than
grayscale images, there is a lot of research in steganalysis
of grayscale images compared to color images [7].
In this article, we describe further extensions of the
recent method described by Addulrahman et al. [8]. We
propose new features to enhance the Color Rich Model [9],
which is formed by co-occurrence matrices of residuals
taken across the color channels.
The rest of this paper is organized as follows.
Section 2is dedicated to steganalysis methods for digital
color images. Section 2.1 describes Color Spatial Model
steganalysis, and Section 2.2 describes Color Filter Array
aware features for steganalysis [22]. We present a detailed
description of our proposed method in Section 3by
recalling the color channel correlation and the mirror
transformations. The ensemble classifier used in this
work is explained in Section 4. Experimental results and
comparisons are given in Section 5. Finally, Section 6gives
some conclusions and perspectives.
2. RELATED WORK
In recent years, there have been a few techniques involving
color steganalysis methods. In this regard, the earliest work
was reported by Fridrich et al. [7]. The authors have
developed an influential approach for color steganalysis
to detect stego images which are created by embedding
a message inside the pixels randomly (using the Last
Significant Bit (LSB) steganography method). They
have found the relative number of close colors pairs
between the original image and the stego-image. Let us
note (R1, G1, B1) and (R2, G2, B 2) respectively the
three color channels specifying the red, green and blue
components of two color images. They show that if two
colored pixels (R1, G1, B1) and (R2, G2, B2) for these
two images are close, then the condition (R1−R2)2+
(G1−G2)2+ (B1−B2)2≤3must be satisfied. Thus,
after the embedding process, the number of unique colors
will be increased in stego images more than the number of
unique colors in the cover image.
Fridrich et al. [10] have introduced a reliable
steganalysis algorithm to detect LSB embedding in
randomly non-sequential scattered pixels in both 24-bit
color and grayscale images. In this method, the message
length is derived by searching the lossless capacity
in the LSB. Additionally, Westfeld and Pfitzman [11]
have applied a robust statistical attack method based
on statistical analysis of Pairs of Values (P oV s) that
are exchanged during message embedding. This method
detects very reliable stego images with hidden messages
which are embedded in sequential pixels using EZ Stego,
S-tools, J-Steg, and Steganos methods. A set of P oV s
is used to detect the presence of secret messages in
digital images. However, this method is not efficient with
embedded messages in random pixels.
Ker, in [12], enhanced techniques for the detection of
LSB Matching method from grayscale images into the
color images experiment. Beginning with the outlining of
Harmsen method [13], by using Histogram Characteristic
Function (HC F ), Ker has described two new ways: the
first one by calibrating the output Center Of Mass (COM)
using a down sampled image, and the second way by
computing the adjacency histogram instead of the usual
histogram to detect an additive noise based steganography.
Thiyagarajan et al. [14] has developed a steganalysis
method based on color model conversion. Indeed,
considering color images, to detect hidden messages, they
convert Red (R), Green (G) and Blue (B) channels of the
images to the Hue Saturation and Intensity (HS I) color
model. Stego images are then generated by implementing
different color image formats, using the last significant bit
steganography method. Finally, cover and stego images
are recognized using a threshold value which depends
on the correlation between pixel pairs in terms of color
components.
Lyu et al. [15] have described a steganalysis algorithm
that exploits the inherent statistical regularities of the
original images. The statistical model consists of first and
higher order color wavelet statistics of noise residuals
obtained using predictors of coefficients in Quadratic
Mirror Filter (QM F ) decomposition of the image from
all three color channels. Finally, they estimate that
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the addition of color statistics provides considerable
improvement in overall detection accuracy.
Krichner et al. [16] proposed a steganalysis method to
detect LSB replacement steganography in color images.
Also, the authors have enhanced the Weighted Stego (W S)
image steganalysis method [17] by replacing the cover
predictor in W S with position specific predictors, to detect
stego images produced from covers that exhibit traces of
Color Filter Array (CF A) interpolation. This technique
explains the local predictability of pixels, depending on
their position in the (CFA) interpolation to compute the
differences between cover images and stego images. The
detector exploits only dependencies within a color channel
due to color interpolation at cover generation.
Olguin-Garcia et al. [19] have developped a new
approach for color image steganalysis depending on
Histogram Characteristic Function Center of Mass
(HC F CoM )detecting histogram changes in each
R, G,and Bchannels. The stego images are created by
using LSB Matching steganography method. Then, the
Probability Density Function (P DF )is computed to find
the adequate threshold, and different threshold values are
determined with different payloads.
The most recent and efficient methods in color image
steganalysis are explained in detail in the two following
sections.
2.1. Color Spatial Rich Model steganalysis
As it is well known, embedding a message in an image
modifies some pixel values. Indeed, this modification
provides slight changes to the pixel values where the
message is embedded. It is a difficult task to detect and
extract the sensitive features. Many methods apply high-
pass filters to the target image, and then compute high
order statistics on the filtered images. Goljan et al. [9]
have introduced efficient color image features which are
an extension of the Spatial Rich Model [18], produced
from two different sets of features. First of all, this
method extracts the noise residual from each color channel
separately. Let us note that Xij is a pixel value of an 8-bit
grayscale cover image. We can specify the red, green and
blue channel of color images by the following formula:
Rij =ˆ
Xij (Nij )−c·Xij ,(1)
where:
•c∈N, is the residual order,
• Nij , is a local neighborhood of pixel Xij
at coordinates (i, j),
•ˆ
Xij (·)is a predictor of c·Xij ,Xij 6∈ Nij ,
Xij ∈ {0, ...., 255}.
Many diverse submodels built from the differences
between neighboring pixels are combined in the Rich
Model, all of the submodels (Rij )∈Rn1×n2are formed
from noise residual images of size n1×n2computed using
high pass filters of the following form:
Rij ←trancTround Rij
q,(2)
where:
•Rij =(trancT(x) = xfor x∈[−T, T ],
trancT(x) = T·sign(x)otherwise.
•qis the quantization step,
•round is a function for rounding
to an integer value.
The Spatio-Color Rich Model consists of two different
components. On one hand, the Spatial Rich Model
(SRM Q1) [18] with a fixed quantization q= 1 and
truncation T= 2 yields a dimensionality of 12753
features. These features are computed from each R,
Gand Bcolor channel separately. Finally, the three
dimensionality features are added together to keep the
same dimensionality as for grayscale images. On the other
hand, from the same noise residuals (i.e. SRM Q1), the
CRM Q1builds a collection of 3D color co-occurrence
matrices, taking three color values at the same position
(across the three channels of each pixel). Thus, with
fixed truncation T= 3 and quantization q= 1,CRM Q1
produces 5404 features per image.
2.2. CFA-aware features steganalysis
Digital cameras capture color images using a single
sensor in conjunction with a Color Filter Array (CF A)
interpolation. The CF A allows us to capture only one
part of the spectrum though the sensor so that only one
color is measured at each pixel (red, blue or green) and
so the resulting images are called mosaic images. To
construct a color image, a demosaicking algorithm is
used in order to interpolate each color plane (i.e. CF A
interpolations). Several patterns exist for the color filter
array, with the most common being Bayer CF A [20].
During this process, the green color channel is the most
important factor which determines the luminance of the
color image, 50% of the pixels in the Bayer CF A structure
are assigned to the green channel, while 25% are assigned
to the red channel and 25% to the blue color channel [21].
Goljan et al. introduced in [22] the CFA-aware CRM
for color image steganalysis. The features are made
from two parts, the first one is the Color Rich Model
CRM Q1explained in section 2.1 with T∈ {2,3}. The
second part is the CFA-aware feature, which consists of
three combinations: RB/GG split,R/B /GG split and
NII/I N I split.
Let us note, if Xhas a true-color image size of n1×n2,
where n1and n2are even numbers, (0≤i < n1,0≤j <
n2). Considering a typical Bayer mosaic, the Gsub-image
has twice as many pixels as the Rand Bsub-images. We
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must mention that, all the color images used in this method
are cropped from one pixel position which is the upper left
pixel corresponding to a non-interpolated blue in the Bayer
CF A. The color noise residuals Z=(z(R)
ij ,z(G)
ij ,z(B)
ij ) is
computed as Eq.1, corresponding to CF A used map.
First of all, the following four index sets must be
generated:
XB={(i, j)|ieven, j even},
XG1={(i, j)|iodd, j even},
XG2={(i, j)|ieven, j odd},
XR={(i, j)|iodd, j odd}.
Four 3D co-occurrence matrices are computed from
residual samples due to the above index sets.
C(B)
d1d2d3=X
(i,j)∈XBh(z(R)
ij , z(G)
ij , z(B)
ij ) = (d1, d2, d3)i,
(3)
C(G1)
d1d2d3=X
(i,j)∈XG1h(z(R)
ij , z(G)
ij , z(B)
ij ) = (d1, d2, d3)i,
(4)
C(G2)
d1d2d3=X
(i,j)∈XG2h(z(R)
ij , z(G)
ij , z(B)
ij ) = (d1, d2, d3)i,
(5)
C(R)
d1d2d3=X
(i,j)∈XRh(z(R)
ij , z(G)
ij , z(B)
ij ) = (d1, d2, d3)i.
(6)
From the above four co-occurrence matrices, three
combinations of features are generated to form the total
number of features with the CRM Q1set:
The first combination is called RB/GGsplit which
generates 4146 features. C(R)
d1d2d3and C(B)
d1d2d3are treated
and added together, the same thing is applied to C(G1)
d1d2d3
and C(G2)
d1d2d3as in Eq.’s 5and 6.
C(RB)
d1d2d3=C(B)
d1d2d3+C(B)
d3d2d1+C(R)
d1d2d3+C(R)
d3d2d1,
(7)
C(GG)
d1d2d3=C(G1)
d1d2d3+C(G1)
d3d2d1+C(G2)
d1d2d3+C(G2)
d3d2d1.
(8)
R/B/GG split represents the second set and produces
10323 features. This part can be considered as an
important component in this method, because it gives a
considerable number of features. It can be generated from
the concatenation of C(R)
d1d2d3,C(B)
d1d2d3, and C(G1)
d1d2d3+
C(G2)
d1d2d3.
The third set corresponds to the NII /I N I split; ’N’
meaning non-interpolated and ’I’ interpolated respectively,
in the RGB triple. The ’NII’ pixels correspond to the
same set as RB but the two co-occurrence matrices are
directionally symmetrized differently. This set generates
5514 features from two co-occurrence matrices:
C(NI I)
d1d2d3=C(B)
d3d2d1+C(R)
d1d2d3,(9)
C(IN I)
d1d2d3=C(GG)
d1d2d3.(10)
All these features are gathered in a one dimensional
vector, while all detectors are trained as binary classifiers
implemented using Kodovsky ensemble classifiers [26], as
explained in the following Section 4.
3. FEATURES DESCRIPTION
Our proposition is to enrich the SC RM Q1with an
inter-channel correlation which is composed of three sets
of features. The first set, produced by [9], gives 18157
features. The second set, produced by our first method [8],
gives 3000 features. Additionally, the third set, produced
by a second method, gives 3000 features; they are obtained
from the new correlation of different R, G and Bchannel
gradients, as shown in Table I.
Table I. Features description with their dimmensionalities
corresponding to qand T.
Feature set SC RM Q1CRG /CRB SRG /SRB
Dim. Symmetry yes yes yes
Dimension 18157 3000 3000
The following section recalls the RGB Channel
Correlations which gives an explanation to our proposition,
then section 4explains the ensemble classifiers used in this
approach.
3.1. RGB Channel Correlation
In this section, we introduce an inter-channel correlation
measure, and demonstrate that it can be linked to first
order Euclidean invariants (see Hilbert [23] for the
invariant theory). Such invariants have mainly been used
for stereo-matching [24]. In this paper, we show that
the information provided can enhance steganography
detection. The underlying idea here, is that if one channel
has been affected by steganography, the inter channel
correlation will measure the local modifications.
Starting from the local correlation of red and green
channels (similar to the correlation of red and blue
channels):
CorrR,G (i, j, k, l) = X
(i0,j0)∈Wi,j
X(R)
i0,j0·X(G)
k+i0,l+j0
(11)
with:
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Cover / Stego
Red channel
Green channel
Blue channel
Figure 2. Features extraction: Cosine of the gradient angles [8].
•X(R)
i0,j0∈[0,255], being a pixel value at position
(i0, j0)in the red channel,
•X(G)
k,l ∈[0,255], being a pixel value at position
(k, l)in the green channel,
• Wi,j , representing a small window centered in
(i, j).
Considering (k, l) = (0,0) and a limited development of
X(R)and X(G)around (i, j), then:
CorrR,G (i, j, 0,0) =
X
h= (i0−i, j0−j)
(i0, j0)∈ Wi,j
X(R)
i,j +∇X(R)
i,j ·hX(G)
i,j +∇X(G)
i,j ·h.
(12)
Developing this equation leads to four terms. Three of
which are constant or not informative, then there is only
one informative term :
∇X(R)
i,j · ∇X(G)
i,j .(13)
If only one channel has been altered locally, the gradient in
this channel is modified. Consequently, the scalar product
of two channel gradients reflects the change in the cosine
of the difference between the two gradient angles.
Similarly, we can apply the same computation for the
red and blue channel and then obtain :
∇X(R)
i,j · ∇X(B)
i,j .(14)
As stated by Gouet et al. [24] (and following the
Hilbert theory [23]), it is unnecessary to investigate the
∇X(G)
i,j · ∇X(B)
i,j term, as it is already implicitly contained
in the first two expressions (Eq. 13 and 14).
Normalizing these expressions, we obtain the cosine of
rotation angles, between channel gradients:
CRG =∇X(R)
i,j · ∇X(G)
i,j
|∇X(R)
i,j | |∇X(G)
i,j |,(15)
CRB =∇X(R)
i,j · ∇X(B)
i,j
|∇X(R)
i,j | |∇X(B)
i,j |.(16)
Fig. 2illustrates our preprocessing steps [8] to obtain
the cosine of rotation angles, between channel gradient.
Note that gradients derivatives of each channel are
estimated by a convolution with a [-1; 1] mask (horizontal
and vertical).
3.2. Mirror transformations
In the preceding section, we have seen that the inter-
channel correlation is linked with the scalar product of
gradients (i.e. Euclidean invariants). This means that if
we are able to measure the absolute value of a rotation
angle between two channel gradients, we still need the
direction of the rotation, which is linked this time to Mirror
transformations (as illustrated in Fig. 3).
Our proposition is to add two new features sets based
on the determinants of channel gradients. Similar to that
applied in the recent work of Abdulrahman et al. [8], the
features are directly linked to the correlation in order to
obtain new features of Sine of the gradients angle. Finally,
as illustrated in Fig. 4, we normalize these determinants by
gradient norms to obtain the sine of the rotations:
SRG =∇X(R)
i,j [0] · ∇X(G)
i,j [1] − ∇X(R)
i,j [1] · ∇X(G)
i,j [0]
|∇X(R)
i,j | |∇X(G)
i,j |,
(17)
SRB =∇X(R)
i,j [0] · ∇X(B)
i,j [1] − ∇X(R)
i,j [1] · ∇X(B)
i,j [0]
|∇X(R)
i,j | |∇X(B)
i,j |,
(18)
with ∇X[0] (resp. ∇X[1]) the first (resp. second)
component of the vector ∇Xi.e. corresponding to the
horizontal and the vertical derivatives (see Fig. 4).
3.3. Complete feature set
Our features, are computed from CRG ,CRB ,SRG and
SRB correlations by computing the co-occurrence matrices
as in the Rich Model [18]. We used different values of
the quantization q∈ {0.1,0.3,0.5,0.7,0.9,1}with fixed
truncation T=1. The reason for using these different values
of quantization qis that GRG ,GRB ,SRG and SRB belong
Figure 3. Rotation angle between two channel gradients
cos(α1) = cos(α2)but sin(α1) = −sin(α2)
cos(θ1) = cos(θ2)but sin(θ1) = −sin(θ2).
Sine is essential to determine the direction of the rotation.
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Cover/ Stego _
_
Red channel
Green channel
Blue channel
Figure 4. Features of extraction: Sine of the gradients angles extracting information from the direction of the local rotation.
to [−1,1]. Moreover, the use of these values gives more
accurate features and avoids the generation of too many
zero values caused by the truncation step in the co-
occurrence vector. For each quantization, we obtain 12
submodels from methods 1 [8] and 12 submodels from the
new proposed method 2 ∗. The submodels from the Color
Rich Models [9] give 18157 features, those of the method
1 [8] give 3000 features, and those of our proposed method
2 give 3000 features. Accordingly, the final feature vector
collects a final set of 24157 features.
4. THE ENSEMBLE CLASSIFIERS
An ensemble of classifiers [25] is a set of classifiers
whose individual decisions are combined and organized
into weighted or unweighted votes to classify the data sets
(in this work, features represent these data sets, as detailed
in the previous sub-section).
Modern steganalysis methods for digital images are
based on feature extraction. These methods need machine
learning techniques to detect if the media contains hidden
messages or not. In our work, we choose ensemble
classifiers [26] because of their efficient classification
performance for large scale learning.
Kodovsky et al. [26] proposed ensemble classifiers†
which is a machine learning tool for steganalysis,
∗For method 1 (resp. method 2) we use one symmetrized spam14h and
one spam14v submodel, with 25 features each. We also use the minmax22h,
minmax22v, minmax24, minmax34h, minmax34v, minmax41, minmax34,
minmax48h, minmax48v, and minmax54 submodels with 45 features for each.
All submodels are gathered in a one dimension vector to erect a dimensionality
of (2 ×25 + 10 ×45) ×6 = 3000 features. For more details on submodels
construction, the reader is invited to look at article [18].
†Ensemble classifier is available at http://dde.binghamton.edu/
download/ensemble.
consisting of many classifier Lindependently trained (Bl)
designed to keep complexity to a minimum and make the
overall process simple.
Each base learner is trained on randomly selected
subspaces dsub-dimensionals of the original feature space,
from the entire full d-dimension feature space. The authors
use Ficher Linear Discriminants (F LD)as base learners
and the final decision is made by aggregating the decision
of individual base learners. Let dbe a full dimensional
feature space, Ntrn and Ntst the number of training
and testing samples from each class. First, the classifiers
construct a number Lof F LD base learners (Bl)with l∈
{1, ..., L}. Each one performs its learning on a subspace of
dsub dimension, where dsub << d. From the ith image,
a feature vector, fi∈Rd, is extracted, and then mapped,
such as Rd→ {0,1}, where 000stands for cover and 010
for stego.
In the learning phase, each classifier learns to map a
feature vector fi, to the correct class number:
F LDl:Rd→ {0,1}
fi→F LDl(fi).
Each classifier uses the training database to compute the
orthogonal vector to the hyperplane separating the two
classes. For a test feature, the lth base learner reaches
its decision by computing a projection and comparing it
to a threshold. After collecting all Ldecisions, the final
classifier selects the class which has received the most
votes. Then, the decision threshold of each base learner
is adjusted to minimize the total detection error under an
equal prior on the training data [26]:
PE=minPF A
1
2[PF A +PM D (PF A)] ,(19)
where PF A represents the false alarm probability and
PMD the missed detection probability.
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5. EXPERIMENTAL RESULTS
5.1. Experimental setup and protocol
All our features are calculated and formed in a one
dimensional vector from 10000 color covers and 10000
color stego images for each payload of steganography
methods. These features are ready to enter in the classifier.
The classifiers were implemented using the ensemble
classifier [26] with many FLD as a base learner. In this
paper, the detection accuracy is measured by the total
probability of the average of testing errors under equal
priors as in Eq. 19.5000 images from a database are
randomly chosen for the training sets and 5000 for the
testing sets. The ensemble classifiers apply a vote to
estimate the error of detection. This process is repeated
10 times to obtain ¯
PE, the average of testing errors. ¯
PE
quantify the detectability and are collected for each method
and payload to evaluate the steganalysis method. Given the
decision values, ROC curves are obtained. As illustrated
in Fig. 8, the area under the ROC curves is calculated as
the accuracy of the ensemble classifiers.
5.1.1. Image Dataset
A raw image is a class of computer file containing
untouched pixel information coming from the digital
camera sensor (i.e. the pure information). These files
hold a large amount of meta-information about the image
generated by the camera [27].
In our work, the color image database is very carefully
built depending on the CF A idea. We collected raw
images from two subsets which are the most standard,
and have the highest number of images captured (i.e.
the Dresden Image Database’s [28]3500 full-resolution
Nikon digital camera raw color images and the Break Our
Steganographic System (BOSSbase‡), with 1000 Canon
digital camera raw color images).
In order to obtain color images in Portable Pixel Map
(PPM)format of size 512×512, all images take the
same CF A map layout, as illustrated in Fig. 6. For this
process, two steps are required. The first step consists of
using a demosaicking algorithm to convert raw images into
demosaicked images. The second step consists of cropping
five areas from one image. Fig. 5shows sample images
produced by the cropping step.
First we used the demosaicking algorithm Patterned
Pixel Grouping (PPG) from the dcraw software§to convert
raw images into RGB images. As illustrated in Fig.6, the
obtained images are such that the Bayer Pattern is always
of the type RGBG (red channel pixel is placed at an
even position). We wrote a spatial code to start the crop
from the red channel position. Indeed, from one image,
this code randomly selected the red channel position and
‡BOSSbase can be accessed at http://www.agents.cz/boss/
BOSSFinal.
§dcraw code is available at http://www.cybercom.net/defin/dcraw.
a) Original Raw image b) Crop 1 c) Crop 2
d) Crop 3 e) Crop 4 f) Crop 5
Figure 5. Sample images of our database built by random
cropping from locations of red channel pixels (even position) in
a Bayer pattern :
a) Original raw image 3906×2602,
b) crop 1 position x=2116, y=1928,
c) crop 2 position x=902, y=1182,
d) crop 3 position x=3080, y=436,
e) crop 4 position x=1866, y=1778,
f) crop 5 position x=650, y=1032.
cropped five images using a size of 512×512 pixels, so
that all blocks share the same CF A map layout. The final
number of images is 10000 RGB color images with a size
of 512×512.
5.1.2. Embedding methods
The stego images are obtained using three spatial-
domain steganography algorithms. The first method is
the Spatial-UNIversal WAvelet Relative Distortion (S-
UNIWARD¶) steganography algorithm [29]. The second
method is the Wavelet Obtained Weights (WOWk)
steganography algorithm [30]. Finally, the third method is
the Synchronizing the Selection Channel (Synch-HILL∗∗)
steganography algorithm [31].
These algorithms are used to embed messages into
color images by decomposing the R, G and Bchannels as
three grayscale images and embedding the same proportion
payload into each channel. Also, different tested payload
sizes are used {0.01,0.05,0.1,0.2,0.3,0.4and 0.5}Bit
Per Channel (BPC).
¶S-UNIWARD steganography method is available at http://dde.
binghamton.edu/download/stego_algorithms/.
kWOW steganography method is available at http://dde.binghamton.
edu/download/stego_algorithms/.
∗∗Synch-HILL steganography method is available at http://dde.
binghamton.edu/download/stego_algorithms/.
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dcraw
code
Our Crop
code
Raw
image
Raw image
database CFA Bayer
pattern
Start crop from
Red channel
PPM format
color image
database
Figure 6. The preprocessing steps for building our database depending on the CF A idea.
5.2. Results and Discussion
This section contains the experimental results of
our proposed method. We illustrate these results
in Table II. S-UNIWARD, WOW and Synch-HILL
methods were tested with different relative payloads
{0.01,0.05,0.1,0.2,0.3,0.4,0.5}(bpc) against three
approaches: method 1 [8], the Color Rich Model [9] and
the CFA-aware features steganalysis [22]. We used the
same set of payload values with the same embedding
methods. Our proposed second method, that uses both the
sine and cosine of the gradients angle, achieved higher
performance by registering 88.76%,87.93% and 88.07%
detection rates for S-UNIWARD, WOW and synch-HILL
respectively (with the payload 0.5bpc). The Color Rich
Model method [9] is less efficient because it achieved
respectively 86.14%,85.27% and 85.25% detection.
Also, the CFA-aware features method [22] is less efficient
because it achieved respectively 87.61%,87.04% and
87.42% detection rates. Close to the CFA-aware features
method, the method of Abdulrahman et al. [8] is less
efficient because it achieved respectively 87.54%,86.63%
and 86.77% detection rates. We noted the same trend with
the rest of the payload values, as shown in Table II.
Additionally, as shown in Table II, the method of
Abdulrahman et al. [8], that uses the cosine of the
gradients angle, achieved higher performance than Color
Rich Model method [9]; by registering 87.54%,86.63%
and 86.77% detection rates for S-UNIWARD, WOW and
synch-HILL respectively with the payload 0.5bpc. For the
same payloads range, the Color Rich Model method [9]
is less efficient because it achieved respectively 86.14%,
85.27% and 85.25% detection rates on the same test
samples. Also, as shown in Table II, our proposed second
method, that uses the sine and cosine of the gradients
angle, achieved higher performance than CFA-aware
features steganalysis method [22]; by registering 88.76%,
87.93% and 88.07% detection rates for S-UNIWARD,
WOW and synch-HILL respectively with the payload 0.5
bpc. The CFA-aware features steganalysis method [22]
is less efficient because it achieved respectively 87.61%,
87.04% and 87.42% detection rates on the same test
samples.
Moreover, curves in Fig.7(a) S-UNIWARD, (b) WOW
and (c) synch-HILL steganography method also, illustrate
the comparison between the proposed second method and
the compared methods. As a result, the average testing
error of the proposed second method is less than the first
proposition, the Color Rich Model and CFA-aware features
method. That proves the importance of the additional 3000
features proposed by the second method.
Another experiment involved embedding the entire
payload in only one channel of the color image, i.e. with
payload 0.2bpc and 0.4bpc in the green channel only.
In this case, the detection rate becomes higher than the
same payload distributed equally between the three color
channels. Table III illustrates the comparison of detection
rates between the S-UNIWARD, WOW and synch-HILL
methods with payloads 0.2bpc and 0.4bpc embedded
in one channel only and in the three channels separately.
Fig. 8(a), (b) and (c) show the ROC curves, illustrating
the performance of our method 2. Finally, this experiment
revealed that it is easier to detect a hidden message in
only one channel than a message that is spread across all
channels.
Table III. Our proposed method 2 detection rate of S-UNIWARD,
WOW and Synch-HILL steganography methods at 0.2 bpc and
0.4 bpc payload embedding in the green channel compares with
equal embedding in three channels.
S-UNIWARD WOW Synch-HILL
Payload G%RGB%G%RGB%G%RGB%
0.2 90.02 78.09 88.51 76.19 89.23 77.31
0.4 96.77 87.11 94.83 86.16 94.87 86.89
6. CONCLUSION
In this paper, we have proposed new features for
steganalysis of color images. Starting from the Color Rich
Model proposed by Goljan et al. [9], we have shown
that this method could be greatly enhanced by considering
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Table II. Numerical values of the average testing error ¯
PEand the detection rate PD%for three steganography methods. For easier
navigation the dark gray background column presents the first method of Abdulrahman et al. [8] and the light gray background column
presents the second proposed method.
Color Rich CFA-Aware Method 1 Method 2
payload ¯
PEPD%¯
PEPD%¯
PEPD%¯
PEPD%
S-UNIWARD
0.01 0.4841 51.59 0.4863 51.37 0.4830 51.70 0.4680 53.20
0.05 0.4045 59.55 0.4072 59.28 0.4010 59.90 0.3859 61.41
0.10.3298 67.02 0.3194 68.06 0.3203 67.97 0.3037 69.63
0.20.2498 75.02 0.2317 76.83 0.2370 76.30 0.2191 78.09
0.30.1947 80.53 0.1806 81.94 0.1808 81.92 0.1623 83.77
0.40.1599 84.01 0.1429 85.71 0.1470 85.30 0.1289 87.11
0.50.1386 86.14 0.1239 87.61 0.1246 87.54 0.1124 88.76
WOW
0.01 0.4850 51.50 0.4875 51.25 0.4836 51.64 0.4753 52.47
0.05 0.4092 59.08 0.4174 58.26 0.4042 59.58 0.3906 60.94
0.10.3397 66.03 0.3275 67.25 0.3317 66.83 0.3161 68.39
0.20.2654 73.46 0.2440 75.60 0.2502 74.98 0.2381 76.19
0.30.2081 79.19 0.1895 81.05 0.1918 80.82 0.1793 82.07
0.40.1783 82.17 0.1487 85.13 0.1574 84.26 0.1384 86.16
0.50.1473 85.27 0.1296 87.04 0.1307 86.63 0.1207 87.93
Synch-HILL
0.01 0.4893 51.07 0.4843 51.57 0.4814 51.83 0.4687 53.13
0.05 0.3991 60.09 0.4030 59.70 0.3879 61.21 0.3720 62.80
0.10.3311 66.89 0.3189 68.11 0.3258 67.42 0.3086 69.14
0.20.2595 74.05 0.2394 76.06 0.2438 75.62 0.2269 77.31
0.30.1997 80.03 0.1753 82.47 0.1829 81.71 0.1607 83.93
0.40.1684 83.16 0.1478 85.22 0.1540 84.60 0.1311 86.89
0.50.1475 85.25 0.1258 87.42 0.1323 86.77 0.1193 88.07
.01 0.05 0.1 0.2 0.3 0.4 0.5
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Embedding payload
Probabilty of error PE
Color rich model
CFA−Aware
Proposed method 1
Proposed method 2
S-UNIWARD
.01 0.05 0.1 0.2 0.3 0.4 0.5
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Embedding payload
Probabilty of error PE
Color rich model
CFA−Aware
Proposed method 1
Proposed method 2
WOW
.01 0.05 0.1 0.2 0.3 0.4 0.5
0
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Embedding payload
Probabilty of error PE
Color rich model
CFA−Aware
Proposed method 1
Proposed method 2
Synch-HILL
(a) S-UNIWARD (b) WOW (c) Synch-HILL
Figure 7. Avarage testing error ¯
PEas a function of the payload for (a) S-UNIWARD,(b) WOW and (c) WOW steganography methods,
comparison between the steganalysis methods (Color Rich Model, CFA-aware features steganalysis, method 1 [8] and proposed
method 2).
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
True positive rate
S−UNWARD steganography
payload 0.2 bpc.
Green channel only
RGB channels
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
True positive rate
S−UNWARD steganography
payload 0.4 bpc.
Green channel only
RGB channels
(a) S-UNIWARD
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
True positive rate
WOW steganography
payload 0.2 bpc.
Green channel only
RGB channels
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
True positive rate
WOW steganography
payload 0.4 bpc.
Green channel only
RGB channels
(b) WOW
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
True positive rate
Synch−HILL steganography
payload 0.2 bpc.
Green channel only
RGB channels
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
False positive rate
True positive rate
Synch−HILL steganography
payload 0.4 bpc.
Green channel only
RGB channels
(c) Synch-HILL
Figure 8. ROC curves using our proposed method 2 feature set, for (a) S-UNIWARD, (b) WOW and (c) Synch-HILL steganography
methods for payloads 0.2 bpc (up) and 0.4 bpc (down), to compare the detectability when embedding messages in only one channel
with embedding messages spread in all channels.
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local deformation between channels. We have proposed
to add to the Color Rich Model a new set of features
based on local Euclidean and mirror transformation. The
euclidean transformation, proposed by Abdulrahman et al.
[8], is estimated by a first set of features derived from
correlations between the gradients of red, green and blue
channels. Since these features give the cosine of angles
between gradients, we still do not know the direction of
the rotation between two channel gradients. Then, we have
shown that by taking into account mirror transformations,
we can obtain the missing information of the direction of
the local rotation. According to this analysis, we add a new
set of features based on the sine of local rotation angles.
These two sets of features are then incorporated in the Rich
Model using co-occurrence matrices in order to obtain
6000 features. The first and second set gives 3000 features
each [8]. The total feature set is formed from the Color
Rich Model, plus the two new sets demonstrated in this
work, in order to build a vector of a total of 24157 features.
We used a quantization step with a set of values that differs
from the Color Rich Models. All feature vectors are fed to
the Ensemble Classifier. The Ensemble Classifier is used
to detect the presence of hidden messages. Eventually,
multiple steganalysis comparisons have been achieved
between the proposed method and the initial Color Rich
Model [9] and CFA-aware features steganalysis method
[22]. We have used three steganography methods ( S-
UNIWARD, WOW and Synch-HILL ) with seven different
payloads. All the experiments show that our new method
outperforms the Color Rich Model and the CFA-aware
feature steganalysis.
Our future work will focus on developing a new
steganalysis method for digital color images using
steerable filters.
6.1. Acknowledgements
The authors wish to thank the Iraqi Ministry of Higher
Education and Scientific Research for funding and
supporting this work.
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