X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/ded436ff1397fd455304cbae04f58e4c0703ea01..8a7410beb8e5821fa7764d6fdc6843effeed1e0e:/ourapproach.tex?ds=sidebyside

diff --git a/ourapproach.tex b/ourapproach.tex
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+++ b/ourapproach.tex
@@ -1,71 +1,399 @@
-The flowcharts given in Fig.~\ref{fig:sch} summarize our steganography scheme denoted as to
-STABYLO for STeganography with cAnny, Bbs, binarY embedding at LOw cost.
-What follows successively details all the inner steps and flow inside 
-the embedding stage (Fig.\ref{fig:sch:emb}) 
-and inside the extraction one(Fig.~\ref{fig:sch:ext}).
+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 then presented  (Sect.~\ref{sub:extract}) while a running example ends this section.
 
 
-\begin{figure*}[t]
+The flowcharts given in Fig.~\ref{fig:sch}
+summarize our steganography scheme denoted by
+STABYLO, which stands for STe\-ga\-no\-gra\-phy with 
+Adaptive, Bbs, binarY embedding at LOw cost.
+What follows are successively some details of the inner steps and the flows both inside 
+ the embedding stage (Fig.~\ref{fig:sch:emb}) 
+and inside the extraction one (Fig.~\ref{fig:sch:ext}).
+Let us first focus on the data embedding. 
+
+\begin{figure*}%[t]
   \begin{center}
-    \subfloat[Data Embedding.]{
-      \begin{minipage}{0.49\textwidth}
+    \subfloat[Data Embedding]{
+      \begin{minipage}{0.4\textwidth}
         \begin{center}
-%          \includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[width=5cm]{emb.ps}
+            %\includegraphics[scale=0.45]{emb}
+            \includegraphics[scale=0.4]{emb}
         \end{center}
       \end{minipage}
       \label{fig:sch:emb}
-    }%\hfill
-    \subfloat[Data Extraction.]{
+    } 
+\hfill
+    \subfloat[Data Extraction]{
       \begin{minipage}{0.49\textwidth}
         \begin{center}
-%          \includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[width=5cm]{rec.ps}
+            \includegraphics[scale=0.4]{dec}
         \end{center}
       \end{minipage}
       \label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{The STABYLO Scheme.}
+  \caption{The STABYLO scheme}
   \label{fig:sch}
 \end{figure*}
 
 
 
 
-\subsection{Data Embedding} 
 
 
 
 
-\subsubsection{Edge Based Image Steganography}
-Image Quality: Edge Image Steganography
-\JFC{Raphael, les fuzzy edge detection sont souvent utilisÃ©s. 
-  il faudrait comparer les approches en terme de nombre de bits retournÃ©s,
-  en terme de complexitÃ©. } \cite{KF11}
+\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 
+Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
+that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} 
+pseudorandom number generator (PRNG) and the 
+XOR binary function.
+The main justification of this choice 
+is that it has been 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 $x_{i-1}$ 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,
+even if the encrypted message is extracted, 
+it is impossible to retrieve the original one in 
+polynomial time.   
+
+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}\label{sub:edge}
+
+
+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 utilisÃ©s. 
+%  il faudrait comparer les approches en terme de nombre de bits retournÃ©s,
+%  en terme de complexitÃ©. } \cite{KF11}
+%\RC{Ben, Ã  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 dÃ©tectable...  Finalement on devrait surement vendre notre truc en : on a choisi cet algo car il est performant en vitesse/qualitÃ©. Mais on peut aussi en utilisÃ© 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}, and so on, 
+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 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.
+As the Canny algorithm is fast, well known, has been studied in depth, and is implementable
+on many  kinds of architectures like FPGAs, smart phones,  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 $7$. 
+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 $x$.
+
+
+
+ 
 
 
-Presentation des algos de detection de contour
-CaractÃ©ristiques
 
-Comparaison thÃ©oriques, rÃ©fÃ©rences
 
-Algo de stegano basÃ© juste sur cela : (pas de bbs, pas de stc, mÃªme message).
+\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. 
 
-Quels paramÃ¨tres sont optimaux ? Combinaison ? 
+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.
 
 
 
-\subsubsection{Security Considerations}
 
-Security aspect:
-BBS-based cryptographic version of the message 
 
-\subsubsection{Minimizing Distortion with Syndrome-Treillis Codes} 
 
+
+
+\subsection{Minimizing distortion with Syndrome-Trellis Codes}\label{sub:stc}
 \input{stc}
 
 
-\subsection{Data Extraction}
\ No newline at end of file
+
+% Edge Based Image Steganography schemes 
+% already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ 
+% how they select edge pixels, and  
+% how they modify these ones.
+
+% First of all, let us discuss about compexity of edge detetction methods.
+% Let then $M$ and $N$ be the dimension of the original image. 
+% According to~\cite{Hu:2007:HPE:1282866.1282944},
+% even if the fuzzy logic based edge detection methods~\cite{Tyan1993} 
+% have promising results, its complexity is in $C_3 \times O(M \times N)$
+% whereas the complexity on the Canny method~\cite{Canny:1986:CAE:11274.11275} 
+% is in $C_1 \times O(M \times N)$ where  $C_1 < C_3$.
+% \JFC{Verifier ceci...}
+% In experiments detailled in this article, the Canny method has been retained 
+% but the whole approach can be updated to consider 
+% the fuzzy logic edge detector.   
+
+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 sereâ\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 Weirâ\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}
+
+
+
+The STC algorithm is optimized when the rate between message length and 
+cover vector length is lower than 1/2. 
+So, only 9,320 bits  are available for embedding 
+in the  configuration where $b$ is 7.
+
+When $b$ is 6, we could have considered 18,455 bits for the message.
+However, first experiments have shown that modifying this number of bits is too 
+easily detectable. 
+So, we choose to modify the same amount of bits (9,320) and keep STC optimizing
+which bits to change among  the 36,910 ones.
+
+In the two cases, about the third part of the poem is hidden into the cover. 
+Results with {Adaptive} and {STC} strategies 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=0.20]{lena7}
+        \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]{lena6}
+        \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
+$$
+V_{ij}= \left\{
+\begin{array}{rcl}
+0 & \textrm{if} &  X_{ij} = Y_{ij} \\
+75 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
+\end{array}
+\right.
+$$
+This function allows to emphasize differences between contents.
+Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary 
+and this image only contains 0 and 75 values.
+Similarly, if $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary 
+and the image contains all the values in $\{0,75,150,225\}$.
+
+
+
+\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]{diff7}
+        \end{center}
+      \end{minipage}
+      \label{fig:diff7}
+    }%\hfill
+    \subfloat[$b$ is 6.]{
+      \begin{minipage}{0.49\linewidth}
+        \begin{center}
+          %\includegraphics[width=5cm]{rec.pdf}
+          \includegraphics[scale=0.20]{diff6}
+        \end{center}
+      \end{minipage}
+      \label{fig:diff6}
+    }%\hfill
+  \end{center}
+  \caption{Differences  with Lena's cover  wrt $b$}
+  \label{fig:lenadiff}
+\end{figure}
+
+
+
