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# File IJDAR/prediction.tex


 \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 $0.9$. }
+\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.}
 {\small
 \hfill{}
 \begin{tabular}{|c|c|c|c|}
 $\mu$       	& 	$2.44e-02$ 	& 	$<10^{-4}$ \\
 $v$        	& 	$3.26e-04$ 	&       $<10^{-4}$ \\
 \hline
-\multicolumn{3}{|c|}{$R^2 = 0.93$}\\
+\multicolumn{3}{|c|}{$R^2 = 0.93, \hat{mpe} = 5\%$}\\
 \hline
 \end{tabular}}
 \hfill{}

 \begin{center}
 \begin{table}[ht]
-\caption{Sauvola prediction models.}
+\caption{Sauvola prediction models. $\hat{mpe}$ denotes the mean percentage error}
 {\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|}{$R^2 = 0.83$ }\\
+\multicolumn{3}{|c|}{$R^2 = 0.83, \hat{mpe} = 10\%$ }\\
 \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|}{$R^2 = 0.84$ }\\
+\multicolumn{3}{|c|}{$R^2 = 0.84, \hat{mpe} = 7\%$ }\\
 \hline

 \end{tabular}}

 \begin{center}
 \begin{table}[ht]
-\caption{Shijian prediction model.}
+\caption{Shijian prediction model. $\hat{mpe}$ denotes the mean percentage error.}
 {\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|}{$R^2 = 0.86$}\\
+\multicolumn{3}{|c|}{$R^2 = 0.86, \hat{mpe} = 5\%$ }\\
 \hline
 \end{tabular}}
 \hfill{}

 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.

+
 \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 $\bar{R^{2}} > 0.83$).}
+\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.}
 \hfill{}
-\begin{tabular}{|c|c|c|}
+\begin{tabular}{|c|c|c|c|}

 \hline
-Method &  Selected Features & $R^{2}$ \\
+Method &  Selected Features & $R^{2}$ & $\hat{mpe}$ \\
 \hline
-Bernsen & $\mIInk; \mA; \mSG; v; v_{D}; v_{I}$ & 0.83 \\
+Bernsen & $\mIInk; \mA; \mSG; v; v_{D}; v_{I}$ & 0.83 & 6\% \\
 \hline
-Kapur   &   $\mIInk; \mA; \mu; v; s_{D}; v_{I}; \mu_{D}; \mu_{I}$ &  0.78 \\
+Kapur   &   $\mIInk; \mA; \mu; v; s_{D}; v_{I}; \mu_{D}; \mu_{I}$ &  0.78 & 2\% \\
 \hline
-Kittler    &  $\mIInk; \mQ; s; v_{I}; \mu_{B}; v_{B}$ & 0.84  \\
+Kittler    &  $\mIInk; \mQ; s; v_{I}; \mu_{B}; v_{B}$ & 0.84 & 5\% \\
 \hline
-Li	     &  $\mIInk; \mA; \mSG; \mu; v; v_{I}; \mu_{D}; \mu_{I}$ & 0.81 \\
+Li	     &  $\mIInk; \mA; \mSG; \mu; v; v_{I}; \mu_{D}; \mu_{I}$ & 0.81 & 11\% \\
 \hline
-Riddler & $\mIInk; v; v_{D}; v_{I}$ & 0.75 \\
+Riddler & $\mIInk; v; v_{D}; v_{I}$ & 0.75 & 5\% \\
 \hline
-Sahoo & $\mIInk; \mu; s_{B}; v_{I}; \mu_{D}; \mu_{I}$ & 0.68 \\
+Sahoo & $\mIInk; \mu; s_{B}; v_{I}; \mu_{D}; \mu_{I}$ & 0.68 & 5\% \\
 \hline
-Shanbag & $\mIInk; s; v; s_{D}; s_{I}; v_{D}; v_{I}$ & 0.73 \\
+Shanbag & $\mIInk; s; v; s_{D}; s_{I}; v_{D}; v_{I}$ & 0.73 & 6\% \\
 \hline
-White 	& $\mIInk; \mSG; s; v; \mu_{D}; \mu_{I}; v_{D}$ & 0.92 \\
+White 	& $\mIInk; \mSG; s; v; \mu_{D}; \mu_{I}; v_{D}$ & 0.92 & 7\% \\
 \hline

 \end{tabular}