+This edge detection is applied on a filtered version of the image given
+as input.
+More precisely, only $b$ most significant bits are concerned by this step,
+where the parameter $b$ is practically set with $6$ or $7$.
+Notice that 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.
+If set with the same value $b$, the edge detection returns thus the same
+set of pixels for both the cover and the stego image.
+Moreover, to provide edge gradient value,
+the Canny algorithm computes derivatives
+in the two directions with respect to a mask of size $T$.
+The higher $T$ is, the coarse the approach is. Practically,
+$T$ is set with $3$, $5$, or $7$.
+In our flowcharts, this step is represented by ``Edge Detection(b, T, X)''.
+
+
+Let $x$ be the sequence of these bits.
+The next section presents how to adapt our scheme
+with respect to the size
+of the message $m$ to embed and the size of the cover $x$.
+
+
+
+
+
+
+
+
+\subsection{Adaptive embedding rate}\label{sub:adaptive}
+Two strategies have been developed in our approach,
+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 parameters $b=7$ and $T=3$.
+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.
+
+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 increasing values of $T$ and
+until its cardinality
+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 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
+stego content.
+The second method considers the last significant bits of all the pixels
+inside the previous map. It next directly applies the STC
+algorithm~\cite{DBLP:journals/tifs/FillerJF11}.
+It is further referred to as \emph{STC} and is detailed in the next section.
+
+
+
+
+
+
+
+
+\subsection{Minimizing distortion with Syndrome-Trellis Codes}\label{sub:stc}
+\input{stc}
+
+
