corrections christophes

diff --git a/experiments.tex b/experiments.tex
index 9c7302585af6241dcdcd94d1b640cb00b2bd7d4f..2fc8a68527d8156735290d45b82898090e7d4289 100644 (file)
--- a/experiments.tex
+++ b/experiments.tex
@@ -7,8 +7,8 @@ this set of cover images since this paper is more focused on
 the methodology than benchmarking.    
 Our approach is always compared to Hugo~\cite{DBLP:conf/ih/PevnyFB10}
 and to EAISLSBMR~\cite{Luo:2010:EAI:1824719.1824720}.
 the methodology than benchmarking.    
 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 less detectable information hiding tool in spatial domain 
-and the later is the work which is close to ours, as far as we know. 
+The former is the least detectable information hiding tool in spatial domain 
+and the later is the work that is close to ours, as far as we know. 

 
 
 
 
 
 


@@ -23,7 +23,7 @@ the quality analysis and the security of our scheme.
 
  
 
 
  
 

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

 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 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), 


@@ -71,17 +71,17 @@ HUGO and STABYLO with  STC+adaptive parameters.
 \end{footnotesize}
 
 \end{center}
 \end{footnotesize}
 
 \end{center}

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

 \end{table*}
 
 
 
 \end{table*}
 
 
 

-Results are summarized into the Table~\ref{table:quality}.
+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 
 than the one of images resulting from the 10\% fixed strategy.
 Numerical results are indeed always greater for the former strategy than 
 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.
 Numerical results are indeed always greater for the former strategy than 

-for the latter.
+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
 into the edge detection.  
 These results are not surprising since the adaptive strategy aims at 
 embedding messages whose length is decided according to an higher threshold
 into the edge detection.  


@@ -94,7 +94,7 @@ the two least significant bits whereas STABYLO only alter LSB.
 If we combine \emph{adaptive} and \emph{STC} strategies 
 (which leads to an average embedding rate equal to 6.35\%)
 our approach  provides equivalent metrics than HUGO.
 If we combine \emph{adaptive} and \emph{STC} strategies 
 (which leads to an average embedding rate equal to 6.35\%)
 our approach  provides equivalent metrics than HUGO.

-In this column STC(7) stands for embeding data in the LSB whereas
+In this column STC(7) stands for embedding data in the LSB whereas

 in STC(6), data are hidden in the two last significant bits. 
 
 
 in STC(6), data are hidden in the two last significant bits. 
 
 


@@ -121,7 +121,7 @@ give quality metrics for fixed embedding rates from a large base of images.
 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 steganalysers.
 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 steganalysers.

-Both aims at detecting hidden bits in grayscale natural images and are 
+Both aim 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 an adaptive Asymptotically Uniformly Most Powerful
 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 an adaptive Asymptotically Uniformly Most Powerful


@@ -130,7 +130,7 @@ an image has stego content or not.
 This approach is dedicated to verify whether LSB has been modified or not.
 In the latter, the authors show that the 
 machine learning step, which is often
 This approach is dedicated to verify whether LSB has been modified or not.
 In the latter, the authors show that the 
 machine learning step, which is often

-implemented as support vector machine,
+implemented as a support vector machine,

 can be favorably executed thanks to an ensemble classifier.
 
 
 can be favorably executed thanks to an ensemble classifier.
 
 

diff --git a/intro.tex b/intro.tex
index deecdb76e25e766a4216967ba442cf57c92f0f81..ccdad7553ea62011f2c5604748df74a925531391 100644 (file)
--- a/intro.tex
+++ b/intro.tex
@@ -5,21 +5,21 @@ It belongs to the well-known large category
 of spatial least significant bits (LSBs) replacement schemes.
 Let us recall that, in this LSBR category, a subset of all the LSBs of the cover image is modified 
 with a secret bit stream depending on: a secret key, the cover, and the message to embed.
 of spatial least significant bits (LSBs) replacement schemes.
 Let us recall that, in this LSBR category, a subset of all the LSBs of the cover image is modified 
 with a secret bit stream depending on: a secret key, the cover, and the message to embed.

-In this well studied steganographic approach,
+In this well-studied steganographic approach,

 if we consider that a LSB is the last bit of each pixel value,  
 pixels with an even value (resp. an odd value) 
 are never decreased (resp. increased), 
 thus such schemes may break the 
 structural symmetry of the host images.
 And these structural alterations can be detected by 
 if we consider that a LSB is the last bit of each pixel value,  
 pixels with an even value (resp. an odd value) 
 are never decreased (resp. increased), 
 thus such schemes may break the 
 structural symmetry of the host images.
 And these structural alterations can be detected by 

-well designed statistical investigations, leading to known steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.
+well-designed statistical investigations, leading to known steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.

 
 Let us recall too that this drawback 
 can be corrected considering the LSB matching (LSBM) subcategory, in which
 the $+1$ or $-1$ is randomly added to the cover pixel LSB value 
 only if this one does not correspond to the secret bit.
 %TODO : modifier ceci
 
 Let us recall too that this drawback 
 can be corrected considering the LSB matching (LSBM) subcategory, in which
 the $+1$ or $-1$ is randomly added to the cover pixel LSB value 
 only if this one does not correspond to the secret bit.
 %TODO : modifier ceci

-Since it is possible to make that probabilities of increasing or decreasing the pixel value, for instance by considering well encrypted hidden messages, usual statistical approaches 
+Since it is possible to make that probabilities of increasing or decreasing the pixel value, for instance by considering well-encrypted hidden messages, usual statistical approaches 

 cannot be applied here to discover stego-contents in LSBM.
 The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/Ker05,FK12},
 which classify images according to extracted features from neighboring elements of residual noise.  
 cannot be applied here to discover stego-contents in LSBM.
 The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/Ker05,FK12},
 which classify images according to extracted features from neighboring elements of residual noise.  


@@ -72,7 +72,7 @@ Edge based steganographic schemes have already been  studied,
 the most interesting 
 approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and 
 in~\cite{DBLP:journals/eswa/ChenCL10}.
 the most interesting 
 approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and 
 in~\cite{DBLP:journals/eswa/ChenCL10}.

-In the former, the authors presents the Edge Adaptive
+In the former, the authors present the Edge Adaptive

 Image Steganography based on LSB matching revisited further denoted as to 
 EAISLSBMR. This approach selects sharper edge
  regions with respect 
 Image Steganography based on LSB matching revisited further denoted as to 
 EAISLSBMR. This approach selects sharper edge
  regions with respect 


@@ -83,7 +83,7 @@ The authors show that their proposed method is more efficient than all the LSB,
 thanks to extensive experiments.
 However, it has been shown that the distinguishing error with LSB embedding is lower than 
 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.
 thanks to extensive experiments.
 However, it has been shown that the distinguishing error with LSB embedding is lower than 
 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.

-We thus propose to take benefit of these optimized embedding, provided they are not too time consuming.
+We thus propose to take benefit of these optimized embeddings, provided they are not too time consuming.

 In the latter, an hybrid edge detector is presented followed by an ad hoc
 embedding. 
 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993} 
 In the latter, an hybrid edge detector is presented followed by an ad hoc
 embedding. 
 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993} 


@@ -96,7 +96,7 @@ schemes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf
 produce stego contents 
 by only considering the payload, not the type of image signal: the higher the payload is, 
 the better the approach is said to be. 
 produce stego contents 
 by only considering the payload, not the type of image signal: the higher the payload is, 
 the better the approach is said to be. 

-Contrarily, we argue that some images should not be taken as a cover because of the nature of their signal.
+Contrarily, we argue that some images should not be taken as a cover because of the nature of their signals.

 Consider for instance a uniformly black image: a very tiny modification of its pixels can be easily detectable.  
 The approach we propose is thus to provide a self adaptive algorithm with a high payload, which depends on the  cover signal. 
 % Message extraction is achieved by computing the same
 Consider for instance a uniformly black image: a very tiny modification of its pixels can be easily detectable.  
 The approach we propose is thus to provide a self adaptive algorithm with a high payload, which depends on the  cover signal. 
 % Message extraction is achieved by computing the same


@@ -113,7 +113,7 @@ even in the worst case scenario, the attacker
 will not be able to obtain the original message content.
 Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.
 
 will not be able to obtain the original message content.
 Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.
 

-To sum up, in this research work, well studied and experimented
+To sum up, in this research work, well-studied and experimented

 techniques of signal processing (adaptive edges detection), 
 coding theory (syndrome-trellis codes), and cryptography 
 (Blum-Goldwasser encryption protocol) are combined 
 techniques of signal processing (adaptive edges detection), 
 coding theory (syndrome-trellis codes), and cryptography 
 (Blum-Goldwasser encryption protocol) are combined 


@@ -124,7 +124,7 @@ consideration the cover image and to be compatible with small computation resour
 The remainder of this document is organized as follows. 
 Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme and applies it on a running example.
 Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach,
 The remainder of this document is organized as follows. 
 Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme and applies it on a running example.
 Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach,

-and compares it to the state of the art steganographic schemes.
+and compare them to the state of the art steganographic schemes.

 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
 
 
 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
 
 

diff --git a/main.tex b/main.tex
index 5a7e01e23c07fc0f018ea8527b1cc5301809cf2d..c4bb7fc538bf378752d6948cd595c827c5faaaf0 100755 (executable)
--- a/main.tex
+++ b/main.tex
@@ -5,6 +5,8 @@
 \usepackage{subfig}
 \usepackage{color}
 \usepackage{mathtools,etoolbox}
 \usepackage{subfig}
 \usepackage{color}
 \usepackage{mathtools,etoolbox}

+\usepackage{cite}
+

 
 \tolerance=1
 \emergencystretch=\maxdimen
 
 \tolerance=1
 \emergencystretch=\maxdimen


@@ -80,15 +82,15 @@ edge-based steganographic approach}
 
 
 %IEEEtran, journal, \LaTeX, paper, template.
 
 
 %IEEEtran, journal, \LaTeX, paper, template.

-\keywords{Steganography, least-significant-bit (LSB)-based steganography, edge detection, Canny filter, security, syndrome trellis code}
+\keywords{Steganography, least-significant-bit (LSB)-based steganography, edge detection, Canny filter, security, syndrome trellis codes}

 
 
 
 
 \abstracttext{A novel steganographic method called STABYLO is introduced in 
 this research work.
 
 
 
 
 \abstracttext{A novel steganographic method called STABYLO is introduced in 
 this research work.

-Its main advantage for being is to be much lighter than the so-called
-Highly Undetectable steGO (HUGO) scheme, a well known state of the art
+Its main advantage is to be much lighter than the so-called
+Highly Undetectable steGO (HUGO) scheme, a well-known state of the art

 steganographic process in spatial domain.
 Additionally to this effectiveness, 
 quite comparable results through noise measures like PSNR-HVS-M, 
 steganographic process in spatial domain.
 Additionally to this effectiveness, 
 quite comparable results through noise measures like PSNR-HVS-M, 


@@ -123,7 +125,7 @@ a scheme that can reasonably face up-to-date steganalysers.}
 The STABYLO algorithm, whose acronym means STeganography 
 with cAnny, Bbs, binarY embedding at LOw cost, has been introduced 
 in this document as an efficient method having comparable, though
 The STABYLO algorithm, whose acronym means STeganography 
 with cAnny, Bbs, binarY embedding at LOw cost, has been introduced 
 in this document as an efficient method having comparable, though

-somewhat smaller, security than the well known
+somewhat smaller, security than the well-known

 Highly Undetectable steGO (HUGO) steganographic scheme.
 This edge-based steganographic approach embeds a Canny
 detection filter, the Blum-Blum-Shub cryptographically secure
 Highly Undetectable steGO (HUGO) steganographic scheme.
 This edge-based steganographic approach embeds a Canny
 detection filter, the Blum-Blum-Shub cryptographically secure


@@ -131,7 +133,7 @@ pseudorandom number generator, together with Syndrome-Trellis Codes
 for minimizing distortion.
 After having introduced with details the proposed method,
 we have evaluated it through noise measures (namely, the PSNR, PSNR-HVS-M, 
 for minimizing distortion.
 After having introduced with details the proposed method,
 we have evaluated it through noise measures (namely, the PSNR, PSNR-HVS-M, 

-BIQI, and weighted PSNR) and using well established steganalysers.
+BIQI, and weighted PSNR) and using well-established 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 b007dd00eb14f4b016664f6bce01f0aee64783e8..9cf0384609ab84a68d9fe1c22ec114405e3bc807 100644 (file)
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -35,7 +35,7 @@ Let us first focus on the data embedding.
       \label{fig:sch:ext}
     }%\hfill
   \end{center}
       \label{fig:sch:ext}
     }%\hfill
   \end{center}

-  \caption{The STABYLO Scheme.}
+  \caption{The STABYLO scheme}

   \label{fig:sch}
 \end{figure*}
 
   \label{fig:sch}
 \end{figure*}
 


@@ -46,7 +46,7 @@ Let us first focus on the data embedding.
 
 
 
 
 
 

-\subsection{Security Considerations}\label{sub:bbs}
+\subsection{Security considerations}\label{sub:bbs}

 Among 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}
 Among 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}


@@ -57,7 +57,7 @@ It has been indeed 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 

-which allows to find $x_{i-1}$ and $x_{i+L}$ with a probability greater
+which allows to find $x_{i-1}$ or $x_{i+L}$ with a probability greater

 than $1/2$.
 Equivalent formulations of such a property can
 be found. They all lead to the fact that,
 than $1/2$.
 Equivalent formulations of such a property can
 be found. They all lead to the fact that,


@@ -69,7 +69,7 @@ Starting thus with a key $k$ and the message \textit{mess} to hide,
 this step computes a message $m$, which is the encrypted version  of \textit{mess}.
 
 
 this step computes a message $m$, which is the encrypted version  of \textit{mess}.
 
 

-\subsection{Edge-Based Image Steganography}\label{sub:edge}
+\subsection{Edge-based image steganography}\label{sub:edge}

 
 
 The edge-based image
 
 
 The edge-based image


@@ -92,9 +92,9 @@ In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, \ldo
 a first-order derivative (gradient magnitude, etc.) is computed 
 to search for local maxima, whereas in second order ones, zero crossings in a second-order derivative, like the Laplacian computed from the image,
 are searched in order to find edges.
 a first-order derivative (gradient magnitude, etc.) is computed 
 to search for local maxima, whereas in second order ones, zero crossings in a second-order derivative, like the Laplacian computed from the image,
 are searched in order to find edges.

-As for as fuzzy edge methods are concerned, they are obviously based on fuzzy logic to highlight edges.
+As far as fuzzy edge methods are concerned, they are obviously based on fuzzy logic to highlight edges.

 
 

-Canny filters, on their parts, are an old family of algorithms still remaining a state-of-the-art edge detector. They can be well approximated by first-order derivatives of Gaussians.
+Canny filters, on their parts, are an old family of algorithms still remaining a state of the art edge detector. They can be well-approximated by first-order derivatives of Gaussians.

 As the Canny algorithm is well known and studied, fast, and implementable
 on many  kinds of architectures like FPGAs, smartphones,  desktop machines, and
 GPUs, we have chosen this edge detector for illustrative purpose.
 As the Canny algorithm is well known and studied, fast, and implementable
 on many  kinds of architectures like FPGAs, smartphones,  desktop machines, and
 GPUs, we have chosen this edge detector for illustrative purpose.


@@ -118,7 +118,7 @@ and the LSB of pixels if $b$ is 7.
 
 
 Let $x$ be the sequence of these bits. 
 
 
 Let $x$ be the sequence of these bits. 

-The next  section section presents how our scheme 
+The next  section presents how our scheme 

 adapts  when the size of $x$  is not sufficient for the message $m$ to embed.
 
 
 adapts  when the size of $x$  is not sufficient for the message $m$ to embed.
 
 


@@ -127,7 +127,7 @@ adapts  when the size of $x$  is not sufficient for the message $m$ to embed.
 
 
 
 
 
 

-\subsection{Adaptive Embedding Rate}\label{sub:adaptive}
+\subsection{Adaptive embedding rate}\label{sub:adaptive}

 Two strategies have been developed in our scheme, 
 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.
 Two strategies have been developed in our scheme, 
 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.


@@ -136,7 +136,7 @@ Practically, a set of edge pixels is computed according to the
 Canny algorithm with an high threshold.
 The message length is thus defined to be less than 
 half of this set cardinality.
 Canny algorithm with an high threshold.
 The message length is thus defined to be less than 
 half of this set cardinality.

-If $x$ is then to short for $m$, the message is split into sufficient parts
+If $x$ is then too short for $m$, the message is split into sufficient parts

 and a new cover image should be used for the remaining part of the message. 
 
  
 and a new cover image should be used for the remaining part of the message. 
 
  


@@ -182,7 +182,7 @@ 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}
 
 


@@ -216,7 +216,7 @@ It  is further referred to as \emph{STC} and is detailed in the next section.
 
 
 
 
 
 

-\subsection{Data Extraction}\label{sub:extract}
+\subsection{Data extraction}\label{sub:extract}

 The message extraction summarized in Fig.~\ref{fig:sch:ext} 
 follows the data embedding approach 
 since there exists a reverse function for all its steps.
 The message extraction summarized in Fig.~\ref{fig:sch:ext} 
 follows the data embedding approach 
 since there exists a reverse function for all its steps.


@@ -226,19 +226,19 @@ produce the sequence $y$ of LSBs.
 If the STC approach has been selected in embedding, the STC reverse
 algorithm is directly executed to retrieve the encrypted message. 
 This inverse function takes the $H$ matrix as a parameter.
 If the STC approach has been selected in embedding, the STC reverse
 algorithm is directly executed to retrieve the encrypted message. 
 This inverse function takes the $H$ matrix as a parameter.

-Otherwise, \textit{i.e.} if the \emph{sample} strategy is retained,
+Otherwise, \textit{i.e.}, if the \emph{sample} strategy is retained,

 the same random bit selection than in the embedding step 
 is executed with the same seed, given as a key.
 Finally, the Blum-Goldwasser decryption function is executed and the original
 message is extracted.
 
 
 the same random bit selection than in the embedding step 
 is executed with the same seed, given as a key.
 Finally, the Blum-Goldwasser decryption function is executed and the original
 message is extracted.
 
 

-\subsection{Running Example}\label{sub:xpl}
-In this example, the cover image is  Lena 
+\subsection{Running example}\label{sub:xpl}
+In this example, the cover image is  Lena, 

 which is a $512\times512$  image with 256 grayscale levels.
 The message is the poem Ulalume (E. A. Poe), which is constituted by 104 lines, 667
 which is a $512\times512$  image with 256 grayscale levels.
 The message is the poem Ulalume (E. A. Poe), which is constituted by 104 lines, 667

-words, and 3754 characters, \textit{i.e.}  30032 bits.
-Lena and the the first verses are given in Fig.~\ref{fig:lena}.
+words, and 3754 characters, \textit{i.e.},  30032 bits.
+Lena and the first verses are given in Fig.~\ref{fig:lena}.

 
 \begin{figure}
 \begin{center}
 
 \begin{figure}
 \begin{center}


@@ -265,7 +265,7 @@ $~$ In the ghoul-haunted woodland of Weir.
 \end{figure}
 
 The edge detection returns 18641 and 18455 pixels when $b$ is
 \end{figure}
 
 The edge detection returns 18641 and 18455 pixels when $b$ is

-respectively 7 and 6. These edges are represented in Fig.~\ref{fig:edge}
+respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.

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


@@ -289,7 +289,7 @@ respectively 7 and 6. These edges are represented in Fig.~\ref{fig:edge}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}

-  \caption{Edge Detection wrt $b$.}
+  \caption{Edge detection wrt $b$}

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


@@ -297,7 +297,7 @@ respectively 7 and 6. These edges are represented in Fig.~\ref{fig:edge}
 
 Only 9320 bits (resp. 9227 bits) are available for embedding 
 in the former configuration where $b$ is 7 (resp. where $b$ is 6).
 
 Only 9320 bits (resp. 9227 bits) are available for embedding 
 in the former configuration where $b$ is 7 (resp. where $b$ is 6).

-In the both case, about the third part of the poem is hidden into the cover.
+In both cases, about the third part of the poem is hidden into the cover.

 Results with \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.
 
 Results with \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.
 


@@ -322,13 +322,13 @@ Fig.~\ref{fig:lenastego}.
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}

-  \caption{Stego Images wrt $b$.}
+  \caption{Stego images wrt $b$}

   \label{fig:lenastego}
 \end{figure}
 
 
 Finally, differences between the original cover and the stego images  
   \label{fig:lenastego}
 \end{figure}
 
 
 Finally, differences between the original cover and the stego images  

-are presented in Fig.~\ref{fig:lenadiff}. For each pixel pair of pixel $X_{ij}$ and  $Y_{ij}$ ($X$ and $Y$ being the cover and the stego content respectively), 
+are presented in Fig.~\ref{fig:lenadiff}. For each pair of pixel $X_{ij}$ and  $Y_{ij}$ ($X$ and $Y$ being the cover and the stego content respectively), 

 the pixel value $V_{ij}$ of the difference is defined with the following map
 $$
 V_{ij}= \left\{
 the pixel value $V_{ij}$ of the difference is defined with the following map
 $$
 V_{ij}= \left\{


@@ -340,7 +340,7 @@ V_{ij}= \left\{
 \end{array}
 \right..
 $$
 \end{array}
 \right..
 $$

-This function allows to emphasize differences between content.
+This function allows to emphasize differences between contents.

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


@@ -363,6 +363,6 @@ This function allows to emphasize differences between content.
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}

-  \caption{Differences  with Lena's Cover  wrt $b$.}
+  \caption{Differences  with Lena's cover  wrt $b$}

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

diff --git a/stc.tex b/stc.tex
index 91f38d7abb1a7789c37ee8e399c38c99112fa41c..09ae4363ed1e98775c4499b5cdd1c826212bd659 100644 (file)
--- a/stc.tex
+++ b/stc.tex
@@ -71,7 +71,7 @@ First of all, Filler \emph{et al.} compute the matrix $H$
 by placing a small sub-matrix $\hat{H}$ of size $h × w$ next
 to each other and by shifting down by one row. 
 Thanks to this special form of $H$, one can represent
 by placing a small sub-matrix $\hat{H}$ of size $h × w$ next
 to each other and by shifting down by one row. 
 Thanks to this special form of $H$, one can represent

-every solution of  $m=Hy$ as a path through a trellis.
+any solution of  $m=Hy$ as a path through a trellis.

 
 Next, the  process of finding $y$ consists in two stages: a forward and a backward part.
 \begin{enumerate}
 
 Next, the  process of finding $y$ consists in two stages: a forward and a backward part.
 \begin{enumerate}