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}
\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
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.
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
-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 fuzzy logic edge detector.
For a given set of parameters,
-the canny algorithm returns a numerical value and
+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.
+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 $T=3$)
+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
$$
\rho_X= \left\{
\begin{array}{l}
-1 \textrm{ if an edge for $T=3$} \\
-10 \textrm{ if an edge for $T=5$} \\
-100 \textrm{ if an edge for $T=7$}
+1 \textrm{ if an edge for $T=3$,} \\
+10 \textrm{ if an edge for $T=5$,} \\
+100 \textrm{ if an edge for $T=7$.}
\end{array}
\right.
-$$.
+$$
since there exists a reverse function for all its steps.
More precisely, let $b$ be the most significant bits and
-$T$ be the size of the canny mask, both be given as a key.
+$T$ be the size of the Canny mask, both be given as a key.
Thus, the same edge detection is applied on a stego content $Y$ to
produce the sequence $y$ of LSBs.
If the STC approach has been selected in embedding, the STC reverse
150 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 2 \\
225 & \textrm{if} & \vert X_{ij} - Y_{ij} \vert = 3
\end{array}
-\right..
+\right.
$$
This function allows to emphasize differences between contents.
Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary
