
This work considers digital images as covers and foundation is
spatial least significant-bit (LSB) replacement.
In this data hiding scheme a subset of all the LSB of the cover image is modified 
with a secret bit stream depending on to 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
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
scheme can avoid the LSB replacement style asymmetry, and
thus it should make the detection slightly more difficult than the
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.
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
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 contains large variation with neighbouring 
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 bee 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 coarse 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 
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.
In the latter, an hybrid edge detector is presented followed by an ad'hoc
embedding approach. 
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. 


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, 
the better the approach is said to be. 
Contrarely, we argue that some images should'nt be taken as a cover because of the nature of their signal.
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.

 

\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 organised 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}





