X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/b04e55fbbcdcbca04098f1bf05ec4473e47b5c51..ef06623aa40e69d9e5332208f9ead5af2e7ea4b6:/ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index ec73f7d..249e1be 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -18,20 +18,19 @@ Let us first focus on the data embedding.
 \begin{figure*}%[t]
   \begin{center}
     \subfloat[Data Embedding]{
-      \begin{minipage}{0.49\textwidth}
+      \begin{minipage}{0.4\textwidth}
         \begin{center}
-          %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.45]{emb}
+            %\includegraphics[scale=0.45]{emb}
+            \includegraphics[scale=0.4]{emb}
         \end{center}
       \end{minipage}
       \label{fig:sch:emb}
     } 
-
+\hfill
     \subfloat[Data Extraction]{
       \begin{minipage}{0.49\textwidth}
         \begin{center}
-          %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.45]{rec}
+            \includegraphics[scale=0.4]{dec}
         \end{center}
       \end{minipage}
       \label{fig:sch:ext}
@@ -101,27 +100,28 @@ As the Canny algorithm is fast, well known, has been studied in depth, and is im
 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}
+
 
 
 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 LSBs of pixels if $b$ is 7.
-
-
-
+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 $3$, $3$, 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 
-  when the size of $x$  is not sufficient for the message $m$ to embed.
+when the size of $x$  is not sufficient for the message $m$ to embed.
 
 
  
@@ -135,18 +135,17 @@ 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.
+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 a threshold that is decreasing 
+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. 
@@ -210,11 +209,13 @@ 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, the same edge detection is applied on the $b$ first bits  to 
+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 $H$ matrix as a parameter.
+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.
@@ -233,7 +234,7 @@ Lena and the first verses are given in Fig.~\ref{fig:lena}.
 \begin{center}
 \begin{minipage}{0.49\linewidth}
 \begin{center}
-\includegraphics[scale=0.20]{Lena.eps}
+\includegraphics[scale=0.20]{lena512}
 \end{center}
 \end{minipage}
 \begin{minipage}{0.49\linewidth}
@@ -256,7 +257,8 @@ $\qquad$ In the ghoul-haunted woodland of Weir.
 \end{figure}
 
 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 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.  
@@ -267,7 +269,7 @@ and 36,910 if $b$ is 6.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.20]{edge7.eps}
+          \includegraphics[scale=0.20]{edge7}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}
@@ -276,13 +278,13 @@ and 36,910 if $b$ is 6.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.20]{edge6.eps}
+          \includegraphics[scale=0.20]{edge6}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}
     }%\hfill
   \end{center}
-  \caption{Edge detection wrt $b$}
+  \caption{Edge detection wrt $b$ with $T=3$}
   \label{fig:edge}
 \end{figure}
 
@@ -300,7 +302,7 @@ 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 
+Results with \emph{adaptive} and \textit{STC} strategies are presented in 
 Fig.~\ref{fig:lenastego}.
 
 \begin{figure}[t]
@@ -309,7 +311,7 @@ Fig.~\ref{fig:lenastego}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.20]{lena7.eps}
+          \includegraphics[scale=0.20]{lena7}
         \end{center}
       \end{minipage}
       %\label{fig:sch:emb}
@@ -318,7 +320,7 @@ Fig.~\ref{fig:lenastego}.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{rec.pdf}
-          \includegraphics[scale=0.20]{lena6.eps}
+          \includegraphics[scale=0.20]{lena6}
         \end{center}
       \end{minipage}
       %\label{fig:sch:ext}
@@ -343,6 +345,8 @@ V_{ij}= \left\{
 \right..
 $$
 This function allows to emphasize differences between contents.
+Notice that 
+
 
 \begin{figure}[t]
   \begin{center}
@@ -350,19 +354,19 @@ This function allows to emphasize differences between contents.
       \begin{minipage}{0.49\linewidth}
         \begin{center}
           %\includegraphics[width=5cm]{emb.pdf}
-          \includegraphics[scale=0.20]{diff7.eps}
+          \includegraphics[scale=0.20]{diff7}
         \end{center}
       \end{minipage}
-      %\label{fig:sch:emb}
+      \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.eps}
+          \includegraphics[scale=0.20]{diff6}
         \end{center}
       \end{minipage}
-      %\label{fig:sch:ext}
+      \label{fig:diff6}
     }%\hfill
   \end{center}
   \caption{Differences  with Lena's cover  wrt $b$}
@@ -370,3 +374,8 @@ This function allows to emphasize differences between contents.
 \end{figure}
 
 
+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, when $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary 
+and the image contains all the values in $\{0,75,150,225\}$.
+
