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commentaire table 8

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# File IJDAR/prediction.tex

 \begin{figure*}[!htbp]
 \begin{center}
 \includegraphics[width=500px]{imgs/shema.png}
-\caption{Overall process to create a prediction model for a specific binarisation algorithm.}
+\caption{Overall process to create a prediction model for a specific binarization algorithm.}
 \label{shema}
 \end{center}
 \end{figure*}

 \begin{center}
 \begin{table}[ht]
-\caption{Otsu prediction model : all selected features are significant (p-value $<0.1$), and the model is likely to correctly predict  future unknown images given that the $R^{2}$ value is higher than $0.9$. $\hat{mpe}$ denotes the mean percentage error.}
+\caption{Otsu prediction model : all selected features are significant (p-value $<0.1$), and the model is likely to correctly predict  future unknown images given that the $R^{2}$ value is higher than $0.9$. The mean percentage error is denoted by $mpe$.}
 {\small
 \hfill{}
 \begin{tabular}{|c|c|c|c|}
 $\mu$       	& 	$2.44e-02$ 	& 	$<10^{-4}$ \\
 $v$        	& 	$3.26e-04$ 	&       $<10^{-4}$ \\
 \hline
-\multicolumn{3}{|c|}{$R^2 = 0.93, \hat{mpe} = 5\%$}\\
+\multicolumn{3}{|c|}{$R^2 = 0.93, mpe = 5\%$}\\
 \hline
 \end{tabular}}
 \hfill{}

 \begin{center}
 \begin{table}[ht]
-\caption{Sauvola prediction models. $\hat{mpe}$ denotes the mean percentage error}
+\caption{Sauvola prediction models.}
 {\small
 \hfill{}
 \begin{tabular}{|c|c|c|c|}
 $s_{I}$   		&	$1.34e-01$	&  $<10^{-4}$  \\
 $v_{I}$     		&     $4.41e-04$    	&  $<10^{-4}$  \\
 \hline
-\multicolumn{3}{|c|}{$R^2 = 0.83, \hat{mpe} = 10\%$ }\\
+\multicolumn{3}{|c|}{$R^2 = 0.83, mpe = 10\%$ }\\
 \hline
 %\hline
 \multicolumn{3}{|c|}{ Sauvola (manually chosen parameters) prediction model }\\
 $s_{I}$   		&	$1.43e-01$	&  $<10^{-4}$  \\
 $v_{I}$     		&       $4.26e-04$    	&  $<10^{-4}$  \\
 \hline
-\multicolumn{3}{|c|}{$R^2 = 0.84, \hat{mpe} = 7\%$ }\\
+\multicolumn{3}{|c|}{$R^2 = 0.84, mpe = 7\%$ }\\
 \hline

 \end{tabular}}

 \begin{center}
 \begin{table}[ht]
-\caption{Shijian prediction model. $\hat{mpe}$ denotes the mean percentage error.}
+\caption{Shijian prediction model. The mean percentage error is denoted by $mpe$.}
 {\small
 \hfill{}
 %% \begin{tabular}{|c|c|c|c|}
 $s_{D}$  	        & 	$1.33e-01$  		&  $<10^{-3}$  \\
 $\mu_{I}$      		&	$-4.00e-04$		&  $< 0.5$ \\
 \hline
-\multicolumn{3}{|c|}{$R^2 = 0.86, \hat{mpe} = 5\%$ }\\
+\multicolumn{3}{|c|}{$R^2 = 0.86, mpe = 5\%$ }\\
 \hline
 \end{tabular}}
 \hfill{}
 \subsection{Accuracy of other prediction models}
 \label{subsection-other-prediction}

-The same experiment was conducted on the other binarization methods (see Table~\ref{otherPredictionModel}). Except for Sahoo's method, all prediction models have an $R^{2}$ value higher than $0.7$, indicating that it is possible to predict the results of $10$ of $11$ binarization methods.
+The same experiment was conducted on the other binarization methods. Table~\ref{otherPredictionModel} sums up the selected features and the significant information to validate or not a binarization prediction model.

-<------- modifier à partir d'ici pour la prochaine fois --->
-expliquer un peu plus le tableau
-ajouter erreur moyenne
+Among the 18 features, most models embed about 7 features. Globally the selected features are consistent with the binarization algorithm : the step wise selection process tends to keep global (resp. local) features for global (resp. local) binarization algorithms. We also note that $\mS$ is never selected by any prediction model. Indeed, the binarization accuracy is measured at the pixel level (f-score). With this accuracy measure, the feature $\mSG$ becomes more significant than $\mS$, which may not have been the case with another evaluation measure.

-We also note that $\mS$ is never selected by any prediction model. Indeed, the binarization accuracy is measured at the pixel level (f-score). With this accuracy measure, the feature $\mSG$ becomes more significant than $\mS$, which may not have been the case with another evaluation measure.
-
+The two values $R^2$ and $mpe$ show the quality of each prediction model.
+A $R^{2}$ value higher than $0.7$ indicates that it is possible to predict the results of a binarization method~\cite{cohen}. Only Sahoo's method has a $R^{2}$ value inferior to $0.7$, which means that $10$ of $11$ binarization methods can be well predicted. The mean percentage error ($mpe$) is the average difference between predicted f-scores and real f-scores. This value is around $5\%$.

 \begin{center}
 \begin{table}[ht]
-\caption{Accuracy of the prediction model for the other eight binarization methods. The selected features are different from one method to another. The accuracy and robustness of the prediction models are good ($R^2 > 0.7$, cross validation $\bar{R^{2}} > 0.83$). $\hat{mpe}$ denotes the mean percentage error of each model.}
+\caption{Accuracy of the prediction model for the other eight binarization methods. The selected features are different from one method to another. The accuracy and robustness of the prediction models are good ($R^2 > 0.7$, cross validation $\bar{R^{2}} > 0.83$). The mean percentage error of each model is denoted by $mpe$.}
 \hfill{}
 \begin{tabular}{|c|c|c|c|}

 \hline
-Method &  Selected Features & $R^{2}$ & $\hat{mpe}$ \\
+Method &  Selected Features & $R^{2}$ & $mpe$ \\
 \hline
 Bernsen & $\mIInk; \mA; \mSG; v; v_{D}; v_{I}$ & 0.83 & 6\% \\
 \hline