X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/b417a74f270da1ad1a8b11552a8508c45cb75085..fdec47fad10cd693dc899d18ba02c166c1f5349f:/ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index 74c1b55..12b3a32 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -1,33 +1,42 @@
+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 (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.]{
-      \begin{minipage}{0.49\textwidth}
+    \subfloat[Data Embedding]{
+      \begin{minipage}{0.4\textwidth}
         \begin{center}
-          %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.5]{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[scale=0.5]{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*}
 
@@ -38,18 +47,20 @@ Let us first focus on the data embedding.
 
 
 
-\subsection{Security Considerations}
-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}
+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.
-It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG 
+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 $x_{i-1}$ 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 +72,7 @@ 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
@@ -80,57 +91,90 @@ 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.
 
+
+
+
 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 $7$. 
+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.   
-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.
+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 $x$.
+
+
+
  
-\JFC{il faudrait comparer les complexites des algo fuzy and canny}
 
 
-% 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{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 less 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 is adapting 
+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 modified. 
+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.
 
 
 
 
 
 
-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 +208,178 @@ 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,  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 sere—\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 Weir—\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}
+
+
+