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-For the whole experiment, a set of 500 images is randomly extracted 
-from the database taken from the BOSS contest~\cite{Boss10}. 
+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 $512\times 512$
 In this set, each cover is a $512\times 512$

-grayscale digital image.
+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 best 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}

 
 

-\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.
-In this strategy, two methods are thus applied to extract bits that 
-are modified. The first one is a direct application of the STC algorithm.
-This method is further referred as \emph{adaptive+STC}.
-The second one randomly choose the subset of pixels to modify by 
-applying the BBS PRNG again. This method is denoted \emph{adaptive+sample}.
-Notice that the rate between 
-available bits  and bit message length is always equal to two.
-This constraint is indeed induced by the fact that the efficiency 
-of the STC algorithm is unsatisfactory under that threshold.
+Our approach is always compared to Hugo~\cite{DBLP:conf/ih/PevnyFB10}
+and to EAISLSBMR~\cite{Luo:2010:EAI:1824719.1824720}.
+The former is the least detectable information hiding tool in spatial domain 
+and the latter is the work that is the closest to ours, as far as we know. 

 
 

-On our experiments and with the adaptive scheme, 
-the average size of the message that can be embedded is 16445.
-Its corresponds to an  average payload of 6.35\%. 

 
 
 
 

+First of all,  in our experiments and with the adaptive scheme, 
+the average size of the message that can be embedded is 16,445 bits.
+It corresponds to an  average payload of 6.35\%. 
+The two other tools will then be compared with this payload. 
+Sections~\ref{sub:quality} and~\ref{sub:steg} respectively present 
+the quality analysis and the security of our scheme. 

 
 
 
 

-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 step is again applied.
-Otherwise, pixels are again randomly chosen with BBS.

 
  
 
 
  
 

-\subsection{Image Quality}
+\subsection{Image quality}\label{sub:quality}

 The visual quality of the STABYLO scheme is evaluated in this section.
 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 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}, 
+%the BIQI~\cite{MB10}, 
+and 

 the weighted PSNR (wPSNR)~\cite{DBLP:conf/ih/PereiraVMMP01}.
 The first one is widely used but does not take into
 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, 
+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{center}

-\begin{tabular}{|c|c|c||c|c|}
-\hline
-Schemes & \multicolumn{3}{|c|}{STABYLO} & HUGO\\
+\begin{small}
+\begin{tabular}{|c|c|c||c|c|c|c|c|c|c|c|c|c|}

 \hline
 \hline

-Embedding &   \multicolumn{2}{|c||}{Adaptive} & Fixed & Fixed \\
+Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\

 \hline
 \hline

-Rate &   + STC &  + sample & 10\% & 10\%\\ 
+Embedding &   Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} &  Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive \\

 \hline
 \hline

-PSNR &  66.55 & 63.48  & 61.86  & 64.65   \\ 
+Rate &   10\% &  + sample &  +STC(7) & +STC(6) &  10\%&6.35\%& 10\%&6.35\%& 10\%&6.35\%& 10\%&6.35\%\\ 

 \hline
 \hline

-PSNR-HVS-M & 78.6 & 75.39 & 72.9 & 76.67\\ 
+PSNR & 61.86 & 63.48 &  66.55 (\textbf{-0.8\%}) &  63.7  & 64.65 & {67.08} & 60.8 & 62.9&65.9 & 68.3 & 65.8 & 69.2\\ 

 \hline
 \hline

-BIQI & 28.3 & 28.28 & 28.4 & 28.28\\ 
+PSNR-HVS-M & 72.9 & 75.39 & 78.6 (\textbf{-0.8\%}) & 75.5  & 76.67 & {79.23} & 71.8  & 74.3\\ 
+%\hline
+%BIQI & 28.3 & 28.28 & 28.4 & 28.28 & 28.28 & 28.2 & 28.2\\ 

 \hline
 \hline

-wPSNR & 86.43& 80.59 & 77.47& 83.03\\ 
+wPSNR & 77.47 & 80.59 & 86.43(\textbf{-1.6\%})& 86.28  & 83.03 & {88.6} & 76.7 & 83& 83.8 & 90.4 & 85.2 & 91.9\\ 

 \hline
 \end{tabular}
 \hline
 \end{tabular}

+\end{small}
+\begin{footnotesize}
+\vspace{2em}
+Variances given in bold font express the quality differences between 
+HUGO and STABYLO with  STC+adaptive parameters.
+\end{footnotesize}
+

 \end{center}
 \end{center}

-\caption{Quality Measures of Steganography Approaches\label{table:quality}} 
-\end{table}
+\caption{Quality measures of steganography approaches\label{table:quality}}
+\end{table*}

 
 

+
+
+Results are summarized in Table~\ref{table:quality}.

 Let us give an interpretation of these experiments.
 First of all, the adaptive strategy produces images with lower distortion 
 Let us give an interpretation of these experiments.
 First of all, the adaptive strategy produces images with lower distortion 

-than the one of images resulting from the 10\% fixed strategy.
+than the images resulting from the 10\% fixed strategy.

 Numerical results are indeed always greater for the former strategy than 
 Numerical results are indeed always greater for the former strategy than 

-for the latter, except for the BIQI metrics where differences are not relevant.
+for the latter one.

 These results are not surprising since the adaptive strategy aims at 
 These results are not surprising since the adaptive strategy aims at 

-embedding messages whose length is decided according to a higher threshold
+embedding messages whose length is decided according to an higher threshold

 into the edge detection.  
 Let us focus on the quality of HUGO images: with a given fixed 
 into the edge detection.  
 Let us focus on the quality of HUGO images: with a given fixed 

-embedding rate (10\%) 
+embedding rate (10\%), 

 HUGO always produces images whose quality is higher than the STABYLO's one.
 HUGO always produces images whose quality is higher than the STABYLO's one.

-However, our approach nevertheless provides better results with the strategy 
-adaptive+STC in a lightweight manner, as motivated in the introduction.      
+However our approach is always better than EAISLSBMR since this one may modify 
+the two least significant bits.
+
+If we combine \emph{adaptive} and \emph{STC} strategies 
+(which leads to an average embedding rate equal to 6.35\%)
+our approach  provides metrics equivalent to those provided by HUGO.
+In this column STC(7) stands for embedding data in the LSB whereas
+in STC(6), data are hidden in the last two  significant bits. 

 
 
 
 

-Let us now compare the STABYLO approach with other edge based steganography
-schemes with respect to the image quality.
-First of all, the Edge Adaptive
-scheme detailed in~\cite{Luo:2010:EAI:1824719.1824720} 
-executed with a 10\% embedding rate 
-has the same PSNR but a lower wPSNR than our:
-these two metrics are respectively equal to 61.9 and 68.9. 
-Next both the approaches~\cite{DBLP:journals/eswa/ChenCL10,Chang20101286}
-focus on increasing the payload while the PSNR is acceptable, but 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.

 
 

+The quality variance between HUGO and STABYLO for these parameters
+is given in bold font. It is always close to 1\% which confirms 
+the objective presented in the motivations:
+providing an efficient steganography approach in a lightweight manner.

 
 
 
 

+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. 

 
 

-\subsection{Steganalysis}

 
 
 
 
 
 

-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.
+\subsection{Steganalysis}\label{sub:steg}

 
 
 
 
 
 

-\begin{table}
+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.
+This approach  aims at detecting hidden bits in grayscale natural
+images and is 
+considered as state of the art steganalysers in the spatial domain~\cite{FK12}.
+%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{center}

-\begin{tabular}{|c|c|c|c|c|}
+\begin{small}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}

 \hline
 \hline

-Schemes & \multicolumn{3}{|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
 \hline

-Embedding &   \multicolumn{2}{|c|}{Adaptive} & Fixed & Fixed \\
+Embedding & Fixed &   \multicolumn{3}{|c|}{Adaptive (about 6.35\%)}  & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. \\

 \hline
 \hline

-Rate &   + STC &  + sample & 10\% & 10\%\\ 
+Rate & 10\% &  + sample &   +STC(7) & +STC(6)   & 10\%& 6.35\%& 10\%& 6.35\% & 10\%& 6.35\%& 10\%& 6.35\%\\ 

 \hline
 \hline

-AUMP & 0.39  & 0.33  & 0.22     &  0.50     \\
-\hline
-Ensemble Classifier & 0.47 & 0.44 & 0.35     & 0.48     \\
+%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}
 
 \hline
 \end{tabular}

+\end{small}

 \end{center}
 \caption{Steganalysing STABYLO\label{table:steganalyse}} 
 \end{center}
 \caption{Steganalysing STABYLO\label{table:steganalyse}} 

-\end{table}
+\end{table*}
+
+
+Results 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, which
+is the most secure steganographic tool, as far as we know. 
+However by combining \emph{adaptive} and \emph{STC} strategies
+our approach obtains similar results to HUGO ones.

 
 

+%%%%et pour b= 6 ?

 
 

-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.   

 
 

+Compared to EAILSBMR, we obtain better results when the strategy is 
+\emph{adaptive}. 
+However due to its 
+huge number of integration features, it is not lightweight, which justifies 
+in the authors' opinion the consideration of the proposed method.