X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/b417a74f270da1ad1a8b11552a8508c45cb75085..f9ab101f6a209bfd67ee84f3aea5bf5ca2582d9b:/ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index 74c1b55..9cce7a2 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -1,3 +1,11 @@
+This section first presents the embedding scheme through its 
+four main steps: the data encryption (Sect.~\ref{sub:bbs}),
+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 finally presented  (Sect.~\ref{sub:extract}) and a running example ends this section (Sect.~\ref{sub:xpl}). 
+
+
 The flowcharts given in Fig.~\ref{fig:sch}
 summarize our steganography scheme denoted by
 STABYLO, which stands for STeganography with cAnny, Bbs, binarY embedding at LOw cost.
@@ -12,7 +20,7 @@ Let us first focus on the data embedding.
       \begin{minipage}{0.49\textwidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.5]{emb.ps}
+          \includegraphics[scale=0.45]{emb.ps}
         \end{center}
       \end{minipage}
       \label{fig:sch:emb}
@@ -21,13 +29,13 @@ Let us first focus on the data embedding.
       \begin{minipage}{0.49\textwidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.5]{rec.ps}
+          \includegraphics[scale=0.45]{rec.ps}
         \end{center}
       \end{minipage}
       \label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{The STABYLO Scheme.}
+  \caption{The STABYLO scheme}
   \label{fig:sch}
 \end{figure*}
 
@@ -38,7 +46,7 @@ Let us first focus on the data embedding.
 
 
 
-\subsection{Security Considerations}
+\subsection{Security considerations}\label{sub:bbs}
 Among methods of message encryption/decryption 
 (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
 we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
@@ -49,7 +57,7 @@ It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG
 has the property of cryptographical security, \textit{i.e.}, 
 for any sequence of $L$ output bits $x_i$, $x_{i+1}$, \ldots, $x_{i+L-1}$,
 there is no algorithm, whose time complexity is polynomial  in $L$, and 
-which allows to find $x_{i-1}$ and $x_{i+L}$ with a probability greater
+which allows to find $x_{i-1}$ or $x_{i+L}$ with a probability greater
 than $1/2$.
 Equivalent formulations of such a property can
 be found. They all lead to the fact that,
@@ -61,7 +69,7 @@ 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}
+\subsection{Edge-based image steganography}\label{sub:edge}
 
 
 The edge-based image
@@ -84,13 +92,16 @@ In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, \ldo
 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.
+As far 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.
+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.
 
+%\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+
+
 This edge detection is applied on a filtered version of the image given 
 as input.
 More precisely, only $b$ most 
@@ -101,9 +112,56 @@ 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.
+
+
+
+
+
+Let $x$ be the sequence of these bits. 
+The next  section presents how our scheme 
+adapts  when the size of $x$  is not sufficient for the message $m$ to embed.
+
+
+ 
+
+
+
+
+\subsection{Adaptive embedding rate}\label{sub:adaptive}
+Two strategies have been developed in our scheme, 
+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 a high threshold.
+The message length is thus defined to be less than 
+half of this set cardinality.
+If $x$ is then 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. 
+
  
-\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+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 a threshold that is decreasing 
+until its cardinality
+is sufficient. 
+
+
+
+Two methods may further be applied to select bits that 
+will be modified. 
+The first one randomly chooses the subset of pixels to modify by 
+applying the BBS PRNG again. This method is further denoted  as to \emph{sample}.
+Once this set is selected, a classical LSB replacement is applied to embed the 
+stego content.
+The second method is a direct application of the 
+STC algorithm~\cite{DBLP:journals/tifs/FillerJF11}. 
+It  is further referred to as \emph{STC} and is detailed in the next section.
+
+
+
 
 
 % First of all, let us discuss about compexity of edge detetction methods.
@@ -123,14 +181,8 @@ Let $x$ be the sequence of these bits.
 
 
 
-As argue in the introduction section, we do not adapt the parameters of the
-the edge detection as in~\cite{Luo:2010:EAI:1824719.1824720} but we modify 
-the size of the embedding message. Practically, the lenght of $x$ 
-has to be at least twice as large 
-as the size of the embedded encrypted message. 
-Otherwise, a new image is used to hide the remaning part of the message.  
 
-\subsection{Minimizing Distortion with Syndrome-Treillis Codes} 
+\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
 \input{stc}
 
 
@@ -164,12 +216,153 @@ Otherwise, a new image is used to hide the remaning part of the message.
 
 
 
-\subsection{Data Extraction}
-The message extraction summarized in Fig.~\ref{fig:sch:ext} follows data embedding
+\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.
-First of all, the same edge detection is applied (on the 7 first bits) to 
-get the set of LSBs,
-which is  sufficiently large with respect to the message size given as a key.  
-Then the STC reverse algorithm is applied to retrieve the encrypted message.
+
+More precisely, the same edge detection is applied on the $b$ first bits  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 $H$ 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 3754 characters, \textit{i.e.},  30032 bits.
+Lena and the first verses are given in Fig.~\ref{fig:lena}.
+
+\begin{figure}
+\begin{center}
+\begin{minipage}{0.4\linewidth}
+\includegraphics[width=3cm]{Lena.eps}
+\end{minipage}
+\begin{minipage}{0.59\linewidth}
+\begin{flushleft}
+\begin{scriptsize}
+The skies they were ashen and sober;\linebreak
+$~$ The leaves they were crisped and sere—\linebreak
+$~$ The leaves they were withering and sere;\linebreak
+It was night in the lonesome October\linebreak
+$~$ Of my most immemorial year;\linebreak
+It was hard by the dim lake of Auber,\linebreak
+$~$ In the misty mid region of Weir—\linebreak
+It was down by the dank tarn of Auber,\linebreak
+$~$ 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 18641 and 18455 pixels when $b$ is
+respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
+
+
+\begin{figure}[t]
+  \begin{center}
+    \subfloat[$b$ is 7.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{emb.pdf}
+          \includegraphics[scale=0.15]{edge7.eps}
+        \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=0.15]{edge6.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:ext}
+    }%\hfill
+  \end{center}
+  \caption{Edge detection wrt $b$}
+  \label{fig:edge}
+\end{figure}
+
+
+
+Only 9320 bits (resp. 9227 bits) are available for embedding 
+in the former configuration where $b$ is 7 (resp. where $b$ is 6).
+In both cases, about the third part of the poem is hidden into the cover.
+Results with \emph{adaptive+STC} strategy 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=0.15]{lena7.eps}
+        \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=0.15]{lena6.eps}
+        \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
+$$
+V_{ij}= \left\{
+\begin{array}{rcl}
+0 & \textrm{if} &  X_{ij} = Y_{ij} \\
+75 & \textrm{if} &  \abs{ X_{ij} - Y_{ij}} = 1 \\
+150 & \textrm{if} &  \abs{ X_{ij} - Y_{ij}} = 2 \\
+225 & \textrm{if} &  \abs{ X_{ij} - Y_{ij}} = 3 
+\end{array}
+\right..
+$$
+This function allows to emphasize differences between contents.
+
+\begin{figure}[t]
+  \begin{center}
+    \subfloat[$b$ is 7.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{emb.pdf}
+          \includegraphics[scale=0.15]{diff7.eps}
+        \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=0.15]{diff6.eps}
+        \end{center}
+      \end{minipage}
+      %\label{fig:sch:ext}
+    }%\hfill
+  \end{center}
+  \caption{Differences  with Lena's cover  wrt $b$}
+  \label{fig:lenadiff}
+\end{figure}