après raph

diff --git a/complexity.tex b/complexity.tex
index 6932afaf6883139148707cf3d1114866a2dfaa58..6e108f80c1c69feebc2c9dbb44e3b5211a43b6fa 100644 (file)
--- a/complexity.tex
+++ b/complexity.tex
@@ -4,7 +4,7 @@ To be more precise, we compare the complexity of our schemes to the
 state of the art steganography, namely HUGO~\cite{DBLP:conf/ih/PevnyFB10}.
 
 
 state of the art steganography, namely HUGO~\cite{DBLP:conf/ih/PevnyFB10}.
 
 

-In what follows, we consider an $n \times n$ square image. 
+In what follows, we consider a $n \times n$ square image. 

 First of all, HUGO starts with computing the second order SPAM Features.
 This steps is in  $O(n^2 + 2.343^2)$ due to the calculation 
 of the difference arrays and next of the 686 features (of size 343).
 First of all, HUGO starts with computing the second order SPAM Features.
 This steps is in  $O(n^2 + 2.343^2)$ due to the calculation 
 of the difference arrays and next of the 686 features (of size 343).


@@ -13,12 +13,12 @@ its value and computing again the SPAM
 features. Pixels are thus selected according to their ability to provide
 an image whose SPAM features are close to the original one. 
 The algorithm is thus computing a distance between each computed feature, 
 features. Pixels are thus selected according to their ability to provide
 an image whose SPAM features are close to the original one. 
 The algorithm is thus computing a distance between each computed feature, 

-andthe original ones
+and the original ones

 which is at least in $O(343)$ and an overall distance between these 
 metrics which is in $O(686)$. Computing the distance is thus in 
 $O(2\times 343^2)$ and this modification
 is thus in $O(2\times 343^2 \times n^2)$.
 which is at least in $O(343)$ and an overall distance between these 
 metrics which is in $O(686)$. Computing the distance is thus in 
 $O(2\times 343^2)$ and this modification
 is thus in $O(2\times 343^2 \times n^2)$.

-Ranking these results may be achieved with a insertion sort which is in 
+Ranking these results may be achieved with an insertion sort which is in 

 $2.n^2 \ln(n)$.
 The overall complexity of the pixel selection is thus 
 $O(n^2 +2.343^2 + 2\times 343^2 \times n^2 + 2.n^2 \ln(n))$, \textit{i.e}
 $2.n^2 \ln(n)$.
 The overall complexity of the pixel selection is thus 
 $O(n^2 +2.343^2 + 2\times 343^2 \times n^2 + 2.n^2 \ln(n))$, \textit{i.e}


@@ -32,12 +32,17 @@ at least $343^2/\ln{n}$ times higher than
 our scheme. For instance, for a squared image with 4M pixel per slide,
 this part of our algorithm is more than 14100 faster than Hugo.
 
 our scheme. For instance, for a squared image with 4M pixel per slide,
 this part of our algorithm is more than 14100 faster than Hugo.
 

-We are then left to express the complexity of the STC algorithm .
+We are then left to express the complexity of the STC algorithm.

 According to~\cite{DBLP:journals/tifs/FillerJF11}, it  is 
 in $O(2^h.n)$ where $h$ is the size of the duplicated 
 matrix. Its complexity is thus negligeable compared with the embedding map
 construction.
 
 According to~\cite{DBLP:journals/tifs/FillerJF11}, it  is 
 in $O(2^h.n)$ where $h$ is the size of the duplicated 
 matrix. Its complexity is thus negligeable compared with the embedding map
 construction.
 

+
+
+
+
+

 Thanks to these complexity result, we claim that STABYLO is lightweight. 
 
 
 Thanks to these complexity result, we claim that STABYLO is lightweight. 
 
 

diff --git a/experiments.tex b/experiments.tex
index 7afd27cb88c7e0877857d9dceed97dc0955eddec..3babfb3a5ae60325ffb0cf5d1a4848baba6ead1c 100644 (file)
--- a/experiments.tex
+++ b/experiments.tex
@@ -4,16 +4,17 @@ In this set, each cover is a $512\times 512$
 grayscale digital image in a RAW format. 
 We restrict experiments to 
 this set of cover images since this paper is more focused on 
 grayscale digital image in a RAW format. 
 We restrict experiments to 
 this set of cover images since this paper is more focused on 

-the methodology than benchmarking.    
+the methodology than on benchmarking.    

 
 We use the matrices $\hat{H}$ 
 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.
 
 We use the matrices $\hat{H}$ 
 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.

-For instance if the rate between the size of message and the size of the host is 
-1/4, each number in $\{81, 95, 107, 121\}$ is translated into a binary number 
-and each one consitutes thus an column of $\hat{H}$. 
+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 
+and each one consitutes thus a column of $\hat{H}$. 

 
 \begin{table}
 $$
 
 \begin{table}
 $$


@@ -52,7 +53,7 @@ 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.
 
 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.

-Its corresponds to an  average payload of 6.35\%. 
+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. 
 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. 


@@ -133,7 +134,7 @@ 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
 (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 two last significant bits. 
+in STC(6), data are hidden in the last two  significant bits. 

 
 
 
 
 
 


@@ -156,20 +157,22 @@ give quality metrics for fixed embedding rates from a large base of images.
 
 
 
 
 
 

-The steganalysis quality of our approach has been evaluated through the two 
-AUMP~\cite{Fillatre:2012:ASL:2333143.2333587}
-and Ensemble Classifier~\cite{DBLP:journals/tifs/KodovskyFH12} based steganalysers.
-Both aim at detecting hidden bits in grayscale natural images and are 
+The steganalysis quality of our approach has been evaluated through the % two 
+% 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}.
 considered as state of the art steganalysers in the spatial domain~\cite{FK12}.

-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
-an image has stego content or not.
-This approach is dedicated to verify whether LSB has been modified or not.
-In the latter, the authors show that the 
-machine learning step, which is often
-implemented as a support vector machine,
-can be favorably executed thanks to an ensemble classifier.
+%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
+% an image has stego content or not.
+% This approach is dedicated to verify whether LSB has been modified or not.
+% , the authors show that the 
+% machine learning step, which is often
+% implemented as a support vector machine,
+% can be favorably executed thanks to an ensemble classifier.

 
 
 \begin{table*}
 
 
 \begin{table*}


@@ -183,8 +186,8 @@ Embedding & Fixed &   \multicolumn{3}{|c|}{Adaptive (about 6.35\%)}  & \multicol
 \hline
 Rate & 10\% &  + sample &   +STC(7) & +STC(6)   & 10\%& 6.35\%& 10\%& 6.35\%\\ 
 \hline
 \hline
 Rate & 10\% &  + sample &   +STC(7) & +STC(6)   & 10\%& 6.35\%& 10\%& 6.35\%\\ 
 \hline

-AUMP & 0.22 & 0.33 & 0.39  &   0.45    &  0.50 &  0.50 & 0.49 & 0.50 \\
-\hline
+%AUMP & 0.22 & 0.33 & 0.39  &   0.45    &  0.50 &  0.50 & 0.49 & 0.50 \\
+%\hline

 Ensemble Classifier & 0.35 & 0.44 & 0.47 & 0.47     & 0.48 &  0.49  &  0.43  & 0.46 \\
 
 \hline
 Ensemble Classifier & 0.35 & 0.44 & 0.47 & 0.47     & 0.48 &  0.49  &  0.43  & 0.46 \\
 
 \hline


@@ -196,13 +199,19 @@ Ensemble Classifier & 0.35 & 0.44 & 0.47 & 0.47     & 0.48 &  0.49  &  0.43  & 0
 
 
 Results are summarized in Table~\ref{table:steganalyse}.
 
 
 Results are summarized in Table~\ref{table:steganalyse}.

-First of all, STC outperforms the sample strategy for the two steganalysers, as 
+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.
 
 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 ?
+
+
+Compared to EAILSBMR, we obtain better results when the strategy is 
+\emph{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.   
 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.   

diff --git a/intro.tex b/intro.tex
index d1ee49985fec80103c8bc370dfa7c7c4699a754c..751fae8e095f2e1476df56e566e11fc61f49cd6a 100644 (file)
--- a/intro.tex
+++ b/intro.tex
@@ -1,9 +1,8 @@
-This research work takes place in the field of information hiding, considerably developed
-these last two decades. The proposed method for 
+This research work takes place in the field of information hiding, considerably developed for the 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.
 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 
+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,  
 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,  


@@ -12,14 +11,15 @@ 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 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 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
 
 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

-By considering well-encrypted hidden messages, probabilities of increasing or of decreasing value of pixels  are equal. Then usual statistical approaches 
+By considering well-encrypted hidden messages, the probabilities of increasing or decreasing the alue 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.  
 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.  


@@ -47,7 +47,7 @@ Instead of (efficiently) modifying LSBs, there is also a need to select pixels w
 modification minimizes a distortion function.
 This distortion may be computed thanks to feature vectors that are embedded for instance in the steganalysers
 referenced above. 
 modification minimizes a distortion function.
 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.
+The 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 
 It takes into account so-called SPAM features 
 %(whose size is larger than $10^7$) 
 to avoid overfitting a particular 


@@ -76,7 +76,7 @@ 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 
 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
+to a given embedding rate: the larger the number of bits to be embedded is, the coarser

 the edge regions are.
 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 
 the edge regions are.
 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 


@@ -87,7 +87,8 @@ We thus propose to take advantage of these optimized embeddings, provided they a
 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} 

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


@@ -125,8 +126,8 @@ 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
 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 compare it to the HUGO's one.
-Section~\ref{sec:experiments} shows experiments on image quality, steganalysis evaluation, and compare them to the state of the art steganographic schemes.
+and compares it to the HUGO's one.
+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}.
 
 
 Finally, concluding notes and future work are given in Section~\ref{sec:concl}.
 
 

diff --git a/main.tex b/main.tex
index bb3f1432e1e533e0f8f6e928d14433d73dfbb0a2..e2b25eda51930e76528ed047f5b99be47fffeff9 100755 (executable)
--- a/main.tex
+++ b/main.tex
@@ -42,7 +42,7 @@ Adaptive,  Bbs, and binarY embedding at LOw cost.}
   Computer Science Laboratory DISC,
   University of Franche-Comt\'{e},
   Besan\c con, France.}
   Computer Science Laboratory DISC,
   University of Franche-Comt\'{e},
   Besan\c con, France.}

-\email{\{raphael.couturier, jean-francois.couchot, christophe.guyeux\}@univ-fcomte.fr}
+\email{\{jean-francois.couchot, raphael.couturier, christophe.guyeux\}@univ-fcomte.fr}

 
 \shortauthors{J.-F. Couchot, R. Couturier, and  C. Guyeux}
 
 
 \shortauthors{J.-F. Couchot, R. Couturier, and  C. Guyeux}
 


@@ -78,7 +78,7 @@ Adaptive,  Bbs, and binarY embedding at LOw cost.}
 
 \begin{abstract}
 
 
 \begin{abstract}
 

-A novel steganographic method called STABYLO is introduced in 
+A new steganographic method called STABYLO is introduced in 

 this research work.
 Its main advantage is to be much lighter than the so-called
 Highly Undetectable steGO (HUGO) scheme, a well-known state of the art
 this research work.
 Its main advantage is to be much lighter than the so-called
 Highly Undetectable steGO (HUGO) scheme, a well-known state of the art

diff --git a/ourapproach.tex b/ourapproach.tex
index eeabc982608e33b4ffb88a7e8681713257f72d1c..1410d5b9365d546bc23e8cc30813ea49deab16c0 100644 (file)
--- a/ourapproach.tex
+++ b/ourapproach.tex
@@ -49,7 +49,7 @@ Let us first focus on the data embedding.
 
 
 \subsection{Security considerations}\label{sub:bbs}
 
 
 \subsection{Security considerations}\label{sub:bbs}

-Among methods of the message encryption/decryption 
+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}
 that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} 
 (see~\cite{DBLP:journals/ejisec/FontaineG07} for a survey)
 we implement the Blum-Goldwasser cryptosystem~\cite{Blum:1985:EPP:19478.19501}
 that is based on the Blum Blum Shub~\cite{DBLP:conf/crypto/ShubBB82} 


@@ -88,7 +88,7 @@ how they modify them.
 
 Many techniques have been proposed in the literature to  detect 
 edges in  images (whose noise has been initially reduced). 
 
 Many techniques have been proposed in the literature to  detect 
 edges in  images (whose noise has been initially reduced). 

-They can be separated in two categories: first and second order detection
+They can be separated into two categories: first and second order detection

 methods on the one hand, and fuzzy detectors on the other  hand~\cite{KF11}.
 In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, \ldots, 
 a first-order derivative (gradient magnitude, etc.) is computed 
 methods on the one hand, and fuzzy detectors on the other  hand~\cite{KF11}.
 In first order methods like Sobel, Canny~\cite{Canny:1986:CAE:11274.11275}, \ldots, 
 a first-order derivative (gradient magnitude, etc.) is computed 


@@ -149,7 +149,7 @@ Practically, the Canny algorithm generates
 a set of edge pixels related to a threshold that is decreasing 
 until its cardinality
 is sufficient. Even in this situation, our scheme is adapting 
 a set of edge pixels related to a threshold that is decreasing 
 until its cardinality
 is sufficient. Even in this situation, our scheme is adapting 

-its algorithm to met all the user requirements. 
+its algorithm to meet all the user's requirements. 

 
 
 Once the map of possibly modified pixels is computed, 
 
 
 Once the map of possibly modified pixels is computed, 


@@ -254,14 +254,14 @@ Lena and the first verses are given in Fig.~\ref{fig:lena}.
 \begin{flushleft}
 \begin{scriptsize}
 The skies they were ashen and sober;\linebreak
 \begin{flushleft}
 \begin{scriptsize}
 The skies they were ashen and sober;\linebreak

-$~$ The leaves they were crisped and sere—\linebreak
-$~$ The leaves they were withering and sere;\linebreak
+$\qquad$ The leaves they were crisped and sere—\linebreak
+$\qquad$ The leaves they were withering and sere;\linebreak

 It was night in the lonesome October\linebreak
 It was night in the lonesome October\linebreak

-$~$ Of my most immemorial year;\linebreak
+$\qquad$ Of my most immemorial year;\linebreak

 It was hard by the dim lake of Auber,\linebreak
 It was hard by the dim lake of Auber,\linebreak

-$~$ In the misty mid region of Weir—\linebreak
+$\qquad$ In the misty mid region of Weir—\linebreak

 It was down by the dank tarn of Auber,\linebreak
 It was down by the dank tarn of Auber,\linebreak

-$~$ In the ghoul-haunted woodland of Weir.
+$\qquad$ In the ghoul-haunted woodland of Weir.

 \end{scriptsize}
 \end{flushleft}
 \end{minipage}
 \end{scriptsize}
 \end{flushleft}
 \end{minipage}


@@ -271,7 +271,9 @@ $~$ In the ghoul-haunted woodland of Weir.
 
 The edge detection returns 18,641 and 18,455 pixels when $b$ is
 respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
 
 The edge detection returns 18,641 and 18,455 pixels when $b$ is
 respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.

-
+When $b$ is 7, it remains one bit per pixel to build the cover vector.
+in this configuration, this leads to a cover vector of size  18,641 and
+36,910 if $b$ is 6.  

 
 \begin{figure}[t]
   \begin{center}
 
 \begin{figure}[t]
   \begin{center}


@@ -300,9 +302,12 @@ respectively 7 and 6. These edges are represented in Figure~\ref{fig:edge}.
 
 
 
 
 
 

-Only 9,320 bits (resp. 9,227 bits) are available for embedding 
+The STC algorithm is optimized when the rate between message length and 
+cover vector length is less than 1/2. 
+So, only 9,320 bits (resp. 18,455 bits) are available for embedding 

 in the former configuration where $b$ is 7 (resp. where $b$ is 6).
 in the former configuration where $b$ is 7 (resp. where $b$ is 6).

-In both cases, about the third part of the poem is hidden into the cover.
+In the first cases, about the third part of the poem is hidden into the cover
+whereas the latter allows to embed more than the half part of it. 

 Results with \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.
 
 Results with \emph{adaptive+STC} strategy are presented in 
 Fig.~\ref{fig:lenastego}.