complexity

[canny.git] / experiments.tex

diff --git a/experiments.tex b/experiments.tex
index aed050525ea5126f9b317d53ae0ca3ef3519d930..776a5a5c8a39a68db06346fba4cc24d64d233958 100644 (file)
--- a/experiments.tex
+++ b/experiments.tex
@@ -1,56 +1,50 @@
-For whole experiments, the whole set of 10000 images 
+For whole experiments, the whole set of 10,000 images 

 of the BOSS contest~\cite{Boss10} database is taken. 
 In this set, each cover is a $512\times 512$
 grayscale digital image in a RAW format. 
 We restrict experiments to 
 of the BOSS contest~\cite{Boss10} database is taken. 
 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 focussed on 
+this set of cover images since this paper is more focused on 

 the methodology than benchmarking.    
 the methodology than benchmarking.    

-Our approach is always compared to Hugo~\cite{DBLP:conf/ih/PevnyFB10}
-and to EAISLSBMR~\cite{Luo:2010:EAI:1824719.1824720}.
+We use the matrices given in table~\ref{table:matrices:H}
+as introduced in~\cite{}, since these ones have experimentally 
+be proven to have the best modification efficiency.

 
 

+\begin{table}
+$$
+\begin{array}{|l|l|}
+\textrm{rate} & \textrm{matrix generators} \\
+$\frac{1}{2} & \{71,109\}
+$\frac{1}{3} & \{95, 101, 121\}
+$\frac{1}{4} & \{81, 95, 107, 121\}
+$\frac{1}{5} & \{75, 95, 97, 105, 117\}
+$\frac{1}{6} & \{73, 83, 95, 103, 109, 123\}
+$\frac{1}{7} & \{69, 77, 93, 107, 111, 115, 121\}
+$\frac{1}{8} & \{69, 79, 81, 89, 93, 99, 107, 119\}
+$\frac{1}{9} & \{69, 79, 81, 89, 93, 99, 107, 119, 125]

 
 
 
 
 
 

+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. 

 
 

-\subsection{Adaptive Embedding Rate} 
-Two strategies have been developed in our scheme, 
-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 
-Canny algorithm with an high threshold.
-The message length is thus defined to be half of this set cardinality.
-In this strategy, two methods are thus applied to extract bits that 
-are modified. The first one is a direct application of the STC algorithm.
-This method is further referred to as \emph{adaptive+STC}.
-The second one randomly chooses the subset of pixels to modify by 
-applying the BBS PRNG again. This method is denoted \emph{adaptive+sample}.
-Notice that the rate between 
-available bits  and bit message length is always equal to 2.
-This constraint is indeed induced by the fact that the efficiency 
-of the STC algorithm is unsatisfactory under that threshold.
-In our experiments and with the adaptive scheme, 
+
+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\%. 
 the average size of the message that can be embedded is 16,445 bits.
 Its 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. 

 
 
 
 
 
 

-
-In the latter, the embedding rate is defined as a percentage between the 
-number of modified pixels and the length of the bit message.
-This is the classical approach adopted in steganography.
-Practically, the Canny algorithm generates  
-a set of edge pixels related to a threshold that is decreasing until its cardinality
-is sufficient. If the set cardinality is more than twice larger than the 
-bit message length, a STC step is again applied.
-Otherwise, pixels are again randomly chosen with BBS.
-

  
 
  
 

-\subsection{Image Quality}
+\subsection{Image quality}\label{sub:quality}

 The visual quality of the STABYLO scheme is evaluated in this section.
 The visual quality of the STABYLO scheme is evaluated in this section.

-For the sake of completeness, four metrics are computed in these experiments: 
+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}, 
 the Peak Signal to Noise Ratio (PSNR), 
 the PSNR-HVS-M family~\cite{psnrhvsm11}, 
 %the BIQI~\cite{MB10}, 


@@ -60,53 +54,70 @@ 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.
 
 account the Human Visual System (HVS).
 The other ones have been designed to tackle this problem.
 

+If we apply them on the running example, 
+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 
+65.43, 77.2, and 89.35.
+

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

-\begin{tabular}{|c|c|c||c|c|c|c|c|}
+\begin{tabular}{|c|c|c||c|c|c|c|c|c|}

 \hline
 \hline

-Schemes & \multicolumn{3}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} \\
+Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR} \\

 \hline
 \hline

-Embedding &   \multicolumn{2}{|c||}{Adaptive} & Fixed & \multicolumn{2}{|c|}{Fixed}& \multicolumn{2}{|c|}{Fixed} \\
+Embedding &   Fixed & \multicolumn{3}{|c|}{Adaptive (about 6.35\%)} &  \multicolumn{2}{|c|}{Fixed}& \multicolumn{2}{|c|}{Fixed} \\

 \hline
 \hline

-Rate &   + STC &  + sample & 10\% & 10\%&6.35\%& 10\%&6.35\%\\ 
+Rate &   10\% &  + sample &  +STC(7) & +STC(6) &  10\%&6.35\%& 10\%&6.35\%\\ 

 \hline
 \hline

-PSNR &  66.55 (\textbf{-0.8\%}) & 63.48  & 61.86  & 64.65 & {67.08} & 60.8 & 62.9\\ 
+PSNR & 61.86 & 63.48 &  66.55 (\textbf{-0.8\%}) &  63.7  & 64.65 & {67.08} & 60.8 & 62.9\\ 

 \hline
 \hline

-PSNR-HVS-M & 78.6 (\textbf{-0.8\%})  & 75.39 & 72.9 & 76.67 & {79.23} & 61.3  & 63.4\\ 
+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\\ 
 \hline
 %\hline
 %BIQI & 28.3 & 28.28 & 28.4 & 28.28 & 28.28 & 28.2 & 28.2\\ 
 \hline

-wPSNR & 86.43(\textbf{-1.6\%}) & 80.59 & 77.47& 83.03 & {87.8} & & 80.6\\ 
+wPSNR & 77.47 & 80.59 & 86.43(\textbf{-1.6\%})& 86.28  & 83.03 & {87.8} & 76.7 & 80.6\\ 

 \hline
 \end{tabular}
 \hline
 \end{tabular}

+
+\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}
 \end{center}

-\caption{Quality Measures of Steganography Approaches\label{table:quality}}
-\label{table:quality}
+\caption{Quality measures of steganography approaches\label{table:quality}}

 \end{table*}
 
 
 
 \end{table*}
 
 
 

-Results are summarized into the Table~\ref{table:quality}.
-Let us give an interpretation of these first experiments.
+Results are summarized in Table~\ref{table:quality}.
+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 one of images resulting from the 10\% fixed strategy.
+than the images resulting from the 10\% fixed strategy.

 Numerical results are indeed always greater for the former strategy than 
 Numerical results are indeed always greater for the former strategy than 

-for the latter.
+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
 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.
 These results are not surprising since the adaptive strategy aims at 
 embedding messages whose length is decided according to an 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 appraoch always outperforms EAISLSBMR since this one may modify 
-the two least significant bits whereas STABYLO only alter LSB.
+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\%)
 
 If we combine \emph{adaptive} and \emph{STC} strategies 
 (which leads to an average embedding rate equal to 6.35\%)

-our approach  provides equivalent metrics than HUGO.
+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. 
+
+
+

 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:
 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:


@@ -122,15 +133,15 @@ give quality metrics for fixed embedding rates from a large base of images.
 
 
 
 
 
 

-\subsection{Steganalysis}
+\subsection{Steganalysis}\label{sub:steg}

 
 
 
 
 
 

-The quality of our approach has been evaluated through the two 
+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.
 AUMP~\cite{Fillatre:2012:ASL:2333143.2333587}
 and Ensemble Classifier~\cite{DBLP:journals/tifs/KodovskyFH12} based steganalysers.

-Both aims at detecting hidden bits in grayscale natural images and are 
-considered as the state of the art of steganalysers in spatial domain~\cite{FK12}.
+Both aim at detecting hidden bits in grayscale natural images and are 
+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
 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


@@ -138,25 +149,24 @@ 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
 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 support vector machine,
+implemented as a support vector machine,

 can be favorably executed thanks to an ensemble classifier.
 
 can be favorably executed thanks to an ensemble classifier.
 

-%citer le second tableau, comparer avec EAISLSBMR

 
 \begin{table*}
 \begin{center}
 %\begin{small}
 
 \begin{table*}
 \begin{center}
 %\begin{small}

-\begin{tabular}{|c|c|c|c|c|c|c|c|}
+\begin{tabular}{|c|c|c|c|c|c|c|c|c|}

 \hline
 \hline

-Schemes & \multicolumn{3}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR}\\
+Schemes & \multicolumn{4}{|c|}{STABYLO} & \multicolumn{2}{|c|}{HUGO}& \multicolumn{2}{|c|}{EAISLSBMR}\\

 \hline
 \hline

-Embedding &   \multicolumn{2}{|c|}{Adaptive} & Fixed & \multicolumn{2}{|c|}{Fixed}& \multicolumn{2}{|c|}{Fixed} \\
+Embedding & Fixed &   \multicolumn{3}{|c|}{Adaptive (about 6.35\%)}  & \multicolumn{2}{|c|}{Fixed}& \multicolumn{2}{|c|}{Fixed} \\

 \hline
 \hline

-Rate &   + STC &  + sample & 10\% & 10\%& 6.35\%& 10\%& 6.35\%\\ 
+Rate & 10\% &  + sample &   +STC(7) & +STC(6)   & 10\%& 6.35\%& 10\%& 6.35\%\\ 

 \hline
 \hline

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

 \hline
 \hline

-Ensemble Classifier & \textbf{0.47} & 0.44 & 0.35     & 0.48 &  0.49  &  0.43  & 0.46 \\
+Ensemble Classifier & 0.35 & 0.44 & 0.47 & 0.47     & 0.48 &  0.49  &  0.43  & 0.46 \\

 
 \hline
 \end{tabular}
 
 \hline
 \end{tabular}


@@ -166,8 +176,15 @@ Ensemble Classifier & \textbf{0.47} & 0.44 & 0.35     & 0.48 &  0.49  &  0.43  &
 \end{table*}
 
 
 \end{table*}
 
 

-Results show that our approach is more easily detectable than HUGO, which
-is the most secure steganographic tool, as far as we know. However due to its 
-huge number of features integration, it is not lightweight, which justifies 
+Results 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.
+
+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.   
 
 in the authors' opinion the consideration of the proposed method.