quelques modifs

[canny.git] / ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index 12b3a32e57196247fac6bfca83e750c98f9d444c..36fefc31a4cba7ed397041b6eee2884ba28482bb 100644 (file)
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -3,7 +3,7 @@ four main steps: the data encryption (Sect.~\ref{sub:bbs}),
 the cover pixel selection (Sect.~\ref{sub:edge}),
 the adaptive payload considerations (Sect.~\ref{sub:adaptive}),
 and how the distortion has been minimized (Sect.~\ref{sub:stc}).
 the cover pixel selection (Sect.~\ref{sub:edge}),
 the adaptive payload considerations (Sect.~\ref{sub:adaptive}),
 and how the distortion has been minimized (Sect.~\ref{sub:stc}).

-The message extraction is then presented  (Sect.~\ref{sub:extract}) while a running example ends this section (Sect.~\ref{sub:xpl}). 
+The message extraction is then presented  (Sect.~\ref{sub:extract}) while a running example ends this section.

 
 
 The flowcharts given in Fig.~\ref{fig:sch}
 
 
 The flowcharts given in Fig.~\ref{fig:sch}


@@ -48,6 +48,8 @@ Let us first focus on the data embedding.
 
 
 \subsection{Security considerations}\label{sub:bbs}
 
 
 \subsection{Security considerations}\label{sub:bbs}

+To provide a self-contained article without any bias, we shor\-tly 
+present the selected encryption process.

 Among the methods of  message encryption/decryption 
 (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
 we implement the asymmetric 
 Among the methods of  message encryption/decryption 
 (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
 we implement the asymmetric 


@@ -140,7 +142,7 @@ 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 
 Canny algorithm with parameters $b=7$ and $T=3$.
 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 
 Canny algorithm with parameters $b=7$ and $T=3$.

-The message length is thus defined to be less than 
+The message length is thus defined to be lesser than 

 half of this set cardinality.
 If $x$ is 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. 
 half of this set cardinality.
 If $x$ is 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. 


@@ -151,13 +153,13 @@ This is the classical approach adopted in steganography.
 Practically, the Canny algorithm generates  
 a set of edge pixels related to increasing values of $T$ and 
 until its cardinality
 Practically, the Canny algorithm generates  
 a set of edge pixels related to increasing values of $T$ and 
 until its cardinality

-is sufficient. Even in this situation, our scheme is adapting 
+is sufficient. Even in this situation, our scheme adapts

 its algorithm to meet all the user's requirements. 
 
 
 Once the map of possibly modified pixels is computed, 
 two methods may further be applied to extract bits that 
 its algorithm to meet all the user's requirements. 
 
 
 Once the map of possibly modified pixels is computed, 
 two methods may further be applied to extract bits that 

-are really modified. 
+are really changed. 

 The first one randomly chooses the subset of pixels to modify by 
 applying the BBS PRNG again. This method is further denoted  as a \emph{sample}.
 Once this set is selected, a classical LSB replacement is applied to embed the 
 The first one randomly chooses the subset of pixels to modify by 
 applying the BBS PRNG again. This method is further denoted  as a \emph{sample}.
 Once this set is selected, a classical LSB replacement is applied to embed the 


@@ -196,14 +198,26 @@ It  is further referred to as \emph{STC} and is detailed in the next section.
 % but the whole approach can be updated to consider 
 % the fuzzy logic edge detector.   
 
 % but the whole approach can be updated to consider 
 % the fuzzy logic edge detector.   
 

-% Next, following~\cite{Luo:2010:EAI:1824719.1824720}, our scheme automatically
-% modifies Canny parameters to get a sufficiently large set of edge bits: this 
-% one is practically enlarged untill its size is at least twice as many larger 
-% than the size of embedded message.
-
-
-
-%%RAPH: paragraphe en double :-)
+For a given set of parameters, 
+the Canny algorithm returns a numerical value and
+states whether a given pixel is an edge or not.
+In this article, in the Adaptive strategy 
+we consider that all the edge pixels that 
+have been selected by this algorithm have the same
+distortion cost, \textit{i.e.}, $\rho_X$ is always 1 for these bits. 
+In the Fixed strategy, since pixels that are detected to be edge
+with small values of $T$ (e.g., when $T=3$) 
+are more accurate than these with higher values of $T$,
+we give to STC the following distortion map of the corresponding bits
+$$  
+\rho_X= \left\{ 
+\begin{array}{l}
+1 \textrm{ if an edge for $T=3$,} \\
+10 \textrm{ if an edge for $T=5$,} \\
+100 \textrm{ if an edge for $T=7$.}
+\end{array}
+\right.
+$$

 
 
 
 
 
 


@@ -214,7 +228,7 @@ follows the data embedding approach
 since there exists a reverse function for all its steps.
 
 More precisely,  let $b$ be the most significant bits and 
 since there exists a reverse function for all its steps.
 
 More precisely,  let $b$ be the most significant bits and 

-$T$ be the size of the canny mask, both be given as a key.
+$T$ be the size of the Canny mask, both be given as a key.

 Thus, the same edge detection is applied on a stego content $Y$ to 
 produce the sequence $y$ of LSBs. 
 If the STC approach has been selected in embedding, the STC reverse
 Thus, the same edge detection is applied on a stego content $Y$ to 
 produce the sequence $y$ of LSBs. 
 If the STC approach has been selected in embedding, the STC reverse


@@ -346,7 +360,7 @@ V_{ij}= \left\{
 150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
 225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
 \end{array}
 150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
 225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
 \end{array}

-\right..
+\right.

 $$
 This function allows to emphasize differences between contents.
 Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary 
 $$
 This function allows to emphasize differences between contents.
 Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary