+This section first presents the embedding scheme through its
+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 message extraction is finally presented (Sect.\ref{sub:extract}) and a running example ends this section (Sect.~\ref{sub:xpl}).
+
+
The flowcharts given in Fig.~\ref{fig:sch}
summarize our steganography scheme denoted by
STABYLO, which stands for STeganography with cAnny, Bbs, binarY embedding at LOw cost.
-\subsection{Security Considerations}
+\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}
this step computes a message $m$, which is the encrypted version of \textit{mess}.
-\subsection{Edge-Based Image Steganography}
+\subsection{Edge-Based Image Steganography}\label{sub:edge}
The edge-based image
on many kinds of architectures like FPGAs, smartphones, desktop machines, and
GPUs, we have chosen this edge detector for illustrative purpose.
+\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+
+
This edge detection is applied on a filtered version of the image given
as input.
More precisely, only $b$ most
In our flowcharts, this is represented by ``edgeDetection(b bits)''.
Then only the 2 LSBs of pixels in the set of edges are returned if $b$ is 6,
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 presentsd how our scheme
+adapts when the size of $x$ is not sufficient for the message $m$ to embed.
+
+
-\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+
+
+
+
+\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.
+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 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 splitted into sufficient parts.
+In the latter, the embedding rate is defined as a percentage between the
+number of modified pixels and the length of the bit message.
+This is the classical approach adopted in steganography.
+Practically, the Canny algorithm generates
+a set of edge pixels related to a threshold that is decreasing
+until its cardinality
+is sufficient.
+
+
+
+Two methods may further be applied to select bits that
+will be modified.
+The first one randomly chooses the subset of pixels to modify by
+applying the BBS PRNG again. This method is further denoted as to \emph{sample}.
+The second one is a direct application of the
+STC algorithm~\cite{DBLP:journals/tifs/FillerJF11}.
+It is further referred to as \emph{adaptive+STC} and is detailled in the nex section.
+
+
+
% First of all, let us discuss about compexity of edge detetction methods.
-As argue in the introduction section, we do not adapt the parameters of the
-the edge detection as in~\cite{Luo:2010:EAI:1824719.1824720} but we modify
-the size of the embedding message. Practically, the lenght of $x$
-has to be at least twice as large
-as the size of the embedded encrypted message.
-Otherwise, a new image is used to hide the remaning part of the message.
-\subsection{Minimizing Distortion with Syndrome-Treillis Codes}
+\subsection{Minimizing Distortion with Syndrome-Treillis Codes}\label{sub:stc}
\input{stc}
-\subsection{Data Extraction}
+\subsection{Data Extraction}\label{sub:extract}
The message extraction summarized in Fig.~\ref{fig:sch:ext} follows data embedding
since there exists a reverse function for all its steps.
First of all, the same edge detection is applied (on the 7 first bits) to
Then the STC reverse algorithm is applied to retrieve the encrypted message.
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
+which is a 512*512 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}.
+
+\begin{figure}
+\begin{center}
+\begin{minipage}{0.4\linewidth}
+\includegraphics[width=3cm]{Lena.eps}
+\end{minipage}
+\begin{minipage}{0.59\linewidth}
+\begin{flushleft}
+\begin{scriptsize}
+The skies they were ashen and sober;\linebreak
+$~$ The leaves they were crisped and sere—\linebreak
+$~$ The leaves they were withering and sere;\linebreak
+It was night in the lonesome October\linebreak
+$~$ Of my most immemorial year;\linebreak
+It was hard by the dim lake of Auber,\linebreak
+$~$ In the misty mid region of Weir—\linebreak
+It was down by the dank tarn of Auber,\linebreak
+$~$ In the ghoul-haunted woodland of Weir.
+\end{scriptsize}
+\end{flushleft}
+\end{minipage}
+\end{center}
+\caption{Cover and message examples} \label{fig:lena}
+\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}
+
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.15]{edge7.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:emb}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.15]{edge6.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Edge Detection wrt $b$.}
+ \label{fig:edge}
+\end{figure}
+
+
+
+In the former configuration, only 9320 bits are available
+for embeding whereas in the latter we have 9227.
+In the both case, 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}.
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.15]{lena7.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:emb}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.15]{lena6.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Stego Images wrt $b$.}
+ \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 picel $X_{ij}$
+$Y_{ij}$, $X$ and $Y$ being the cover and the stego content respectively,
+The pixel value $V_{ij}$ of the difference is defined with the following map
+$$
+V_{ij}= \left\{
+\begin{array}{rcl}
+0 & \textrm{if} & X_{ij} = Y_{ij} \\
+75 & \textrm{if} & \abs{ (X_{ij} - Y_{ij})} = 1 \\
+75 & \textrm{if} & \abs{ (X_{ij} - Y_{ij})} = 2 \\
+225 & \textrm{if} & \abs{ (X_{ij} - Y_{ij})} = 1
+\end{array}
+\right.
+$$.
+This function allows to emphase differences between content.
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.15]{diff7.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:emb}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.15]{diff6.eps}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Differences with Lena's Cover wrt $b$.}
+ \label{fig:lenadiff}
+\end{figure}
