+
+
+\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
+words, and 3,754 characters, \textit{i.e.}, 30,032 bits.
+Lena and the first verses are given in Fig.~\ref{fig:lena}.
+
+\begin{figure}
+\begin{center}
+\begin{minipage}{0.49\linewidth}
+\begin{center}
+\includegraphics[scale=0.20]{lena512}
+\end{center}
+\end{minipage}
+\begin{minipage}{0.49\linewidth}
+\begin{flushleft}
+\begin{scriptsize}
+The skies they were ashen and sober;\linebreak
+$\qquad$ The leaves they were crisped and sere—\linebreak
+$\qquad$ The leaves they were withering and sere;\linebreak
+It was night in the lonesome October\linebreak
+$\qquad$ Of my most immemorial year;\linebreak
+It was hard by the dim lake of Auber,\linebreak
+$\qquad$ In the misty mid region of Weir—\linebreak
+It was down by the dank tarn of Auber,\linebreak
+$\qquad$ 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 18,641 and 18,455 pixels when $b$ is
+respectively 7 and 6 and $T=3$.
+These edges are represented in Figure~\ref{fig:edge}.
+When $b$ is 7, it remains one bit per pixel to build the cover vector.
+This configuration leads to a cover vector of size 18,641 if b is 7
+and 36,910 if $b$ is 6.
+
+\begin{figure}[t]
+ \begin{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.20]{edge7}
+ \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=0.20]{edge6}
+ \end{center}
+ \end{minipage}
+ %\label{fig:sch:ext}
+ }%\hfill
+ \end{center}
+ \caption{Edge detection wrt $b$ with $T=3$}
+ \label{fig:edge}
+\end{figure}
+
+
+
+The STC algorithm is optimized when the rate between message length and
+cover vector length is lower than 1/2.
+So, only 9,320 bits are available for embedding
+in the configuration where $b$ is 7.
+
+When $b$ is 6, we could have considered 18,455 bits for the message.
+However, first experiments have shown that modifying this number of bits is too
+easily detectable.
+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.
+Results with {Adaptive} and {STC} strategies 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=0.20]{lena7}
+ \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=0.20]{lena6}
+ \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 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
+$$
+V_{ij}= \left\{
+\begin{array}{rcl}
+0 & \textrm{if} & X_{ij} = Y_{ij} \\
+75 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 3
+\end{array}
+\right.
+$$
+This function allows to emphasize differences between contents.
+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{center}
+ \subfloat[$b$ is 7.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{emb.pdf}
+ \includegraphics[scale=0.20]{diff7}
+ \end{center}
+ \end{minipage}
+ \label{fig:diff7}
+ }%\hfill
+ \subfloat[$b$ is 6.]{
+ \begin{minipage}{0.49\linewidth}
+ \begin{center}
+ %\includegraphics[width=5cm]{rec.pdf}
+ \includegraphics[scale=0.20]{diff6}
+ \end{center}
+ \end{minipage}
+ \label{fig:diff6}
+ }%\hfill
+ \end{center}
+ \caption{Differences with Lena's cover wrt $b$}
+ \label{fig:lenadiff}
+\end{figure}
+
+
+
