style ante + complexite canny

[canny.git] / ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index 9cf0384609ab84a68d9fe1c22ec114405e3bc807..2378139e821b501c86f0f68f2a6d0f632b95427a 100644 (file)
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -3,18 +3,19 @@ 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 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}) 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
 
 
 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 STeganography 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. 
 
 Let us first focus on the data embedding. 
 

-\begin{figure*}[t]
+\begin{figure*}%[t]

   \begin{center}
     \subfloat[Data Embedding.]{
       \begin{minipage}{0.49\textwidth}
   \begin{center}
     \subfloat[Data Embedding.]{
       \begin{minipage}{0.49\textwidth}


@@ -24,7 +25,8 @@ Let us first focus on the data embedding.
         \end{center}
       \end{minipage}
       \label{fig:sch:emb}
         \end{center}
       \end{minipage}
       \label{fig:sch:emb}

-    }%\hfill
+    } 
+

     \subfloat[Data Extraction.]{
       \begin{minipage}{0.49\textwidth}
         \begin{center}
     \subfloat[Data Extraction.]{
       \begin{minipage}{0.49\textwidth}
         \begin{center}


@@ -47,7 +49,7 @@ Let us first focus on the data embedding.
 
 
 \subsection{Security considerations}\label{sub:bbs}
 
 
 \subsection{Security considerations}\label{sub:bbs}

-Among methods of message encryption/decryption 
+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} 
 (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} 


@@ -86,7 +88,7 @@ how they modify them.
 
 Many techniques have been proposed in the literature to  detect 
 edges in  images (whose noise has been initially reduced). 
 
 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
+They can be separated into 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 
 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 


@@ -95,11 +97,11 @@ 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 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
+As the Canny algorithm is fast, well known, has been studied in depth, and is implementable

 on many  kinds of architectures like FPGAs, smartphones,  desktop machines, and
 GPUs, we have chosen this edge detector for illustrative purpose.
 
 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}
+%\JFC{il faudrait comparer les complexites des algo fuzy and canny}

 
 
 This edge detection is applied on a filtered version of the image given 
 
 
 This edge detection is applied on a filtered version of the image given 


@@ -133,7 +135,7 @@ 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 
 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 too short for $m$, the message is split into sufficient parts
 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


@@ -146,14 +148,15 @@ 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
 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 
 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}.
+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 is a direct application of the 
 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 


@@ -237,26 +240,28 @@ message is extracted.
 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
 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.
+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}
 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}
 \end{minipage}

-\begin{minipage}{0.59\linewidth}
+\begin{minipage}{0.49\linewidth}

 \begin{flushleft}
 \begin{scriptsize}
 The skies they were ashen and sober;\linebreak
 \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
+$\qquad$ 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
 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
 It was hard by the dim lake of Auber,\linebreak

-$~$ In the misty mid region of Weir—\linebreak
+$\qquad$ In the misty mid region of Weir—\linebreak

 It was down by the dank tarn of Auber,\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}
 \end{scriptsize}
 \end{flushleft}
 \end{minipage}


@@ -264,9 +269,11 @@ $~$ In the ghoul-haunted woodland of Weir.
 \caption{Cover and message examples} \label{fig:lena}
 \end{figure}
 
 \caption{Cover and message examples} \label{fig:lena}
 \end{figure}
 

-The edge detection returns 18641 and 18455 pixels when $b$ is
+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}.
 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.
+in this configuration, this 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}
 
 \begin{figure}[t]
   \begin{center}


@@ -274,7 +281,7 @@ respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
       \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}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}


@@ -283,7 +290,7 @@ respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
       \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}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}


@@ -295,9 +302,18 @@ respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
 
 
 
 
 
 

-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.
+The STC algorithm is optimized when the rate between message length and 
+cover vector length is less 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 bits.
+
+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}.
 
 Results with \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.
 


@@ -307,7 +323,7 @@ Fig.~\ref{fig:lenastego}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
       \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}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}


@@ -316,7 +332,7 @@ Fig.~\ref{fig:lenastego}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
       \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}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}


@@ -334,9 +350,9 @@ $$
 V_{ij}= \left\{
 \begin{array}{rcl}
 0 & \textrm{if} &  X_{ij} = Y_{ij} \\
 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 
+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..
 $$
 \end{array}
 \right..
 $$


@@ -348,7 +364,7 @@ This function allows to emphasize differences between contents.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
       \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}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}


@@ -357,7 +373,7 @@ This function allows to emphasize differences between contents.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
       \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}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}


@@ -366,3 +382,6 @@ This function allows to emphasize differences between contents.
   \caption{Differences  with Lena's cover  wrt $b$}
   \label{fig:lenadiff}
 \end{figure}
   \caption{Differences  with Lena's cover  wrt $b$}
   \label{fig:lenadiff}
 \end{figure}

+
+
+