+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
+$$
+\rho_X= \left\{
+\begin{array}{l}
+1 \textrm{ if an edge for $T=3$,} \\
+10 \textrm{ if an edge for $T=5$,} \\
+100 \textrm{ if an edge for $T=7$.}
+\end{array}
+\right.
+$$
+
+
+
+
+\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.
+
+More precisely, let $b$ be the most significant bits and
+$T$ 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
+algorithm is directly executed to retrieve the encrypted message.
+This inverse function takes the $\hat{H}$ matrix as a parameter.
+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.
+
+
+\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}
+
