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-
-This research work takes place into the field of information hiding, considerably developed
+This research work takes place in the field of information hiding, considerably developed

 these last two decades. The proposed method for 
 these last two decades. The proposed method for 

-steganography considers digital images as covers, it belongs in the well investigated large category
+steganography considers digital images as covers.
+It belongs to the well-known large category

 of spatial least significant bits (LSBs) replacement schemes.
 Let us recall that, in this LSBR category, a subset of all the LSBs of the cover image is modified 
 with a secret bit stream depending on: a secret key, the cover, and the message to embed.
 of spatial least significant bits (LSBs) replacement schemes.
 Let us recall that, in this LSBR category, a subset of all the LSBs of the cover image is modified 
 with a secret bit stream depending on: a secret key, the cover, and the message to embed.

-In this well studied steganographic approach,
-pixels with even values (resp. odd values) are never decreased (resp. increased), 
+In this well-studied steganographic approach,
+if we consider that a LSB is the last bit of each pixel value,  
+pixels with an even value (resp. an odd value) 
+are never decreased (resp. increased), 

 thus such schemes may break the 
 structural symmetry of the host images.
 And these structural alterations can be detected by 
 thus such schemes may break the 
 structural symmetry of the host images.
 And these structural alterations can be detected by 

-well designed statistical investigations, leading to known steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.
+well-designed statistical investigations, leading to known steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.

 
 Let us recall too that this drawback 
 can be corrected considering the LSB matching (LSBM) subcategory, in which
 the $+1$ or $-1$ is randomly added to the cover pixel LSB value 
 only if this one does not correspond to the secret bit.
 
 Let us recall too that this drawback 
 can be corrected considering the LSB matching (LSBM) subcategory, in which
 the $+1$ or $-1$ is randomly added to the cover pixel LSB value 
 only if this one does not correspond to the secret bit.

-Since it is possible to make that probabilities of increasing or decreasing the pixel value are the same, for instance by considering well encrypted hidden messages, usual statistical approaches 
+%TODO : modifier ceci
+Since it is possible to make that probabilities of increasing or decreasing the pixel value, for instance by considering well-encrypted hidden messages, usual statistical approaches 

 cannot be applied here to discover stego-contents in LSBM.
 cannot be applied here to discover stego-contents in LSBM.

-The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/2005,FK12},
+The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/Ker05,FK12},

 which classify images according to extracted features from neighboring elements of residual noise.  
 
 
 which classify images according to extracted features from neighboring elements of residual noise.  
 
 

-Finally, LSB matching revisited (LSBMR) has been recently introduced in~\cite{Mielikainen06}. 
+Finally, LSB matching revisited (LSBMR) has recently been introduced in~\cite{Mielikainen06}. 

 It works as follows: for a given pair of pixels, the LSB
 of the first pixel carries a first bit of the secret message, while the parity relationship
 (odd/even combination) of the two pixel values carries
 It works as follows: for a given pair of pixels, the LSB
 of the first pixel carries a first bit of the secret message, while the parity relationship
 (odd/even combination) of the two pixel values carries


@@ -42,38 +45,45 @@ LSBM approach. % based on our experiments
 
 Instead of (efficiently) modifying LSBs, there is also a need to select pixels whose value 
 modification minimizes a distortion function.
 
 Instead of (efficiently) modifying LSBs, there is also a need to select pixels whose value 
 modification minimizes a distortion function.

-This distortion may be computed thanks to feature vectors that are embedded for instance in steganalysers
+This distortion may be computed thanks to feature vectors that are embedded for instance in the steganalysers

 referenced above. 
 Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10} is one of the most efficient instance of such a scheme.
 referenced above. 
 Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10} is one of the most efficient instance of such a scheme.

-It takes into account so-called SPAM features (whose size is larger than $10^7$) to avoid overfitting a particular 
-steganalyser. Thus a distortion measure for each pixel is individually determined as the sum of differences between
-features of SPAM computed from the cover and from the stego images.
-Thanks to this features set, HUGO allows to embed $7\times$ longer messages with the same level of 
-indetectability than LSB matching. 
+It takes into account so-called SPAM features 
+%(whose size is larger than $10^7$) 
+to avoid overfitting a particular 
+steganalyser. Thus a distortion measure for each pixel is individually determined as the sum of the differences between
+the features of the SPAM computed from the cover and from the stego images.
+Thanks to this features set, HUGO allows to embed messages that are $7\times$ longer than the former ones with the same level of 
+indetectability as LSB matching. 

 However, this improvement is time consuming, mainly due to the distortion function
 computation. 
 
 
 There remains a large place between random selection of LSB and feature based modification of pixel values.
 We argue that modifying edge pixels is an acceptable compromise. 
 However, this improvement is time consuming, mainly due to the distortion function
 computation. 
 
 
 There remains a large place between random selection of LSB and feature based modification of pixel values.
 We argue that modifying edge pixels is an acceptable compromise. 

-Edges form the outline of an object: they are the boundary between overlapping objects or between an object
-and the background. When producing the stego-image, a small modification of some pixel values in such edges should not impact the image quality, which is a requirement when
+Edges form the outline of an object: they are the boundaries between overlapping objects or between an object
+and its background. When producing the stego-image, a small modification of some pixel values in such edges should not impact the image quality, which is a requirement when

 attempting to be undetectable. Indeed,
 attempting to be undetectable. Indeed,

-in cover image, edges already break the  continuity of pixels' intensity map and thus already present large variations with theirs neighboring 
-pixels. In other words, minor changes in regular area are more dramatic than larger modifications in edge ones. 
+in a cover image, edges already break the  continuity of pixels' intensity map and thus already present large variations with their neighboring 
+pixels. In other words, minor changes in regular areas are more dramatic than larger modifications in edge ones. 

 Our first proposal is thus to embed message bits into edge shapes while preserving other smooth regions. 
 
 Our first proposal is thus to embed message bits into edge shapes while preserving other smooth regions. 
 

-Edge based steganographic schemes have been already studied, the most interesting 
-approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and \cite{DBLP:journals/eswa/ChenCL10}.
-In the former, the authors show how to select sharper edge regions with respect 
+Edge based steganographic schemes have already been  studied, 
+the most interesting 
+approaches being detailed in~\cite{Luo:2010:EAI:1824719.1824720} and 
+in~\cite{DBLP:journals/eswa/ChenCL10}.
+In the former, the authors present the Edge Adaptive
+Image Steganography based on LSB matching revisited further denoted as  
+EAISLSBMR. This approach selects sharper edge
+ regions with respect 

 to a given embedding rate: the larger the number of bits to be embedded, the coarser
 the edge regions are.
 to a given embedding rate: the larger the number of bits to be embedded, the coarser
 the edge regions are.

-Then the data hiding algorithm is achieved by applying LSBMR on pixels of these regions. 
+Then the data hiding algorithm is achieved by applying LSBMR on some of the pixels of these regions. 

 The authors show that their proposed method is more efficient than all the LSB, LSBM, and LSBMR approaches 
 thanks to extensive experiments.
 However, it has been shown that the distinguishing error with LSB embedding is lower than 
 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.
 The authors show that their proposed method is more efficient than all the LSB, LSBM, and LSBMR approaches 
 thanks to extensive experiments.
 However, it has been shown that the distinguishing error with LSB embedding is lower than 
 the one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.

-We thus propose to take benefit of these optimized embedding, provided they are not too time consuming.
+We thus propose to take advantage of these optimized embeddings, provided they are not too time consuming.

 In the latter, an hybrid edge detector is presented followed by an ad hoc
 embedding. 
 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993} 
 In the latter, an hybrid edge detector is presented followed by an ad hoc
 embedding. 
 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993} 


@@ -86,32 +96,35 @@ schemes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf
 produce stego contents 
 by only considering the payload, not the type of image signal: the higher the payload is, 
 the better the approach is said to be. 
 produce stego contents 
 by only considering the payload, not the type of image signal: the higher the payload is, 
 the better the approach is said to be. 

-Contrarily, we argue that some images should not be taken as a cover because of the nature of their signal.
+Contrarily, we argue that some images should not be taken as a cover because of the nature of their signals.

 Consider for instance a uniformly black image: a very tiny modification of its pixels can be easily detectable.  
 Consider for instance a uniformly black image: a very tiny modification of its pixels can be easily detectable.  

-The approach we propose is thus to provide a self adaptive algorithm with a high payload, which depends on the 
-cover signal. 
+The approach we propose is thus to provide a self adaptive algorithm with a high payload, which depends on the  cover signal. 
+% Message extraction is achieved by computing the same
+% edge detection pixels set for the cover and the stego image. 
+% The edge detection algorithm is thus not applied  on all the bits of the image,
+% but to exclude the LSBs which are modified. 

 
 

-Additionally, in the steganographic context, the data hiding procedure is often required
-to be a reversible one. We thus need to be able to compute the same edge detection pixels set for the cover and the stego image. For this, we propose to apply the edge detection algorithm not on all the bits of the image, but to exclude the LSBs. 

 Finally, even if the steganalysis discipline
 Finally, even if the steganalysis discipline

-has done great leaps forward these last years, it is currently impossible to prove rigorously
+ has known  great innovations these last years, it is currently impossible to prove rigorously

 that a given hidden message cannot be recovered by an attacker.
 This is why we add to our scheme a reasonable
 message encryption stage, to be certain that,
 even in the worst case scenario, the attacker
 that a given hidden message cannot be recovered by an attacker.
 This is why we add to our scheme a reasonable
 message encryption stage, to be certain that,
 even in the worst case scenario, the attacker

-will not be able to obtain the message content.
-
+will not be able to obtain the original message content.
+Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.

 
 

-In this research work, we thus propose to combine tried and 
-tested techniques of signal theory (the adaptive edge detection), coding (the binary embedding), and cryptography 
-(encryption of the hidden message) to compute an efficient steganographic
-scheme, which takes into consideration the cover image 
-and that can be executed on small devices.  
+To sum up, in this research work, well-studied and experimented
+techniques of signal processing (adaptive edges detection), 
+coding theory (syndrome-trellis codes), and cryptography 
+(Blum-Goldwasser encryption protocol) are combined 
+to compute an efficient steganographic
+scheme, whose principal characteristic is to take into 
+consideration the cover image and to be compatible with small computation resources.  

 
 The remainder of this document is organized as follows. 
 
 The remainder of this document is organized as follows. 

-Section~\ref{sec:ourapproach} presents the details of our steganographic scheme.
-Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach 
-and compares it to state of the art steganographic schemes.
+Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme and applies it on a running example.
+Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach,
+and compare them to the state of the art steganographic schemes.

 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
 
 
 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.