Each of these scheme starts with the computation of the distortion cost
for each pixel switch and is later followed by the STC algorithm.
Since this last step is shared by all,
-we separately eavluate this complexity.
+we separately evaluate this complexity.
In all the rest of this section, we consider a $n \times n$ square image.
First of all, HUGO starts with computing the second order SPAM Features.
Our edge selection is based on a Canny Filter. When applied on a
$n \times n$ square image, the noise reduction step is in $\theta(5^3 n^2)$.
Next, let $T$ be the size of the canny mask.
-Computing gradients is in $\theta(4Tn)$ since derivatives of each direction (vertical or horizontal)
-are in $\theta(2Tn)$.
+Computing gradients is in $\theta(4Tn^2)$ since derivatives of each direction (vertical or horizontal)
+are in $\theta(2Tn^2)$.
Finally, thresholding with hysteresis is in $\theta(n^2)$.
The overall complexity is thus in $\theta((5^3+4T+1)n^2)$.
construction.
The Fig.~\ref{fig:compared}
-summarizes the complexity of the embedding map construction, for Hugo, Wow
-and Uniward. It deals with square images
+summarizes the complexity of the embedding map construction, for
+WOW/UNIWARD, HUGO, and STABYLO. It deals with square images
of size $n \times n$ when $n$ ranges from
512 to 4096. The $y$-coordinate is expressed in a logarithm scale.
-It shows that the complexity of all algorithms
+It shows that the complexity of all the algorithms
is dramatically larger than the one of the STABYLO scheme.
-Thanks to these complexity results, we claim that STABYLO is lightweight.
+Thanks to these complexity results, we claim that our approach is lightweight.
\begin{figure}
\begin{center}
\includegraphics[scale=0.4]{complexity}
\end{center}
-\caption{Complexity evaluation of Wow/Uniward, Hugo, and Stabylo}
+\caption{Complexity evaluation of WOW/UNIWARD, HUGO, and STABYLO}
\label{fig:compared}
\end{figure}
+First of all, the whole code of STABYLO can be downloaded
+\footnote{\url{http://members.femto-st.fr/raphael-couturier/stabylo/}}.
For all the experiments, the whole set of 10,000 images
of the BOSS contest~\cite{Boss10} database is taken.
In this set, each cover is a $512\times 512$
generated by the integers given
in Table~\ref{table:matrices:H}
as introduced in~\cite{FillerJF11}, since these ones have experimentally
-be proven to have the best modification efficiency.
+be proven to have the strongest modification efficiency.
For instance if the rate between the size of the message and the size of the
cover vector
is 1/4, each number in $\{81, 95, 107, 121\}$ is translated into a binary number
\end{table}
-Our approach is always compared to Hugo~\cite{DBLP:conf/ih/PevnyFB10}
-and to EAISLSBMR~\cite{Luo:2010:EAI:1824719.1824720}.
-The former is the least detectable information hiding tool in spatial domain
-and the latter is the work that is the closest to ours, as far as we know.
-
-
-
-First of all, in our experiments and with the adaptive scheme,
-the average size of the message that can be embedded is 16,445 bits.
-It corresponds to an average payload of 6.35\%.
-The two other tools will then be compared with this payload.
-Sections~\ref{sub:quality} and~\ref{sub:steg} respectively present
-the quality analysis and the security of our scheme.
+Our approach is always compared to HUGO, to EAISLSBMR, to WOW and to UNIWARD
+for the two strategies Fixed and Adaptive.
+For the former one, the payload has been set to 10\%.
+For the latter one, the Canny parameter $T$ has been set to 3.
+When $b$ is 7, the average size of the message that can be embedded
+is 16,445 bits,
+that corresponds to an average payload of 6.35\%.
+For each cover image the STABYLO's embedding rate with these two parameters
+is memorized.
+Next each steganographic scheme is executed to produce the stego content of
+this cover with respect to this embedding rate.
For the sake of completeness, three metrics are computed in these experiments:
the Peak Signal to Noise Ratio (PSNR),
the PSNR-HVS-M family~\cite{psnrhvsm11},
-%the BIQI~\cite{MB10},
and
the weighted PSNR (wPSNR)~\cite{DBLP:conf/ih/PereiraVMMP01}.
The first one is widely used but does not take into
account the Human Visual System (HVS).
The other ones have been designed to tackle this problem.
-If we apply them on the running example,
+If we apply them on the running example with the Adaptive and STC strategies,
the PSNR, PSNR-HVS-M, and wPSNR values are respectively equal to
68.39, 79.85, and 89.71 for the stego Lena when $b$ is equal to 7.
If $b$ is 6, these values are respectively equal to
\begin{table*}
\begin{center}
\begin{small}
+\setlength{\tabcolsep}{3pt}
\begin{tabular}{|c|c|c||c|c|c|c|c|c|c|c|c|c|}
\hline
Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\
\hline
Embedding & Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive & Fixed &Adaptive \\
\hline
-Rate & 10\% & + sample & +STC(7) & +STC(6) & 10\%&6.35\%& 10\%&6.35\%& 10\%&6.35\%& 10\%&6.35\%\\
+Rate & 10\% & + sample & +STC(7) & +STC(6) & 10\%&$\approx$6.35\%& 10\%&$\approx$6.35\%& 10\%&$\approx$6.35\%& 10\%&$\approx$6.35\%\\
\hline
-PSNR & 61.86 & 63.48 & 66.55 (\textbf{-0.8\%}) & 63.7 & 64.65 & {67.08} & 60.8 & 62.9&65.9 & 68.3 & 65.8 & 69.2\\
+PSNR & 61.86 & 63.48 & 66.55 & 63.7 & 64.65 & {67.08} & 60.8 & 62.9&65.9 & 68.3 & 65.8 & 69.2\\
\hline
-PSNR-HVS-M & 72.9 & 75.39 & 78.6 (\textbf{-0.8\%}) & 75.5 & 76.67 & {79.23} & 71.8 & 74.3\\
-%\hline
-%BIQI & 28.3 & 28.28 & 28.4 & 28.28 & 28.28 & 28.2 & 28.2\\
+PSNR-HVS-M & 72.9 & 75.39 & 78.6 & 75.5 & 76.67 & {79.6} & 71.8 & 76.0 &
+76.7 & 80.35 & 77.6 & 81.2 \\
\hline
-wPSNR & 77.47 & 80.59 & 86.43(\textbf{-1.6\%})& 86.28 & 83.03 & {88.6} & 76.7 & 83& 83.8 & 90.4 & 85.2 & 91.9\\
+wPSNR & 77.47 & 80.59 & 86.43& 86.28 & 83.03 & {88.6} & 76.7 & 83& 83.8 & 90.4 & 85.2 & 91.9\\
\hline
\end{tabular}
\end{small}
-\begin{footnotesize}
-\vspace{2em}
-Variances given in bold font express the quality differences between
-HUGO and STABYLO with STC+adaptive parameters.
-\end{footnotesize}
-
\end{center}
\caption{Quality measures of steganography approaches\label{table:quality}}
\end{table*}
Results are summarized in Table~\ref{table:quality}.
+In this table, STC(7) stands for embedding data in the LSB whereas
+in STC(6), data are hidden in the last two significant bits.
+
+
Let us give an interpretation of these experiments.
-First of all, the adaptive strategy produces images with lower distortion
+First of all, the Adaptive strategy produces images with lower distortion
than the images resulting from the 10\% fixed strategy.
Numerical results are indeed always greater for the former strategy than
for the latter one.
-These results are not surprising since the adaptive strategy aims at
-embedding messages whose length is decided according to an higher threshold
+These results are not surprising since the Adaptive strategy aims at
+embedding messages whose length is decided according to a higher threshold
into the edge detection.
-Let us focus on the quality of HUGO images: with a given fixed
-embedding rate (10\%),
-HUGO always produces images whose quality is higher than the STABYLO's one.
-However our approach is always better than EAISLSBMR since this one may modify
-the two least significant bits.
-
-If we combine \emph{adaptive} and \emph{STC} strategies
-(which leads to an average embedding rate equal to 6.35\%)
-our approach provides metrics equivalent to those provided by HUGO.
-In this column STC(7) stands for embedding data in the LSB whereas
-in STC(6), data are hidden in the last two significant bits.
-
-The quality variance between HUGO and STABYLO for these parameters
-is given in bold font. It is always close to 1\% which confirms
-the objective presented in the motivations:
-providing an efficient steganography approach in a lightweight manner.
+If we combine Adaptive and STC strategies
+the STABYLO scheme provides images whose quality is higher than
+the EAISLSBMR's one but lower than the quality of high complexity
+schemes. Notice that the quality of the less respectful scheme (EAILSBMR)
+is lower than 6\% than the one of the most one.
-Let us now compare the STABYLO approach with other edge based steganography
-approaches, namely~\cite{DBLP:journals/eswa/ChenCL10,Chang20101286}.
-These two schemes focus on increasing the
-payload while the PSNR is acceptable, but do not
-give quality metrics for fixed embedding rates from a large base of images.
+% Let us now compare the STABYLO approach with other edge based steganography
+% approaches, namely~\cite{DBLP:journals/eswa/ChenCL10,Chang20101286}.
+% These two schemes focus on increasing the
+% payload while the PSNR is acceptable, but do not
+% give quality metrics for fixed embedding rates from a large base of images.
% AUMP~\cite{Fillatre:2012:ASL:2333143.2333587}
% and
Ensemble Classifier~\cite{DBLP:journals/tifs/KodovskyFH12} based steganalyser.
-This approach aims at detecting hidden bits in grayscale natural
-images and is
-considered as state of the art steganalysers in the spatial domain~\cite{FK12}.
+Its particularization to spatial domain is
+considered as state of the art steganalysers.
+Firstly, a space
+of 686 co-occurrence and Markov features is extracted from the
+set of cover images and the set of training images. Next a small
+set of weak classifiers is randomly built,
+each one working on a subspace of all the features.
+The final classifier is constructed by a majority voting
+between the decisions of these individual classifiers.
+
+
%The former approach is based on a simplified parametric model of natural images.
% Parameters are firstly estimated and an adaptive Asymptotically Uniformly Most Powerful
% (AUMP) test is designed (theoretically and practically), to check whether
\begin{table*}
\begin{center}
\begin{small}
+\setlength{\tabcolsep}{3pt}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} & \multicolumn{2}{|c|}{WOW} & \multicolumn{2}{|c|}{UNIWARD}\\
\hline
Embedding & Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. & Fixed & Adapt. \\
\hline
-Rate & 10\% & + sample & +STC(7) & +STC(6) & 10\%& 6.35\%& 10\%& 6.35\% & 10\%& 6.35\%& 10\%& 6.35\%\\
+Rate & 10\% & + sample & +STC(7) & +STC(6) & 10\%& $\approx$6.35\%& 10\%& $\approx$6.35\% & 10\%& $\approx$6.35\%& 10\%& $\approx$6.35\%\\
\hline
%AUMP & 0.22 & 0.33 & 0.39 & 0.45 & 0.50 & 0.50 & 0.49 & 0.50 \\
%\hline
\end{table*}
-Results are summarized in Table~\ref{table:steganalyse}.
+Results of average testing errors
+are summarized in Table~\ref{table:steganalyse}.
First of all, STC outperforms the sample strategy %for % the two steganalysers
as
already noticed in the quality analysis presented in the previous section.
-Next, our approach is more easily detectable than HUGO, which
-is the most secure steganographic tool, as far as we know.
-However by combining \emph{adaptive} and \emph{STC} strategies
-our approach obtains similar results to HUGO ones.
-
-%%%%et pour b= 6 ?
-
+Next, our approach is more easily detectable than HUGO,
+WOW and UNIWARD which are the most secure steganographic tool,
+as far as we know.
+However by combining Adaptive and STC strategies
+our approach obtains similar results than the ones of these schemes.
Compared to EAILSBMR, we obtain better results when the strategy is
-\emph{adaptive}.
+Adaptive.
However due to its
-huge number of integration features, it is not lightweight, which justifies
-in the authors' opinion the consideration of the proposed method.
+huge number of integration features, it is not lightweight.
+
+All these numerical experiments confirm
+the objective presented in the motivations:
+providing an efficient steganography approach in a lightweight manner.
A new steganographic method called STABYLO is introduced in
this research work.
Its main advantage is to be much lighter than the so-called
-HUGO, WOW, and UNIWARDS schemes, the state of the art
+HUGO, WOW, and UNIWARD schemes, the state of the art
steganographic processes.
Additionally to this effectiveness,
quite comparable results through noise measures like PSNR-HVS-M
Adaptive, Bbs, and binarY embedding at LOw cost, has been introduced
in this document as an efficient method having comparable, though
somewhat smaller, security than well-known
-steganographic schemes lite
+steganographic schemes
HUGO, WOW, and UNIWARD.
This edge-based steganographic approach embeds a Canny
-detection filter, the Blum-Blum-Shub cryptographically secure
-pseudorandom number generator, together with Syndrome-Trellis Codes
+detection filter, the secure Blum-Blum-Shub cryptosystem
+with its pseudorandom number generator,
+together with Syndrome-Trellis Codes
for minimizing distortion.
-After having introduced with details the proposed method,
-we have evaluated it through noise measures (namely, the PSNR, PSNR-HVS-M,
-and weighted PSNR), we have used well-established steganalysers.
+The complexity study of our proposed method and of the
+state of the art steganographic tools has shown that our approach
+has the lowest computation cost among all.
+This justifies the lightweight attribute of our scheme.
+The evaluation of introduced noise measures
+(namely, the PSNR, PSNR-HVS-M, and weighted PSNR),
+and of its embedding through stegenalysers (namely Ensemble Classifier)
+have shown that STABYLO is efficient enough to
+produce qualitative images and
+to face steganalysers.
+
+
+
% Of course, other detectors like the fuzzy edge methods
% deserve much further attention, which is why we intend
\subsection{Security considerations}\label{sub:bbs}
Among the methods of message encryption/decryption
(see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
-we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
+we implement the asymmetric
+Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82}
pseudorandom number generator (PRNG) and the
XOR binary function.
-It has been proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG
+The main justification of this choice
+is that it has been proven~\cite{DBLP:conf/crypto/ShubBB82} that this PRNG
has the property of cryptographical security, \textit{i.e.},
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
the Canny algorithm computes derivatives
in the two directions with respect to a mask of size $T$.
The higher $T$ is, the coarse the approach is. Practically,
-$T$ is set with $3$, $3$, or $7$.
+$T$ is set with $3$, $5$, or $7$.
In our flowcharts, this step is represented by ``Edge Detection(b, T, X)''.
Let $x$ be the sequence of these bits.
The next section presents how to adapt our scheme
-when the size of $x$ is not sufficient for the message $m$ to embed.
+with respect to the size
+of the message $m$ to embed and the size of the cover $x$.
+
\subsection{Adaptive embedding rate}\label{sub:adaptive}
Two strategies have been developed in our approach,
-depending on the embedding rate that is either \emph{adaptive} or \emph{fixed}.
+depending on the embedding rate that is either \emph{Adaptive} or \emph{Fixed}.
In the former the embedding rate depends on the number of edge pixels.
The higher it is, the larger the message length that can be inserted is.
Practically, a set of edge pixels is computed according to the
-\subsection{Minimizing distortion with syndrome-trellis codes}\label{sub:stc}
+\subsection{Minimizing distortion with Syndrome-Trellis Codes}\label{sub:stc}
\input{stc}
which bits to change among the 36,910 ones.
In the two cases, about the third part of the poem is hidden into the cover.
-Results with \emph{adaptive} and \textit{STC} strategies are presented in
+Results with {Adaptive} and {STC} strategies are presented in
Fig.~\ref{fig:lenastego}.
\begin{figure}[t]
\right..
$$
This function allows to emphasize differences between contents.
-Notice that
+Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary
+and this image only contains 0 and 75 values.
+Similarly, if $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary
+and the image contains all the values in $\{0,75,150,225\}$.
+
\begin{figure}[t]
\end{figure}
-Notice that since $b$ is 7 in Fig.~\ref{fig:diff7}, the embedding is binary
-and this image only contains 0 and 75 values.
-Similarly, when $b$ is 6 as in Fig.~\ref{fig:diff6}, the embedding is ternary
-and the image contains all the values in $\{0,75,150,225\}$.
