X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/100ac9908382b8de480dae1fd68829f2a7778b5d..24da70a2907152b45f175222de4962951669ac12:/ourapproach.tex

diff --git a/ourapproach.tex b/ourapproach.tex
index 4dce984..f832695 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -41,11 +41,33 @@ scheme.
 
 \subsubsection{Edge Based Image Steganography}
 
+
 Edge Based Image Steganography schemes 
 already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ 
 how they select edge pixels, and  
 how they modify these ones.
 
+Image Quality: Edge Image Steganography
+\JFC{Raphael, les fuzzy edge detection sont souvent utilisés. 
+  il faudrait comparer les approches en terme de nombre de bits retournés,
+  en terme de complexité. } \cite{KF11}
+\RC{Ben, à voir car on peut choisir le nombre de pixel avec canny. Supposons que les fuzzy edge soient retourne un peu plus de points, on sera probablement plus détectable...  Finalement on devrait surement vendre notre truc en : on a choisi cet algo car il est performant en vitesse/qualité. Mais on peut aussi en utilisé d'autres :-)}
+
+There are  many techniques to  detect edges in  images. Main methods  are filter
+edge detection methods such as Sobel  or Canny filter, low order methods such as
+first order  and second order  methods, these methods  are based on  gradient or
+Laplace  operators and  fuzzy edge  methods which  are based  on fuzzy  logic to
+highlight edges.
+
+Of course, all the algorithms have  advantages and drawbacks which depend on the
+motivation  to  highlight  edges.   Unfortunately  unless testing  most  of  the
+algorithms, which  would require many  times, it is  quite difficult to  have an
+accurate idea on what would produce  such algorithm compared to another. That is
+why we have  chosen canny algorithm which is well  known, fast and implementable
+on many  kinds of architecture, such  as FPGA, smartphone,  desktop machines and
+GPU. And of course, we do not pretend that this is the best solution.
+
+
 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},
@@ -63,6 +85,27 @@ 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.
 
+Edge Based Image Steganography schemes 
+already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10} differ 
+how they select edge pixels, and  
+how they modify these ones.
+
+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.   
+
+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.
 
 
 \subsubsection{Security Considerations}
@@ -82,6 +125,21 @@ it would thus be not possible to retrieve the original one in a
 polynomial time.   
 
 
+\subsubsection{Security Considerations}
+Among 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}
+which is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} Pseudo Random Number Generator (PRNG) 
+for security reasons.
+It has been indeed proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG 
+has the cryptographically security property, \textit{i.e.}, 
+for any sequence $L$ of 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
+than $1/2$.
+Thus, even if the encrypted message would be extracted, 
+it would thus be not possible to retrieve the original one in a 
+polynomial time.