X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/e477428ed31d945b364bd9064476c1f0a34f86ef..57f6acd69b21dc27e72b1d6f5b4515e1baf56b5b:/ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index f86c8ae..636b8ba 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -3,39 +3,41 @@ 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 message extraction is then presented  (Sect.~\ref{sub:extract}) while 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.
-What follows are successively details of the inner steps and flows inside 
-both the embedding stage (Fig.~\ref{fig:sch:emb}) 
-and the extraction one (Fig.~\ref{fig:sch:ext}).
+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{figure*}%[t]
   \begin{center}
-    \subfloat[Data Embedding.]{
+    \subfloat[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}
-    }%\hfill
-    \subfloat[Data Extraction.]{
+    } 
+
+    \subfloat[Data Extraction]{
       \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*}
 
@@ -46,18 +48,18 @@ Let us first focus on the data embedding.
 
 
 
-\subsection{Security Considerations}\label{sub:bbs}
-Among methods of message encryption/decryption 
+\subsection{Security considerations}\label{sub:bbs}
+Among the 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}
 that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} 
 pseudorandom number generator (PRNG) and the 
 XOR binary function.
-It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG 
+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 $x_{i-1}$ 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,
@@ -69,7 +71,7 @@ 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}\label{sub:edge}
+\subsection{Edge-based image steganography}\label{sub:edge}
 
 
 The edge-based image
@@ -88,18 +90,18 @@ 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, 
+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 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.
-As the Canny algorithm is well known and studied, fast, and implementable
-on many  kinds of architectures like FPGAs, smartphones,  desktop machines, and
+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.
 
-\JFC{il faudrait comparer les complexites des algo fuzy and canny}
+%\JFC{il faudrait comparer les complexites des algo fuzy and canny}
 
 
 This edge detection is applied on a filtered version of the image given 
@@ -111,15 +113,15 @@ 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.
+and the LSBs of pixels if $b$ is 7.
 
 
 
 
 
 Let $x$ be the sequence of these bits. 
-The next  section section presentsd how our scheme 
-adapts  when the size of $x$  is not sufficient for the message $m$ to embed.
+The next  section presents how to adapt our scheme 
+  when the size of $x$  is not sufficient for the message $m$ to embed.
 
 
  
@@ -127,57 +129,49 @@ 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, 
+\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 an high threshold.
+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 to short for $m$, the message is splitted into sufficient parts. 
+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 a threshold that is decreasing 
 until its cardinality
-is sufficient. 
+is sufficient. Even in this situation, our scheme is adapting 
+its algorithm to meet all the user's requirements. 
 
 
-
-Two methods may further be applied to select bits that 
-will be modified. 
+Once the map of possibly modified pixels is computed, 
+two methods may further be applied to extract bits that 
+are really 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}.
-The second one is a direct application of the 
-STC algorithm~\cite{DBLP:journals/tifs/FillerJF11}. 
-It  is further referred to as \emph{adaptive+STC} and is detailled in the nex section.
+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.
 
 
 
 
 
-% 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.   
-
-
-
 
 
 
-
-\subsection{Minimizing Distortion with Syndrome-Treillis Codes}\label{sub:stc}
+\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
 \input{stc}
 
 
@@ -211,41 +205,49 @@ It  is further referred to as \emph{adaptive+STC} and is detailled in the nex se
 
 
 
-\subsection{Data Extraction}\label{sub:extract}
-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*512  image with 256 grayscale levels.
+\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 the first verses are given in Fig.~\ref{fig:lena}.
+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}{0.4\linewidth}
-\includegraphics[width=3cm]{Lena.eps}
+\begin{minipage}{0.49\linewidth}
+\begin{center}
+\includegraphics[scale=0.20]{Lena.eps}
+\end{center}
 \end{minipage}
-\begin{minipage}{0.59\linewidth}
+\begin{minipage}{0.49\linewidth}
 \begin{flushleft}
 \begin{scriptsize}
 The skies they were ashen and sober;\linebreak
-$~$ The leaves they were crisped and sereâ\linebreak
-$~$ The leaves they were withering and sere;\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
-$~$ Of my most immemorial year;\linebreak
+$\qquad$ Of my most immemorial year;\linebreak
 It was hard by the dim lake of Auber,\linebreak
-$~$ In the misty mid region of Weirâ\linebreak
+$\qquad$ In the misty mid region of Weirâ\linebreak
 It was down by the dank tarn of Auber,\linebreak
-$~$ In the ghoul-haunted woodland of Weir.
+$\qquad$ In the ghoul-haunted woodland of Weir.
 \end{scriptsize}
 \end{flushleft}
 \end{minipage}
@@ -253,9 +255,11 @@ $~$ In the ghoul-haunted woodland of Weir.
 \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 Fig.~\ref{fig:edge}
-
+The edge detection returns 18,641 and 18,455 pixels when $b$ is
+respectively 7 and 6. 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}
@@ -263,7 +267,7 @@ respectively 7 and 6. These edges are represented in Fig.~\ref{fig:edge}
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.15]{edge7.eps}
+          \includegraphics[scale=0.20]{edge7.eps}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}
@@ -272,21 +276,30 @@ respectively 7 and 6. These edges are represented in Fig.~\ref{fig:edge}
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.15]{edge6.eps}
+          \includegraphics[scale=0.20]{edge6.eps}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{Edge Detection wrt $b$.}
+  \caption{Edge detection wrt $b$}
   \label{fig:edge}
 \end{figure}
 
 
 
-In the former configuration, only 9320 bits are available 
-for embeding whereas in the latter we have 9227.
-In the both case, about the third part of the poem is hidden into the cover.
+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 \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.
 
@@ -296,7 +309,7 @@ Fig.~\ref{fig:lenastego}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.15]{lena7.eps}
+          \includegraphics[scale=0.20]{lena7.eps}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}
@@ -305,32 +318,31 @@ Fig.~\ref{fig:lenastego}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.15]{lena6.eps}
+          \includegraphics[scale=0.20]{lena6.eps}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{Stego Images wrt $b$.}
+  \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 pixel pair of picel $X_{ij}$  
-$Y_{ij}$, $X$ and $Y$ being the cover and the stego content respectively, 
-The pixel value $V_{ij}$ of the difference is defined with the following map
+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
 $$
 V_{ij}= \left\{
 \begin{array}{rcl}
 0 & \textrm{if} &  X_{ij} = Y_{ij} \\
-75 & \textrm{if} &  \abs{ (X_{ij} - Y_{ij})} = 1 \\
-75 & \textrm{if} &  \abs{ (X_{ij} - Y_{ij})} = 2 \\
-225 & \textrm{if} &  \abs{ (X_{ij} - Y_{ij})} = 1 
+75 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 1 \\
+150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
+225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
 \end{array}
-\right.
-$$.
-This function allows to emphase differences between content.
+\right..
+$$
+This function allows to emphasize differences between contents.
 
 \begin{figure}[t]
   \begin{center}
@@ -338,7 +350,7 @@ This function allows to emphase differences between content.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.15]{diff7.eps}
+          \includegraphics[scale=0.20]{diff7.eps}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}
@@ -347,12 +359,14 @@ This function allows to emphase differences between content.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.15]{diff6.eps}
+          \includegraphics[scale=0.20]{diff6.eps}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{Differences  with Lena's Cover  wrt $b$.}
+  \caption{Differences  with Lena's cover  wrt $b$}
   \label{fig:lenadiff}
 \end{figure}
+
+
