integration de remarques de reviewers

diff --git a/complexity.tex b/complexity.tex
index d19f6e2f11bd5f8c8ce0cc4b8c1d32e2bdae4d21..a5904a7efcc25a84ab0136ae95d860a200ad4eac 100644 (file)
--- a/complexity.tex
+++ b/complexity.tex
@@ -7,7 +7,7 @@ WOW~\cite{conf/wifs/HolubF12}, and UNIWARD~\cite{HFD14}.
 Each of these scheme starts with the computation of the distortion cost 
 for each pixel switch and is later followed by the STC algorithm.
 Since this last step is shared by all, 
 Each of these scheme starts with the computation of the distortion cost 
 for each pixel switch and is later followed by the STC algorithm.
 Since this last step is shared by all, 

-we separately eavluate this complexity.
+we separately evaluate this complexity.

 In all the rest of this section, we consider a $n \times n$ square image. 
 
 First of all, HUGO starts with computing the second order SPAM Features.
 In all the rest of this section, we consider a $n \times n$ square image. 
 
 First of all, HUGO starts with computing the second order SPAM Features.


@@ -55,8 +55,8 @@ This distortion computation step is thus in $\theta(6n^4\ln(n) + n^2)$.
 Our edge selection is based on a Canny  Filter. When applied on a 
 $n \times n$ square image, the noise reduction step is in $\theta(5^3 n^2)$.
 Next, let $T$ be the size of the canny mask.
 Our edge selection is based on a Canny  Filter. When applied on a 
 $n \times n$ square image, the noise reduction step is in $\theta(5^3 n^2)$.
 Next, let $T$ be the size of the canny mask.

-Computing gradients is in $\theta(4Tn)$ since derivatives of each direction (vertical or horizontal) 
-are in $\theta(2Tn)$.
+Computing gradients is in $\theta(4Tn^2)$ since derivatives of each direction (vertical or horizontal) 
+are in $\theta(2Tn^2)$.

 Finally, thresholding with hysteresis is in $\theta(n^2)$.
 The overall complexity is thus in $\theta((5^3+4T+1)n^2)$.
 
 Finally, thresholding with hysteresis is in $\theta(n^2)$.
 The overall complexity is thus in $\theta((5^3+4T+1)n^2)$.
 


@@ -71,18 +71,18 @@ matrix. Its complexity is thus negligible compared with the embedding map
 construction.
 
 The Fig.~\ref{fig:compared}
 construction.
 
 The Fig.~\ref{fig:compared}

-summarizes the complexity of the embedding map construction, for Hugo, Wow 
-and Uniward. It deals with square images
+summarizes the complexity of the embedding map construction, for
+WOW/UNIWARD, HUGO, and STABYLO. It deals with square images

 of size $n \times n$ when $n$ ranges from 
 512 to 4096. The $y$-coordinate is expressed in a logarithm scale.
 of size $n \times n$ when $n$ ranges from 
 512 to 4096. The $y$-coordinate is expressed in a logarithm scale.

-It shows that the complexity of all algorithms
+It shows that the complexity of all the algorithms

 is dramatically larger than the one of the STABYLO scheme. 
 is dramatically larger than the one of the STABYLO scheme. 

-Thanks to these complexity results, we claim that STABYLO is lightweight. 
+Thanks to these complexity results, we claim that our approach is lightweight. 

 \begin{figure}
 \begin{center}
 \includegraphics[scale=0.4]{complexity}
 \end{center}
 \begin{figure}
 \begin{center}
 \includegraphics[scale=0.4]{complexity}
 \end{center}

-\caption{Complexity evaluation of Wow/Uniward, Hugo, and Stabylo}
+\caption{Complexity evaluation of WOW/UNIWARD, HUGO, and STABYLO}

 \label{fig:compared} 
 \end{figure}
 
 \label{fig:compared} 
 \end{figure}
 

diff --git a/experiments.tex b/experiments.tex
index 6660072af5410e4ad0c771183a3c0eb63cd8c17d..5ba43dfa16ae206dcee8557c46adc9ef457b7645 100644 (file)
--- a/experiments.tex
+++ b/experiments.tex
@@ -1,3 +1,5 @@
+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 $512\times 512$
 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 $512\times 512$


@@ -10,7 +12,7 @@ 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 
 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.
+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 
 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 


@@ -44,19 +46,17 @@ $$
 \end{table}
 
 
 \end{table}
 
 

-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. 
-
-
-
-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. 
+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.  

 
 
 
 
 
 


@@ -67,14 +67,13 @@ The visual quality of the STABYLO scheme is evaluated in this section.
 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{psnrhvsm11}, 
 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{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
 account the Human Visual System (HVS).
 The other ones have been designed to tackle this problem.
 
 and 
 the weighted PSNR (wPSNR)~\cite{DBLP:conf/ih/PereiraVMMP01}.
 The first one is widely used but does not take into
 account the Human Visual System (HVS).
 The other ones have been designed to tackle this problem.
 

-If we apply them on the running example, 
+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 
 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 


@@ -86,30 +85,24 @@ If $b$ is 6, these values are respectively equal to
 \begin{table*}
 \begin{center}
 \begin{small}
 \begin{table*}
 \begin{center}
 \begin{small}

+\setlength{\tabcolsep}{3pt}

 \begin{tabular}{|c|c|c||c|c|c|c|c|c|c|c|c|c|}
 \hline
 Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\
 \hline
 Embedding &   Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} &  Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive \\
 \hline
 \begin{tabular}{|c|c|c||c|c|c|c|c|c|c|c|c|c|}
 \hline
 Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\
 \hline
 Embedding &   Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} &  Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive \\
 \hline

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

 \hline
 \hline

-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\\ 
+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
 \hline

-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\\ 
+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
 \hline

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


@@ -117,39 +110,32 @@ HUGO and STABYLO with  STC+adaptive parameters.
 
 
 Results are summarized in Table~\ref{table:quality}.
 
 
 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. 
+
+

 Let us give an interpretation of these experiments.
 Let us give an interpretation of these experiments.

-First of all, the adaptive strategy produces images with lower distortion 
+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.
 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 an higher threshold
+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.  
 into the edge detection.  

-Let us focus on the quality of HUGO images: with a given fixed 
-embedding rate (10\%), 
-HUGO always produces images whose quality is higher than the STABYLO's one.
-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. 

 
 
 
 

-
-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.
+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. 
+% 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. 

 
 
 
 
 
 


@@ -162,9 +148,17 @@ 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.
 % 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}.
+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
 %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


@@ -179,13 +173,14 @@ considered as state of the art steganalysers in the spatial domain~\cite{FK12}.
 \begin{table*}
 \begin{center}
 \begin{small}
 \begin{table*}
 \begin{center}
 \begin{small}

+\setlength{\tabcolsep}{3pt}

 \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
 \hline
 Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} &  \multicolumn{2}{|c|}{WOW} &  \multicolumn{2}{|c|}{UNIWARD}\\
 \hline
 Embedding & Fixed &   \multicolumn{3}{|c|}{Adaptive (about 6.35\%)}  & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. \\
 \hline
 \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
 \hline
 Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} &  \multicolumn{2}{|c|}{WOW} &  \multicolumn{2}{|c|}{UNIWARD}\\
 \hline
 Embedding & Fixed &   \multicolumn{3}{|c|}{Adaptive (about 6.35\%)}  & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. \\
 \hline

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

 \hline
 %AUMP & 0.22 & 0.33 & 0.39  &   0.45    &  0.50 &  0.50 & 0.49 & 0.50 \\
 %\hline
 \hline
 %AUMP & 0.22 & 0.33 & 0.39  &   0.45    &  0.50 &  0.50 & 0.49 & 0.50 \\
 %\hline


@@ -199,20 +194,22 @@ Ensemble Classifier & 0.35 & 0.44 & 0.47 & 0.47     & 0.48 &  0.49  &  0.43  & 0
 \end{table*}
 
 
 \end{table*}
 
 

-Results are summarized in Table~\ref{table:steganalyse}.
+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. 
 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 ?
-
+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 
 
 Compared to EAILSBMR, we obtain better results when the strategy is 

-\emph{adaptive}. 
+Adaptive. 

 However due to its 
 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.   
+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.

diff --git a/intro.tex b/intro.tex
index 28463eebe0471d0c2fb800af4fce359f6424a6a2..4c995485716a5bc6b9d0b6babe006ab7178f5350 100644 (file)
--- a/intro.tex
+++ b/intro.tex
@@ -66,9 +66,9 @@ Due to this distortion measures, HUGO, WOW and UNIWARD allow
 to embed messages that are $7$ times longer than the former
 ones with the same level of 
 indetectability as LSB matching. 
 to embed messages that are $7$ times longer than the former
 ones with the same level of 
 indetectability as LSB matching. 

-However, this improvement is time consuming, mainly due to
+However, this improvement has a larger computation cost, mainly due to

  the distortion function
  the distortion function

-computation. 
+calculus. 

 
 
 There remains a large place between random selection of LSB and feature based modification of pixel values.
 
 
 There remains a large place between random selection of LSB and feature based modification of pixel values.

diff --git a/main.tex b/main.tex
index 281d2d6694e477d08aeb464f0dab939ed8edef77..e6405e611c0e4388f9ba299e0841d39335c8533b 100755 (executable)
--- a/main.tex
+++ b/main.tex
@@ -83,7 +83,7 @@ Adaptive,  Bbs, and binarY embedding at LOw cost}
 A new steganographic method called STABYLO is introduced in 
 this research work.
 Its main advantage is to be much lighter than the so-called
 A new steganographic method called STABYLO is introduced in 
 this research work.
 Its main advantage is to be much lighter than the so-called

-HUGO, WOW, and UNIWARDS schemes, the state of the art
+HUGO, WOW, and UNIWARD schemes, the state of the art

 steganographic processes.
 Additionally to this effectiveness, 
 quite comparable results through noise measures like PSNR-HVS-M 
 steganographic processes.
 Additionally to this effectiveness, 
 quite comparable results through noise measures like PSNR-HVS-M 


@@ -120,15 +120,26 @@ The STABYLO algorithm, whose acronym means STeganography with
 Adaptive,  Bbs, and binarY embedding at LOw cost, has been introduced 
 in this document as an efficient method having comparable, though
 somewhat smaller, security than well-known
 Adaptive,  Bbs, and binarY embedding at LOw cost, has been introduced 
 in this document as an efficient method having comparable, though
 somewhat smaller, security than well-known

-steganographic schemes lite 
+steganographic schemes  

 HUGO, WOW, and UNIWARD.
 This edge-based steganographic approach embeds a Canny
 HUGO, WOW, and UNIWARD.
 This edge-based steganographic approach embeds a Canny

-detection filter, the Blum-Blum-Shub cryptographically secure
-pseudorandom number generator, together with Syndrome-Trellis Codes
+detection filter, the secure Blum-Blum-Shub cryptosystem 
+with its pseudorandom number generator, 
+together with Syndrome-Trellis Codes

 for minimizing distortion.
 for minimizing distortion.

-After having introduced with details the proposed method,
-we have evaluated it through noise measures (namely, the PSNR, PSNR-HVS-M,
-and weighted PSNR), we have used well-established steganalysers.
+The complexity study of our proposed method and of the  
+state of the art steganographic tools has shown that our approach 
+has the lowest computation cost among all. 
+This justifies the lightweight attribute of our scheme.
+The evaluation of introduced noise measures 
+(namely, the PSNR, PSNR-HVS-M, and weighted PSNR), 
+and of its embedding through stegenalysers (namely Ensemble Classifier)  
+have shown that STABYLO is efficient enough to 
+produce qualitative images and 
+to face steganalysers.
+
+
+

 
 % Of course, other detectors like the fuzzy edge methods
 % deserve much further attention, which is why we intend 
 
 % Of course, other detectors like the fuzzy edge methods
 % deserve much further attention, which is why we intend 

diff --git a/ourapproach.tex b/ourapproach.tex
index 249e1bed6954d1ce2310b52a3fec6f56efb2823c..12b3a32e57196247fac6bfca83e750c98f9d444c 100644 (file)
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -50,11 +50,13 @@ Let us first focus on the data embedding.
 \subsection{Security considerations}\label{sub:bbs}
 Among the methods of  message encryption/decryption 
 (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
 \subsection{Security considerations}\label{sub:bbs}
 Among the methods of  message encryption/decryption 
 (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)

-we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
+we implement the asymmetric 
+Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}

 that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} 
 pseudorandom number generator (PRNG) and the 
 XOR binary function.
 that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} 
 pseudorandom number generator (PRNG) and the 
 XOR binary function.

-It has been proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG 
+The main justification of this choice 
+is that it has been proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG 

 has the property of cryptographical security, \textit{i.e.}, 
 for any sequence of $L$ output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
 there is no algorithm, whose time complexity is polynomial  in $L$, and 
 has the property of cryptographical security, \textit{i.e.}, 
 for any sequence of $L$ output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
 there is no algorithm, whose time complexity is polynomial  in $L$, and 


@@ -115,13 +117,15 @@ Moreover, to provide edge gradient value,
 the Canny algorithm computes derivatives  
 in the two directions with respect to a mask of size $T$. 
 The higher $T$ is, the coarse the approach is. Practically, 
 the Canny algorithm computes derivatives  
 in the two directions with respect to a mask of size $T$. 
 The higher $T$ is, the coarse the approach is. Practically, 

-$T$ is set with $3$, $3$, or $7$.
+$T$ is set with $3$, $5$, or $7$.

 In our flowcharts, this step is represented by ``Edge Detection(b, T, X)''.
 
 
 Let $x$ be the sequence of these bits. 
 The next  section presents how to adapt our scheme 
 In our flowcharts, this step is represented by ``Edge Detection(b, T, X)''.
 
 
 Let $x$ be the sequence of these bits. 
 The next  section presents how to adapt our scheme 

-when the size of $x$  is not sufficient for the message $m$ to embed.
+with respect to the size
+of the message $m$ to embed and the size of the cover $x$.
+

 
 
  
 
 
  


@@ -131,7 +135,7 @@ when the size of $x$  is not sufficient for the message $m$ to embed.
 
 \subsection{Adaptive embedding rate}\label{sub:adaptive}
 Two strategies have been developed in our approach, 
 
 \subsection{Adaptive embedding rate}\label{sub:adaptive}
 Two strategies have been developed in our approach, 

-depending on the embedding rate that is either \emph{adaptive} or \emph{fixed}.
+depending on the embedding rate that 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 the message length that can be inserted is.
 Practically, a set of edge pixels is computed according to the 
 In the former the embedding rate depends on the number of edge pixels.
 The higher it is, the larger the message length that can be inserted is.
 Practically, a set of edge pixels is computed according to the 


@@ -170,7 +174,7 @@ It  is further referred to as \emph{STC} and is detailed in the next section.
 
 
 
 
 
 

-\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
+\subsection{Minimizing distortion with Syndrome-Trellis Codes}\label{sub:stc}

 \input{stc}
 
 
 \input{stc}
 
 


@@ -302,7 +306,7 @@ So, we choose to modify the same amount of bits (9,320) and keep STC optimizing
 which bits to change among  the 36,910 ones.
 
 In the two cases, about the third part of the poem is hidden into the cover. 
 which bits to change among  the 36,910 ones.
 
 In the two cases, about the third part of the poem is hidden into the cover. 

-Results with \emph{adaptive} and \textit{STC} strategies are presented in 
+Results with {Adaptive} and {STC} strategies are presented in 

 Fig.~\ref{fig:lenastego}.
 
 \begin{figure}[t]
 Fig.~\ref{fig:lenastego}.
 
 \begin{figure}[t]


@@ -345,7 +349,11 @@ V_{ij}= \left\{
 \right..
 $$
 This function allows to emphasize differences between contents.
 \right..
 $$
 This function allows to emphasize differences between contents.

-Notice that 
+Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary 
+and this image only contains 0 and 75 values.
+Similarly, if $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary 
+and the image contains all the values in $\{0,75,150,225\}$.
+

 
 
 \begin{figure}[t]
 
 
 \begin{figure}[t]


@@ -374,8 +382,4 @@ Notice that
 \end{figure}
 
 
 \end{figure}
 
 

-Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary 
-and this image only contains 0 and 75 values.
-Similarly, when $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary 
-and the image contains all the values in $\{0,75,150,225\}$.