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-
-This work considers digital images as covers and it is based on
-spatial least significant-bit (LSB) replacement.
-In this data hiding scheme a subset of all the LSBs of the cover image is modified 
-with a secret bit stream depending on a key, the cover, and the message to embed.
-This well studied steganographic approach  never decreases (resp. increases)
-pixel with even value (resp. odd value) and may break structural symmetry.
-These structural modification can be detected  by statistical approaches 
-and thus by steganalysis methods~\cite{DBLP:journals/tsp/DumitrescuWW03,DBLP:conf/mmsec/FridrichGD01,Dumitrescu:2005:LSB:1073170.1073176}.
-
-This drawback is avoided in LSB matching (LSBM) where
-the $+1$ or $-1$ is randomly added to the cover pixel LSB value 
-only if this one does not match the secret bit.
-Since probabilities of increasing or decreasing pixel value are the same, statistical approaches 
-cannot be applied there to discover stego-images in LSBM.
-The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/2005,FK12}
-which classify images thanks to extracted features from neighboring elements of noise residual.  
-
-
-LSB matching revisited (LSBMR)~\cite{Mielikainen06} have been recently introduced. 
-For a given pair of pixels, in which the LSB
-of the first pixel carries one bit of secret message, and the relationship
-(odd–even combination) of the two pixel values carries
-another bit of secret message. 
-
-
-
-In such a way, the modification
+This research work takes place in the field of information hiding, considerably developed these last two decades. The proposed method for 
+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 LSB replacement 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,
+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 
+well-designed statistical investigations, leading to well-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 fixed by considering the LSB matching (LSBM) subcategory, in which
+the $+1$ or $-1$ is randomly added to the cover pixel's LSB value 
+only if this one does not correspond to the secret bit.
+%TODO : modifier ceci
+By considering well-encrypted hidden messages, the probabilities of increasing or decreasing the value of pixels  are equal. Then usual statistical approaches 
+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/Ker05,FK12},
+which classify images according to extracted features from neighboring elements of residual noise.  
+
+
+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
+a second bit of the message. 
+By doing so, the modification

 rate of pixels can decrease from 0.5 to 0.375 bits/pixel
 (bpp) in the case of a maximum embedding rate, meaning fewer
 rate of pixels can decrease from 0.5 to 0.375 bits/pixel
 (bpp) in the case of a maximum embedding rate, meaning fewer

-changes to the cover image at the same payload compared to
-LSB replacement and LSBM. It is also shown that such a new
+changes in the cover image at the same payload compared to both
+LSBR and LSBM. It is also shown in~\cite{Mielikainen06} that such a new

 scheme can avoid the LSB replacement style asymmetry, and
 scheme can avoid the LSB replacement style asymmetry, and

-thus it should make the detection slightly more difficult than the
+thus it should make the detection slightly more difficult than in the

 LSBM approach. % based on our experiments
 
 
 
 
 
 LSBM approach. % based on our experiments
 
 
 
 
 

-Instead of (efficiently) modifying LSBs, there is also a need to select pixels whose value 
+Additionally to (efficiently) modifying LSBs, there is also a need to select pixels whose value 

 modification minimizes a distortion function.
 modification minimizes a distortion function.

-This distortion may be computed thanks to feature vectors that are embedded for instance in steganalysers
-given 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 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 feature set, HUGO allows to embed $7\times$ longer messages with the same level of 
-indetectability than LSB matching. 
-However, this improvement is time consuming, mainly due to the distortion function
+This distortion may be computed thanks to feature vectors that
+ are embedded for instance in the steganalysers
+referenced above. 
+The Highly Undetectable steGO (HUGO) method~\cite{DBLP:conf/ih/PevnyFB10},
+WOW~\cite{conf/wifs/HolubF12}, and UNIWARD~\cite{HFD14}
+are some of the  most efficient instances of such a scheme.
+
+HUGO takes into account so-called SPAM features.
+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.
+The features embedded in WOW and UNIWARD are based on Wavelet-based 
+directional filter. Thus, similarelly, the distortion function is 
+the sum  of the differences between these wavelet coefficients  
+computed from the cover and from the stego images.
+
+
+Due to this distortion measures, HUGO, WOW and UNIWARD allow
+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. 
 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. A small modification of pixel value in the stego image should not be harmful to the image quality:
-in cover image, edge pixels already break its continuity  and thus already contain large variation with neighboring 
-pixels. In other words, minor changes in regular area are more dramatic than larger modifications in edge ones. 
-Our proposal is thus to embed message bits into edge shapes while preserving other smooth regions. 
-
-Edge based steganographic schemes have been already studied~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10}.
-In the former, the authors show how to select sharper edge regions with respect 
-to embedding rate: the larger the number of bits to be embedded, the coarser
+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,
+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. 
+
+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 is, the coarser

 the edge regions are.
 the edge regions are.

-Then the data hiding algorithm is achieved by applying LSBMR on pixels of this region. 
-The authors show that this method is more efficient than all the LSB, LSBM, LSBMR approaches 
-thanks to extensive experiments.
-However, it has been shown that the distinguish error with LSB embedding is fewer than 
+Then the data hiding algorithm is achie\-ved 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 
+through 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 one with some binary embedding~\cite{DBLP:journals/tifs/FillerJF11}.

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

 In the latter, an hybrid edge detector is presented followed by an ad hoc
 In the latter, an hybrid edge detector is presented followed by an ad hoc

-embedding approach. 
+embedding. 

 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993} 
 The Edge detection is computed by combining fuzzy logic~\cite{Tyan1993} 

-and Canny~\cite{Canny:1986:CAE:11274.11275} approaches. The goal of this combination 
-is to enlarge the set of modified bits to increase the payload. 
+and Canny~\cite{Canny:1986:CAE:11274.11275} approaches. 
+The goal of this combination 
+is to enlarge the set of modified bits to increase the payload of the data hiding scheme. 

 
 
 
 

-But, one can notice that all the previous referenced 
-schemes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10}
-produce stego content 
-with only considering the payload, not the type of image signal: the higher the payload is, 
+One can notice that all the previously referenced 
+sche\-mes~\cite{Luo:2010:EAI:1824719.1824720,DBLP:journals/eswa/ChenCL10,DBLP:conf/ih/PevnyFB10}
+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. 
 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. 
-
-For some applications it might be interesting to be have a reversible procedure to compute the same edge detection pixel 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 only on all the bits without taking into consideration the LSB. 
- 
-
-\JFC{Christophe : énoncer la problématique du besoin de crypto et de ``cryptographiquement sûr'',  les algo déjà cassés....
-l'efficacité d'un encodage/décodage ...} 
-To deal with security issues, message is encrypted... 
-
-In this paper, we thus propose to combine tried and 
-tested techniques of signal theory (the adaptive edge detection), coding (the binary embedding), and cryptography 
-(the encrypt the message) to compute an efficient steganography 
-scheme, which takes into consideration the cover image 
-an which is amenable to be executed on small devices.  
-
-The rest of the paper 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 compare them to state of the art steganographic schemes.
-Finally, concluding notes and future works are given in section~\ref{sec:concl}
-
-
+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. 
+
+Finally, even if the steganalysis discipline
+ 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
+will not be able to obtain the original message content.
+Doing so makes our steganographic protocol, to a certain extend, an asymmetric one.
+
+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. 
+Section~\ref{sec:ourapproach} presents the details of the proposed steganographic scheme and applies it on a running example. Among its technical description, 
+its adaptive aspect is emphasized.
+Section~\ref{sub:complexity} presents the overall complexity of our approach
+and compares it to HUGO, WOW, and UNIWARD.
+Section~\ref{sec:experiments} shows experiments on image quality, steganalysis evaluation, and compares them to the state of the art steganographic schemes.
+Finally, concluding notes and future work are given in Section~\ref{sec:concl}.