X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/af81455342fce2b4d7f96ecb4f1194635a5a13a4..7aeb1ab6cc41dd51a6dbe4c844c8983809205186:/ourapproach.tex?ds=inline

diff --git a/ourapproach.tex b/ourapproach.tex
index 12b3a32..f9ca3d1 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -140,7 +140,7 @@ 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 
+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. 
@@ -151,13 +151,13 @@ 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 
+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 modified. 
+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 
@@ -196,14 +196,26 @@ It  is further referred to as \emph{STC} and is detailed in the next section.
 % but the whole approach can be updated to consider 
 % the fuzzy logic edge detector.   
 
-% Next, following~\cite{Luo:2010:EAI:1824719.1824720}, our scheme automatically
-% modifies Canny parameters to get a sufficiently large set of edge bits: this 
-% one is practically enlarged untill its size is at least twice as many larger 
-% than the size of embedded message.
-
-
-
-%%RAPH: paragraphe en double :-)
+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
+$$  
+\rho_X= \left\{ 
+\begin{array}{l}
+1 \textrm{ if an edge for $T=3$} \\
+10 \textrm{ if an edge for $T=5$} \\
+100 \textrm{ if an edge for $T=7$}
+\end{array}
+\right.
+$$.
 
 
 
@@ -214,7 +226,7 @@ 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.
+$T$ 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
@@ -346,7 +358,7 @@ V_{ij}= \left\{
 150 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 2 \\
 225 & \textrm{if} &  \vert X_{ij} - Y_{ij} \vert = 3 
 \end{array}
-\right..
+\right.
 $$
 This function allows to emphasize differences between contents.
 Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary