-Of course, all the algorithms have advantages and drawbacks which depend on the
-motivation to highlight edges. Unfortunately unless testing most of the
-algorithms, which would require many times, it is quite difficult to have an
-accurate idea on what would produce such algorithm compared to another. That is
-why we have chosen Canny algorithm which is well known, fast and implementable
-on many kinds of architecture, such as FPGA, smartphone, desktop machines and
-GPU. And of course, we do not pretend that this is the best solution.
+Starting thus with a key $k$ and the message \textit{mess} to hide,
+this step computes a message $m$, which is the encrypted version of \textit{mess}.
+
+
+\subsection{Edge-Based Image Steganography}
+
+
+The edge-based image
+steganography schemes
+already presented \cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10} differ
+in how carefully they select edge pixels, and
+how they modify them.
+
+%Image Quality: Edge Image Steganography
+%\JFC{Raphael, les fuzzy edge detection sont souvent utilisés.
+% il faudrait comparer les approches en terme de nombre de bits retournés,
+% en terme de complexité. } \cite{KF11}
+%\RC{Ben, à voir car on peut choisir le nombre de pixel avec Canny. Supposons que les fuzzy edge soient retourne un peu plus de points, on sera probablement plus détectable... Finalement on devrait surement vendre notre truc en : on a choisi cet algo car il est performant en vitesse/qualité. Mais on peut aussi en utilisé d'autres :-)}
+
+Many techniques have been proposed in the literature to detect
+edges in images (whose noise has been initially reduced).
+They can be separated in two categories: first and second order detection
+methods on the one hand, and fuzzy detectors on the other hand~\cite{KF11}.
+In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, \ldots,
+a first-order derivative (gradient magnitude, etc.) is computed
+to search for local maxima, whereas in second order ones, zero crossings in a second-order derivative, like the Laplacian computed from the image,
+are searched in order to find edges.
+As for as fuzzy edge methods are concerned, they are obviously based on fuzzy logic to highlight edges.
+
+Canny filters, on their parts, are an old family of algorithms still remaining a state-of-the-art edge detector. They can be well approximated by first-order derivatives of Gaussians.
+As the Canny algorithm is well known and studied, fast, and implementable
+on many kinds of architectures like FPGAs, smartphones, desktop machines, and
+GPUs, we have chosen this edge detector for illustrative purpose.
+
+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 $7$.
+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.
+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.
+
+\JFC{il faudrait comparer les complexites des algo fuzy and canny}
