X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/canny.git/blobdiff_plain/f30c909e10a0d758bd045352bc1163b1e4efed16..963b0c034c8a7c7f1fb77fc6b06e3ba6744c1dbd:/ourapproach.tex?ds=sidebyside

diff --git a/ourapproach.tex b/ourapproach.tex
index 0bfe489..02d8735 100644
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -39,37 +39,48 @@ scheme.
 
 
 
-\subsubsection{Edge Based Image Steganography}
+\subsubsection{Edge-Based Image Steganography}
 
 
-The edge based image steganography schemes 
-already presented (\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10}) differ 
+The edge-based image steganography schemes 
+already presented \cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10} differ 
 in how carefully they select edge pixels, and  
 how they modify them.
 
-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 :-)}
+%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 :-)}
 
 Many techniques have been proposed in the literature to  detect 
-edges in  images. 
-The most common ones are filter
-edge detection methods such as Sobel  or Canny filters, low order methods such as
-first order  and second order ones. 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 that depend on the
-motivations behind that edges detection.   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
+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 in the second hand~\cite{KF11}.
+In first order methods like Sobel,
+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.
+For fuzzy edge methods, 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.
+%%
+%
+%Of course, all the algorithms have  advantages and drawbacks that depend on the
+%motivations behind that edges detection.   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
+As Canny algorithm is well known and studied, fast, and implementable
 on many  kinds of architectures like FPGAs, smartphones,  desktop machines, and
-GPUs. And of course, we do not pretend that this is the best solution.
+GPUs, we have chosen this edge detector for illustrative purpose.
+Of course, other detectors like the fuzzy edge methods
+merit much further attention, which is why we intend 
+to investigate systematically all of these detectors in our next work.
+%we do not pretend that this is the best solution.
 
-In order to be able to compute the same set of edge pixels, we suggest to consider all the bits of the image (cover or stego) without the LSB. With an 8 bits image, only the 7 first bits are considered. In our flowcharts, this is represented by ``LSB(7 bits Edge Detection)''.
+In order to be able to compute the same set of edge pixels, we suggest to consider all the bits of the image (cover or stego) without the LSB. Thus, with an 8 bits image, only the 7 first bits are considered. In our flowcharts, this is represented by ``LSB(7 bits Edge Detection)''.
 % 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},
@@ -118,12 +129,14 @@ that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} pseudorando
 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, $x_{i+L-1}$,
+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
 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 
+Equivalent formulations of such a property can
+be found. They all lead to the fact that,
+even if the encrypted message is extracted, 
+it is impossible to retrieve the original one in 
 polynomial time.