-\subsection{Adaptive Embedding Rate}
-
-Two strategies have been developed in our scheme with respect to the rate of
-embedding which is either \emph{ adaptive} or \emph{fixed}.
-
-In the former the embedding rate depends on the number of edge pixels.
-The higher it is, the larger is the message length that can be considered.
-Practically, a set of edge pixels is computed according to the
-Canny algorithm with high threshold.
-The message length is thus defined to be the half of this set cardinality.
-The rate between available bits and bit message length is then more than two.This constraint is indeed induced by the fact that the efficiency
-of the stc algorithm is unsatisfactory under that threshold.
-
-
-In the latter, the embedding rate is defined as a percentage between the
-number of the modified pixels and the length of the bit message.
-This is the classical approach adopted in steganography.
-Practically, the Canny algorithm generates a
-a set of edge pixels with threshold that is decreasing until its cardinality
-is sufficient. If the set cardinality is more than twice larger than the
-bit message length an stc is again applied.
-Otherwise, pixels are randomly chosen from the set of pixels to build the
-subset with a given size. The BBS PRNG is again applied there.
-
+First of all, the whole code of STABYLO can be downloaded
+\footnote{\url{http://members.femto-st.fr/raphael-couturier/stabylo/}}.
+For all the experiments, the whole set of 10,000 images
+of the BOSS contest~\cite{Boss10} database is taken.
+In this set, each cover is a $512\times 512$
+grayscale digital image in a RAW format.
+We restrict experiments to
+this set of cover images since this paper is more focused on
+the methodology than on benchmarks.
+
+We use the matrices $\hat{H}$
+generated by the integers given
+in Table~\ref{table:matrices:H}
+as introduced in~\cite{FillerJF11}, since these ones have experimentally
+be proven to have the strongest modification efficiency.
+For instance if the rate between the size of the message and the size of the
+cover vector
+is 1/4, each number in $\{81, 95, 107, 121\}$ is translated into a binary number
+and each one constitutes thus a column of $\hat{H}$.
+
+\begin{table}
+$$
+\begin{array}{|l|l|}
+\hline
+\textrm{Rate} & \textrm{Matrix generators} \\
+\hline
+{1}/{2} & \{71,109\}\\
+\hline
+{1}/{3} & \{95, 101, 121\}\\
+\hline
+{1}/{4} & \{81, 95, 107, 121\}\\
+\hline
+{1}/{5} & \{75, 95, 97, 105, 117\}\\
+\hline
+{1}/{6} & \{73, 83, 95, 103, 109, 123\}\\
+\hline
+{1}/{7} & \{69, 77, 93, 107, 111, 115, 121\}\\
+\hline
+{1}/{8} & \{69, 79, 81, 89, 93, 99, 107, 119\}\\
+\hline
+{1}/{9} & \{69, 79, 81, 89, 93, 99, 107, 119, 125\}\\
+\hline
+\end{array}
+$$
+\caption{Matrix Generator for $\hat{H}$ in STC}\label{table:matrices:H}
+\end{table}
+
+
+Our approach is always compared to HUGO, to EAISLSBMR, to WOW and to UNIWARD
+for the two strategies Fixed and Adaptive.
+For the former one, the payload has been set to 10\%.
+For the latter one, the Canny parameter $T$ has been set to 3.
+When $b$ is 7, the average size of the message that can be embedded
+is 16,445 bits,
+that corresponds to an average payload of 6.35\%.
+For each cover image the STABYLO's embedding rate with these two parameters
+is memorized.
+Next each steganographic scheme is executed to produce the stego content of
+this cover with respect to this embedding rate.
+
+
-\subsection{Image Quality}
+\subsection{Image quality}\label{sub:quality}
The visual quality of the STABYLO scheme is evaluated in this section.
-Four metrics are computed in these experiments :
+For the sake of completeness, three metrics are computed in these experiments:
the Peak Signal to Noise Ratio (PSNR),
-the PSNR-HVS-M family~\cite{PSECAL07,psnrhvsm11} ,
-the BIQI~\cite{MB10,biqi11} and
+the PSNR-HVS-M family~\cite{psnrhvsm11},
+and
the weighted PSNR (wPSNR)~\cite{DBLP:conf/ih/PereiraVMMP01}.
The first one is widely used but does not take into
-account Human Visual System (HVS).
-The other last ones have been designed to tackle this problem.
+account the Human Visual System (HVS).
+The other ones have been designed to tackle this problem.
-\begin{table}
+If we apply them on the running example with the Adaptive and STC strategies,
+the PSNR, PSNR-HVS-M, and wPSNR values are respectively equal to
+68.39, 79.85, and 89.71 for the stego Lena when $b$ is equal to 7.
+If $b$ is 6, these values are respectively equal to
+65.43, 77.2, and 89.35.
+
+
+
+
+\begin{table*}
\begin{center}
-\begin{tabular}{|c|c|c|}
+\begin{small}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{|c|c|c||c|c|c|c|c|c|c|c|c|c|}
\hline
-Embedding rate & Adaptive & 10 \% \\
+Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\
\hline
-PSNR & 66.55 & 61.86 \\
+Embedding & Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive \\
\hline
-PSNR-HVS-M & 78.6 & 72.9 \\
+Rate & 10\% & + sample & +STC(7) & +STC(6) & 10\%&$\approx$6.35\%& 10\%&$\approx$6.35\%& 10\%&$\approx$6.35\%& 10\%&$\approx$6.35\%\\
\hline
-BIQI & 28.3 & 28.4 \\
+PSNR & 61.86 & 63.48 & 66.55 & 63.7 & 64.65 & {67.08} & 60.8 & 62.9&65.9 & 68.3 & 65.8 & 69.2\\
\hline
-wPSNR & 86.43& 77.47 \\
+PSNR-HVS-M & 72.9 & 75.39 & 78.6 & 75.5 & 76.67 & {79.6} & 71.8 & 76.0 &
+76.7 & 80.35 & 77.6 & 81.2 \\
+\hline
+wPSNR & 77.47 & 80.59 & 86.43& 86.28 & 83.03 & {88.6} & 76.7 & 83& 83.8 & 90.4 & 85.2 & 91.9\\
\hline
\end{tabular}
+\end{small}
\end{center}
-\caption{Quality measures of our steganography approach\label{table:quality}}
-\end{table}
+\caption{Quality measures of steganography approaches\label{table:quality}}
+\end{table*}
-Let us compare the STABYLO approach with other edge based steganography
-schemes with respect to the image quality.
-Fist off all, wPSNR and PSNR of the Edge Adaptive
-scheme detailed in~\cite{Luo:2010:EAI:1824719.1824720} are lower than ours.
-Next both the approaches~\cite{DBLP:journals/eswa/ChenCL10,Chang20101286}
-focus on increasing the payload while the PSNR is acceptable, bu do not
-give quality metrics for fixed embedding rate from a large base of images.
-Our approach outperforms the former thanks to the introduction of the stc
-algorithm.
+Results are summarized in Table~\ref{table:quality}.
+In this table, STC(7) stands for embedding data in the LSB whereas
+in STC(6), data are hidden in the last two significant bits.
-\subsection{Steganalysis}
+Let us give an interpretation of these experiments.
+First of all, the Adaptive strategy produces images with lower distortion
+than the images resulting from the 10\% fixed strategy.
+Numerical results are indeed always greater for the former strategy than
+for the latter one.
+These results are not surprising since the Adaptive strategy aims at
+embedding messages whose length is decided according to a higher threshold
+into the edge detection.
-The quality of our approach has been evaluated through the two
-AUMP~\cite{Fillatre:2012:ASL:2333143.2333587}
-and Ensemble Classifier~\cite{DBLP:journals/tifs/KodovskyFH12} based steganalysers.
-Both aims at detecting hidden bits in grayscale natural images and are
-considered as the state of the art of steganalysers in spatial domain~\cite{FK12}.
-The former approach is based on a simplified parametric model of natural images.
-Parameters are firstly estimated and a adaptive Asymptotically Uniformly Most Powerful
-(AUMP) test is designed (theoretically and practically) to check whether
-a natural image has stego content or not.
-In the latter, the authors show that the
-machine learning step, (which is often
-implemented as support vector machine)
-can be a favourably executed thanks to an Ensemble Classifiers.
+If we combine Adaptive and STC strategies
+the STABYLO scheme provides images whose quality is higher than
+the EAISLSBMR's one but lower than the quality of high complexity
+schemes. Notice that the quality of the less respectful scheme (EAILSBMR)
+is lower than 6\% than the one of the most one.
+% Let us now compare the STABYLO approach with other edge based steganography
+% approaches, namely~\cite{DBLP:journals/eswa/ChenCL10,Chang20101286}.
+% These two schemes focus on increasing the
+% payload while the PSNR is acceptable, but do not
+% give quality metrics for fixed embedding rates from a large base of images.
-\begin{table}
+
+
+
+\subsection{Steganalysis}\label{sub:steg}
+
+
+
+The steganalysis quality of our approach has been evaluated through the % two
+% AUMP~\cite{Fillatre:2012:ASL:2333143.2333587}
+% and
+Ensemble Classifier~\cite{DBLP:journals/tifs/KodovskyFH12} based steganalyser.
+Its particularization to spatial domain is
+considered as state of the art steganalysers.
+Firstly, a space
+of 686 co-occurrence and Markov features is extracted from the
+set of cover images and the set of training images. Next a small
+set of weak classifiers is randomly built,
+each one working on a subspace of all the features.
+The final classifier is constructed by a majority voting
+between the decisions of these individual classifiers.
+
+
+%The former approach is based on a simplified parametric model of natural images.
+% Parameters are firstly estimated and an adaptive Asymptotically Uniformly Most Powerful
+% (AUMP) test is designed (theoretically and practically), to check whether
+% an image has stego content or not.
+% This approach is dedicated to verify whether LSB has been modified or not.
+% , the authors show that the
+% machine learning step, which is often
+% implemented as a support vector machine,
+% can be favorably executed thanks to an ensemble classifier.
+
+
+\begin{table*}
\begin{center}
-\begin{tabular}{|c|c|c|c|}
+\begin{small}
+\setlength{\tabcolsep}{3pt}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
-Schemes & \multicolumn{2}{|c|}{STABYLO} & HUGO\\
+Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\
\hline
-Embedding rate & Adaptive & 10 \% & 10 \%\\
+Embedding & Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. \\
\hline
-AUMP & 0.39 & 0.22 & 0.50 \\
+Rate & 10\% & + sample & +STC(7) & +STC(6) & 10\%& $\approx$6.35\%& 10\%& $\approx$6.35\% & 10\%& $\approx$6.35\%& 10\%& $\approx$6.35\%\\
\hline
-Ensemble Classifier & & & \\
+%AUMP & 0.22 & 0.33 & 0.39 & 0.45 & 0.50 & 0.50 & 0.49 & 0.50 \\
+%\hline
+Ensemble Classifier & 0.35 & 0.44 & 0.47 & 0.47 & 0.48 & 0.49 & 0.43 & 0.47 & 0.48 & 0.49 & 0.46 & 0.49 \\
\hline
\end{tabular}
+\end{small}
\end{center}
\caption{Steganalysing STABYLO\label{table:steganalyse}}
-\end{table}
-
-
-Results show that our approach is more easily detectable than HUGO which is
-is the more secure steganography tool, as far we know. However due to its
-huge number of features integration, it is not lightweight.
-
+\end{table*}
+
+
+Results of average testing errors
+are summarized in Table~\ref{table:steganalyse}.
+First of all, STC outperforms the sample strategy %for % the two steganalysers
+ as
+already noticed in the quality analysis presented in the previous section.
+Next, our approach is more easily detectable than HUGO,
+WOW and UNIWARD which are the most secure steganographic tool,
+as far as we know.
+However by combining Adaptive and STC strategies
+our approach obtains similar results than the ones of these schemes.
+
+Compared to EAILSBMR, we obtain better results when the strategy is
+Adaptive.
+However due to its
+huge number of integration features, it is not lightweight.
+
+All these numerical experiments confirm
+the objective presented in the motivations:
+providing an efficient steganography approach in a lightweight manner.
