
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 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), 
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}.

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.
%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.
The most accurate detectors for this matching are universal steganalysers such as~\cite{LHS08,DBLP:conf/ih/2005,FK12},
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}. 
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
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
thus it should make the detection slightly more difficult than in 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
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 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 $7\times$ 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 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 presents the Edge Adaptive
Image Steganography based on lsb matching revisited further denoted as to 
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.
Then the data hiding algorithm is achieved by applying LSBMR on 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}.
We thus propose to take benefit of these optimized embedding, 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} 
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. 


One can notice that all the previously referenced 
schemes~\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. 
Contrarily, we argue that some images should not 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. 

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 which are modified. 
% Finally, even if the steganalysis discipline
% has done great leaps forward 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-treillis 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.
Section~\ref{sec:experiments} shows experiments on image quality, steganalytic evaluation, complexity of our approach,
and compares it to the state of the art steganographic schemes.
Finally, concluding notes and future work are given in Section~\ref{sec:concl}.





