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Vincent Rabeux  committed e450ca1

Res Niblack + R2 bar + Ajout / modifications des refs + corrections reférences tableaux.

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File IJDAR/ijdar.bib

 %% http://bibdesk.sourceforge.net/
 
 
-%% Created for Vincent Rabeux at 2012-06-07 16:40:44 +0200 
+%% Created for Vincent Rabeux at 2013-03-27 11:42:29 +0100 
 
 
 %% Saved with string encoding Unicode (UTF-8) 
 
 
-@Book{cohen,
-  author = 	 {Cohen, J. and Cohen, P.},
-  editor = 	 {Routledge Academic},
-  title = 	 { Applied multiple regression/correlation analysis for the behavioral sciences},
-  publisher = 	 {Lawrence Erlbaum},
-  year = 	 {2003}
-}
+
+@article{lu2010document,
+	Author = {Lu, Shijian and Su, Bolan and Tan, Chew Lim},
+	Date-Added = {2013-03-27 10:42:27 +0000},
+	Date-Modified = {2013-03-27 10:42:27 +0000},
+	Journal = {International Journal on Document Analysis and Recognition (IJDAR)},
+	Number = {4},
+	Pages = {303--314},
+	Publisher = {Springer},
+	Title = {Document image binarization using background estimation and stroke edges},
+	Volume = {13},
+	Year = {2010}}
+
+@book{niblack1985introduction,
+	Author = {Niblack, Wayne},
+	Date-Added = {2013-03-27 10:24:26 +0000},
+	Date-Modified = {2013-03-27 10:24:26 +0000},
+	Publisher = {Strandberg Publishing Company},
+	Title = {An introduction to digital image processing},
+	Year = {1985}}
+
+@book{cohen,
+	Author = {Cohen, J. and Cohen, P.},
+	Editor = {Routledge Academic},
+	Publisher = {Lawrence Erlbaum},
+	Title = {Applied multiple regression/correlation analysis for the behavioral sciences},
+	Year = {2003}}
 
 @inproceedings{gatos2009icdar,
- title={ICDAR 2009 Document Image Binarization Contest (DIBCO 2009)},
- author={Gatos, B. and Ntirogiannis, K. and Pratikakis, I.},
- booktitle={Document Analysis and Recognition (ICDAR), 2009 International Conference on},
- pages={1375--1382},
- year={2009},
- organization={IEEE}
-}
+	Author = {Gatos, B. and Ntirogiannis, K. and Pratikakis, I.},
+	Booktitle = {Document Analysis and Recognition (ICDAR), 2009 International Conference on},
+	Organization = {IEEE},
+	Pages = {1375--1382},
+	Title = {ICDAR 2009 Document Image Binarization Contest (DIBCO 2009)},
+	Year = {2009}}
+
 @article{hocking,
-   author = {Hocking, R. R.},
-   citeulike-article-id = {8802640},
-   citeulike-linkout-0 = {http://dx.doi.org/10.2307/2529336},
-   citeulike-linkout-1 = {http://www.jstor.org/stable/2529336},
-   doi = {10.2307/2529336},
-   issn = {0006341X},
-   journal = {Biometrics},
-   number = {1},
-   pages = {1--49},
-   posted-at = {2011-12-16 00:50:03},
-   priority = {2},
-   publisher = {International Biometric Society},
-   title = {The analysis and selection of variables in linear regression},
-   url = {http://dx.doi.org/10.2307/2529336},
-   volume = {32},
-   year = {1976}
-}
+	Author = {Hocking, R. R.},
+	Citeulike-Article-Id = {8802640},
+	Citeulike-Linkout-0 = {http://dx.doi.org/10.2307/2529336},
+	Citeulike-Linkout-1 = {http://www.jstor.org/stable/2529336},
+	Doi = {10.2307/2529336},
+	Issn = {0006341X},
+	Journal = {Biometrics},
+	Number = {1},
+	Pages = {1--49},
+	Posted-At = {2011-12-16 00:50:03},
+	Priority = {2},
+	Publisher = {International Biometric Society},
+	Title = {The analysis and selection of variables in linear regression},
+	Url = {http://dx.doi.org/10.2307/2529336},
+	Volume = {32},
+	Year = {1976},
+	Bdsk-Url-1 = {http://dx.doi.org/10.2307/2529336}}
+
 @inproceedings{pratikakis2010h,
- title={H-DIBCO 2010-handwritten document image binarization competition},
- author={Pratikakis, I. and Gatos, B. and Ntirogiannis, K.},
- booktitle={Proceedings of the International Conference on Frontiers in Handwriting Recognition (ICFHR 2010)},
- pages={727--732},
- year={2010},
- organization={IEEE}
-}
+	Author = {Pratikakis, I. and Gatos, B. and Ntirogiannis, K.},
+	Booktitle = {Proceedings of the International Conference on Frontiers in Handwriting Recognition (ICFHR 2010)},
+	Organization = {IEEE},
+	Pages = {727--732},
+	Title = {H-DIBCO 2010-handwritten document image binarization competition},
+	Year = {2010}}
 
 @inproceedings{pratikakis2011icdar,
- title={ICDAR 2011 Document Image Binarization Contest (DIBCO 2011)},
- author={Pratikakis, I. and Gatos, B. and Ntirogiannis, K.},
- booktitle={Proceedings of the International Conference on Document Analysis and Recognition (ICDAR 2011)},
- pages={1506--1510},
- year={2011},
- organization={IEEE}
-}
+	Author = {Pratikakis, I. and Gatos, B. and Ntirogiannis, K.},
+	Booktitle = {Proceedings of the International Conference on Document Analysis and Recognition (ICDAR 2011)},
+	Organization = {IEEE},
+	Pages = {1506--1510},
+	Title = {ICDAR 2011 Document Image Binarization Contest (DIBCO 2011)},
+	Year = {2011}}
 
-@InProceedings{ablavsky2003,
-  author = 	 {Ablavsky, V. and Pollak, J. and Snorrason, M. and Stevens M.R.},
-  title = 	 {OCR Accuracy Prediction as a Script Identification Problem},
-  booktitle = {Proceedings of the Symposium on Document Image Understanding Technology (SDIUT 2003)},
-  pages = 	 {135-142},
-  year = 	 {2003},
-  editor = 	 {D. Doermann}
-}
+@inproceedings{ablavsky2003,
+	Author = {Ablavsky, V. and Pollak, J. and Snorrason, M. and Stevens M.R.},
+	Booktitle = {Proceedings of the Symposium on Document Image Understanding Technology (SDIUT 2003)},
+	Editor = {D. Doermann},
+	Pages = {135-142},
+	Title = {OCR Accuracy Prediction as a Script Identification Problem},
+	Year = {2003}}
 
-@INPROCEEDINGS{zhang2002warped,
-author={Zheng Zhang and Chew Lim Tan},
-booktitle={Proceedings of the International Conference on Image Processing (ICIP 2002) }, 
-title={Straightening warped text lines using polynomial regression},
-year={2002},
-volume={3},
-pages={977--980},
-keywords={ image restoration; perspective distortion; polynomial regression; scanned grayscale image; warped text line straightening; document image processing; image restoration; optical distortion; polynomials; statistical analysis; text analysis;},
-doi={10.1109/ICIP.2002.1039138},
-ISSN={1522-4880 },}
+@inproceedings{zhang2002warped,
+	Author = {Zheng Zhang and Chew Lim Tan},
+	Booktitle = {Proceedings of the International Conference on Image Processing (ICIP 2002)},
+	Doi = {10.1109/ICIP.2002.1039138},
+	Issn = {1522-4880},
+	Keywords = {image restoration; perspective distortion; polynomial regression; scanned grayscale image; warped text line straightening; document image processing; image restoration; optical distortion; polynomials; statistical analysis; text analysis;},
+	Pages = {977--980},
+	Title = {Straightening warped text lines using polynomial regression},
+	Volume = {3},
+	Year = {2002},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1109/ICIP.2002.1039138}}
 
 @inproceedings{shi2004historical,
 	Author = {Shi, Z. and Govindaraju, V.},
 
 @inproceedings{wang2003document,
 	Author = {Wang, Q. and Xia, T. and Li, L. and Tan, C.L.},
-	Booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003}, 
+	Booktitle = {Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003},
 	Date-Added = {2012-06-07 16:38:25 +0200},
 	Date-Modified = {2012-06-07 16:38:25 +0200},
 	Organization = {IEEE},
 
 @inproceedings{su2011combination,
 	Author = {Su, B. and Lu, S. and Tan, C.L.},
-	Booktitle = {Proceedings of of the International Conference on Document Analysis and Recognition (ICDAR 2011) },
+	Booktitle = {Proceedings of of the International Conference on Document Analysis and Recognition (ICDAR 2011)},
 	Date-Added = {2012-06-07 15:24:12 +0200},
 	Date-Modified = {2012-06-07 15:24:12 +0200},
 	Organization = {IEEE},
 	Volume = {142},
 	Year = {1995}}
 
-@book{niblack1985introduction,
-	Author = {Niblack, W.},
-	Date-Added = {2012-06-06 16:16:50 +0200},
-	Date-Modified = {2012-06-06 16:16:50 +0200},
-	Publisher = {Strandberg Publishing Company},
-	Title = {An introduction to digital image processing},
-	Year = {1985}}
-
 @article{li1998iterative,
 	Author = {Li, CH and Tam, PKS},
 	Date-Added = {2012-06-06 16:16:06 +0200},
 	Volume = {29},
 	Year = {1985}}
 
+@inproceedings{bernsen,
+	Author = {Bernsen, J.},
+	Booktitle = {Proceedings of the International Conference on Pattern Recognition (ICPR 1986)},
+	Pages = {252--255},
+	Title = {Dynamic thresholding of gray level images},
+	Volume = {1},
+	Year = {1986}}
 
-@InProceedings{bernsen,
-  author = 	 {Bernsen, J.},
-  title = 	 {Dynamic thresholding of gray level images},
-  booktitle = {Proceedings of the International Conference on Pattern Recognition (ICPR 1986)},
-  pages = 	 {252--255},
-  year = 	 {1986},
-  volume = 	 {1}
-}
-
-
-@InProceedings{reed2008correlating,
-  author = 	{Reed, D.K. and Barney Smith, E.H.}, 
-  title = 	{Correlating degradation models and image quality metrics}, 
-  booktitle = {Proceedings of the 15th Document Recognition and Retrieval Conference (DRR 2008)},
-  year = 	 {2008},
-  volume = 	 {SPIE 6815}
-}
-
+@inproceedings{reed2008correlating,
+	Author = {Reed, D.K. and Barney Smith, E.H.},
+	Booktitle = {Proceedings of the 15th Document Recognition and Retrieval Conference (DRR 2008)},
+	Title = {Correlating degradation models and image quality metrics},
+	Volume = {SPIE 6815},
+	Year = {2008}}
 
 @inproceedings{souza2003automatic,
 	Author = {Souza, A. and Cheriet, M. and Naoi, S. and Suen, C.Y.},
 	Date-Added = {2012-05-02 10:42:55 +0200},
 	Date-Modified = {2012-05-02 10:44:30 +0200},
 	Journal = {International Statistical Review},
+	Number = {1},
 	Pages = {1--19},
-        Volume = {46},
-        Number = {1},
 	Publisher = {ISI},
 	Title = {Selection of variables in multiple regression: Part I. A review and evaluation},
+	Volume = {46},
 	Year = {1978}}
 
 @article{moghaddam2009low,
 	Volume = {10},
 	Year = {2001}}
 
-
-@InProceedings{barney2011mask,
-  author = 	 {Barney Smith, E.H. and Darbon, J. and Likforman-Sulem, L.},
-  title = 	 {A mask-based enhancement method for historical documents},
-  booktitle = {Proceedings of the 18th Document Recognition and Retrieval Conference (DRR 2011)},
-  year = 	 {2011},
-  volume = 	 {SPIE 7874}
-}
+@inproceedings{barney2011mask,
+	Author = {Barney Smith, E.H. and Darbon, J. and Likforman-Sulem, L.},
+	Booktitle = {Proceedings of the 18th Document Recognition and Retrieval Conference (DRR 2011)},
+	Title = {A mask-based enhancement method for historical documents},
+	Volume = {SPIE 7874},
+	Year = {2011}}
 
 @article{farrahi2009rsldi,
 	Author = {Farrahi Moghaddam, R. and Cheriet, M.},
 	Volume = {42},
 	Year = {2009}}
 
-
-@InProceedings{rabeux2011ancient,
-  author = 	 {Rabeux, V. and Nicholas, J. and Jean Philippe, D.},
-  title = 	 {Ancient documents bleed-through evaluation and its application for predicting OCR error rates},
-  booktitle = {Proceedings of the 18th Document Recognition and Retrieval Conference (DRR 2011)},
-  year = 	 {2011},
-  volume = 	 {SPIE 7874}
-}
+@inproceedings{rabeux2011ancient,
+	Author = {Rabeux, V. and Nicholas, J. and Jean Philippe, D.},
+	Booktitle = {Proceedings of the 18th Document Recognition and Retrieval Conference (DRR 2011)},
+	Title = {Ancient documents bleed-through evaluation and its application for predicting OCR error rates},
+	Volume = {SPIE 7874},
+	Year = {2011}}
 
 @article{rice1993evaluation,
 	Author = {Rice, S.V. and Kanai, J. and Nartker, T.A.},
 	Year = {1999}}
 
 @incollection{baird2007state,
-year={2007},
-isbn={978-1-84628-501-1},
-booktitle={Digital Document Processing},
-series={Advances in Pattern Recognition},
-editor={Chaudhuri, B. B.},
-doi={10.1007/978-1-84628-726-8_12},
-title={The state of the art of document image degradation modelling},
-url={http://dx.doi.org/10.1007/978-1-84628-726-8_12},
-publisher={Springer London},
-author={Baird, H. S.},
-pages={261-279}
-}
+	Author = {Baird, H. S.},
+	Booktitle = {Digital Document Processing},
+	Doi = {10.1007/978-1-84628-726-8_12},
+	Editor = {Chaudhuri, B. B.},
+	Isbn = {978-1-84628-501-1},
+	Pages = {261-279},
+	Publisher = {Springer London},
+	Series = {Advances in Pattern Recognition},
+	Title = {The state of the art of document image degradation modelling},
+	Url = {http://dx.doi.org/10.1007/978-1-84628-726-8_12},
+	Year = {2007},
+	Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-1-84628-726-8_12}}

File IJDAR/ijdar.tex

 
 \section{Conclusion and research perspectives}
 
-This paper presented $18$ features that characterize the quality of a document image. These features are used in step-wise multivariate linear regression to create prediction models for  $11$ binarization methods. Repeated random sub-sampling cross-validation shows that $10$ of $11$ models are very accurate and can be used to automatically choose the best binarization method. Moreover, given the step-wise approach of the linear regression, these models are not over parameterized.  
+This paper presented $18$ features that characterize the quality of a document image. These features are used in step-wise multivariate linear regression to create prediction models for  $12$ binarization methods. Repeated random sub-sampling cross-validation shows that these $12$ models are accurate (max percentage error equals 11\%) and can be used to automatically choose the best binarization method. Moreover, given the step-wise approach of the linear regression, these models are not over parameterized.  
 
 One of our future research goals is to apply the same methodology to predict OCR error rates. 
 %In \cite{rabeux2011ancient}, similar features are used with a multivariate linear regression to predict the OCR error rate.

File IJDAR/prediction.tex

 	\item Kapur \cite{kapur1985new} is an entropy-based thresholding method.
 	\item Kittler \cite{kittler1985threshold} is a clustering-based thresholding method.
 	\item Li \cite{li1998iterative} is a cross-entropic thresholding method based on the minimization of an information theoretic distance (Kullback-Leibler).
-%	\item Niblack \cite{niblack1985introduction} : is a locally adaptive thresholding method using pixels intensity variance.
+	\item Niblack \cite{niblack1985introduction} : is a locally adaptive thresholding method using pixels intensity variance.
 %	\item Ramesh \cite{ramesh1995thresholding} : is a shape-modeling thresholding technique.
 	\item Ridler \cite{calvard1978picture} is an iterative thresholding method based on two-class Gaussian mixture models.
 	\item Sahoo \cite{sahoo1997threshold} is an entropy-based thresholding method.
 	\item Shanbag  \cite{shanbhag1994utilization} is a fuzzy entropic thresholding technique that considers fuzzy memberships as an indication of how strongly a gray value belongs to the background or to the foreground.
 	\item Sauvola \cite{sauvola2000adaptive} is a locally adaptive thresholding method using pixel intensity variance.
 	\item Otsu \cite{otsu1975threshold} is a two-class global thresholding method.
-	\item White \cite{white1983image} is a locally adaptive thresholding method using local contrast.
-	\item Shijian \cite{su2011combination} is a recent method based on an \textit{ad-hoc} combination of existing techniques.  \cite{su2011combination} has proven to have very good accuracy on the ICDAR 2011 Binarization Contest.
+	\item White \cite{white1983image} is a locally adaptive thresholding method using local contrast.	
+	\item Shijian \cite{lu2010document} is a recent method based on an \textit{ad-hoc} combination of existing techniques.  \cite{lu2010document} has proven to have very good accuracy on the ICDAR 2009 Binarization Contest.
  \end{enumerate}
  
 Some binarization methods rely on parameters. In this article, we do not focus on parameter optimization. Therefore, we chose to use the parameters given by the authors of each method in their corresponding original articles. Table \ref{parameters} summarizes the values of these parameters. Importantly, note that the prediction models created are only able to predict the performance of a binarization method with a specific set of parameters. However, a binarization method can have several prediction models, one for each set of parameters. To illustrate the difference between two sets of parameters, we will create two different prediction models for Sauvola's method. The second set of parameters was manually chosen (Table \ref{parameters}).
 \begin{table}[htdp]
 \begin{center}
 \caption{Methods parameters: we chose to use the parameters given by each author in their original articles.}
+\label{parameters}
 \begin{tabular}{|l|r|l|}
 \hline
 Method & \multicolumn{2}{|c|}{Paremeters} \\
 \multirow{2}{*}{White}  & window size & 15\\
 					    & bias & 2 \\
 \hline
+\multirow{2}{*}{Niblack}  & window size & 15\\
+					    & K & -0.2 \\
+\hline
 \multirow{3}{*}{Sauvola (original parameters)} & window size & 15 \\
 						 & R & 128 \\
 						 & K & 0.5 \\
 \hline  
 \end{tabular}
 \end{center}
-\label{parameters}
 \end{table}%
 
 
 \begin{table}[ht]
 {\small
 \hfill{}
-\caption{Statistical results of $11$ binarization algorithms applied to all DIBCO images. Except for the Sahoo algorithm, all binarization methods have a significant min/max f-score gap and standard deviation between $0.1$ and $0.3$, indicating that the dataset is heterogeneous and well suited for the learning step of our prediction model.}
+\caption{Statistical results of $12$ binarization algorithms applied to all DIBCO images. Except for the Sahoo algorithm, all binarization methods have a significant min/max f-score gap and standard deviation between $0.1$ and $0.3$, indicating that the dataset is heterogeneous and well suited for the learning step of our prediction model.}
+\label{fscoredistrib}
 \begin{tabular}{|l|c|c|c|c|c|}
 \hline
 F-Score	& Mean	& Std. Dev.  & Min & Max   \\
 Otsu & 0.81 & 0.14 & 0.28 & 0.96\\
 White &	0.40 & 0.22 & 0.00 & 0.83\\
 Shijian	& 0.89& 0.12 & 0.21 & 0.95\\
+Niblack & 0.35 & 0.14 & 0.1 & 0.6 \\
 
 %Ramesh		& 		0.3		& 0.12		& 0.01			& 		0.5		\\			
 \hline					
 \end{tabular}}
 \hfill{}
-\label{fscoredistrib}
 \end{table}
 \end{center}
 
 
 The best theoretical value for $ R^{2}$ is 1. Moreover, a p-value is computed for each selected feature indicating its significance :  a low p-value leads to reject the hypothesis that the selected feature is not significant (null hypothesis).
 
-There is no automatic rule to decide whether a model is valid. In our tests, we choose to keep the model only if $R^2 > 0.7$ and if a majority of p-values are lower than $0.1$.
+At this step, there is no automatic rule to decide whether a model is valid or not. The $R^{2}$ value computed at this step gives an indication of how well the model can be used in practice. The model still needs to be statically validated. This statistical validation is done at the next step. 
+
+%However, in our tests, we choose to keep the model only if a majority of p-values are lower than $0.1$. 
 
 %???  We also look at the slope coefficient of the validation regression, which also needs to be the closest to 1.
 
 \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.}
+\label{otsuPredictionModel}
 {\small
 \hfill{}
 \begin{tabular}{|c|c|c|c|}
 \hline
 \end{tabular}}
 \hfill{}
-\label{otsuPredictionModel}
+
 \end{table}
 \end{center}
 
 \begin{center}
 \begin{table}[ht]
 \caption{Sauvola prediction models. $\hat{mpe}$ denotes the mean percentage error}
+\label{sauvolaPredictionModel}
 {\small
 \hfill{}
 \begin{tabular}{|c|c|c|c|}
 \end{tabular}}
 \hfill{}
 %\caption{Sauvola prediction Model : all features are significant ($p-value <0.1$), the model is also likely to predict correctly future unknown images given that the $R^{2}$ equals $0.8$ and adjusted $R^{2}$ equals 0.77. }
-\label{sauvolaPredictionModel}
+
 \end{table}
 \end{center}
 
 \begin{center}
 \begin{table}[ht]
 \caption{Shijian prediction model. $\hat{mpe}$ denotes the mean percentage error.}
+\label{shijianPredictionModel}
 {\small
 \hfill{}
 %% \begin{tabular}{|c|c|c|c|}
 \end{tabular}}
 \hfill{}
 %\caption{Shijian prediction Model : the model is likely to predict correctly future unknown images given that the $R^{2}$ equals $0.86$ and adjusted $R^{2}$ equals 0.82. }
-\label{shijianPredictionModel}
 \end{table}
 \end{center}
 
 \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 (see Table~\ref{otherPredictionModel}). All prediction models have an $\bar{R^{2}}$ value higher than $0.7$, indicating that it is possible to predict the results of $12$ binarization methods. 
 
 <------- modifier à partir d'ici pour la prochaine fois --->
 expliquer un peu plus le tableau
 
 \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 (cross validation $\bar{R^{2}} > 0.7$). $\hat{mpe}$ denotes the mean percentage error of each model.} 
+\label{otherPredictionModel}
 \hfill{}
-\begin{tabular}{|c|c|c|c|}
+\begin{tabular}{|c|p{3cm}|c|c|c|}
 
 \hline
-Method &  Selected Features & $R^{2}$ & $\hat{mpe}$ \\
+Method &  Selected Features & $R^{2}$ & $\bar{R^{2}}$ & $\hat{mpe}$ \\
 \hline
-Bernsen & $\mIInk; \mA; \mSG; v; v_{D}; v_{I}$ & 0.83 & 6\% \\
+Bernsen & $\mIInk$; $\mA$; $\mSG$; $v$; $v_{D}$; $v_{I}$ & 0.83 & 0.96 & 6\% \\
 \hline
-Kapur   &   $ \mIInk; \mA; \mu; v; s_{D}; v_{I}; \mu_{D}; \mu_{I} $ &  0.78 & 2\% \\
+Kapur   &   $ \mIInk$; $\mA$; $\mu$; $v$; $s_{D}$; $v_{I}$; $\mu_{D}$; $\mu_{I}$ &  0.78 & 0.99 & 2\% \\
 \hline
-Kittler    &  $\mIInk; \mQ; s; v_{I}; \mu_{B}; v_{B} $ & 0.84 & 5\% \\
+Kittler    &  $\mIInk$; $\mQ$; $s$; $v_{I}$; $\mu_{B}$; $v_{B} $ & 0.84 & 0.98 & 5\% \\
 \hline
-Li	     &  $\mIInk; \mA; \mSG; \mu; v; v_{I}; \mu_{D}; \mu_{I} $ & 0.81 & 11\% \\
+Li	     &  $\mIInk$; $\mA$; $\mSG$; $\mu$; $v$; $v_{I}$; $\mu_{D}$; $\mu_{I} $ & 0.81 & 0.95 & 11\% \\
 \hline
-Riddler & $ \mIInk; v; v_{D}; v_{I} $ & 0.75 & 5\% \\
+Riddler & $ \mIInk$; $v$; $v_{D}$; $v_{I} $ & 0.75 & 0.98 & 5\% \\
 \hline
-Sahoo & $ \mIInk; \mu; s_{B}; v_{I}; \mu_{D}; \mu_{I} $ & 0.68 & 5\% \\
+Sahoo & $ \mIInk$; $\mu$; $s_{B}$; $v_{I}$; $\mu_{D}$; $\mu_{I} $ & 0.68 & 0.99 & 5\% \\
 \hline
-Shanbag & $\mIInk; s; v; s_{D}; s_{I}; v_{D}; v_{I}$ & 0.73 & 6\% \\
+Shanbag & $\mIInk$; $s$; $v$; $s_{D}$; $s_{I}$; $v_{D}$; $v_{I}$ & 0.73 & 0.98 & 6\% \\
 \hline
-White 	& $ \mIInk; \mSG; s; v; \mu_{D}; \mu_{I}; v_{D}$ & 0.92 & 7\% \\
+White 	& $ \mIInk$; $\mSG$; $s$; $v$; $\mu_{D}$; $\mu_{I}$; $v_{D}$ & 0.92 & 0.99 & 7\% \\
 \hline
-
+Niblack 	& $ \mu$; $v$; $s_{G}$; $v_{B}$; $\mu_{B}$ & 0.59 & 0.93 & 11\% \\
+\hline
 \end{tabular}
 \hfill{}
-\label{otherPredictionModel}
+
 \end{table}
 \end{center}
 
 \begin{center}
 \begin{table}[ht]
 \caption{Binarization of the DIBCO dataset. Comparison between the best theoretical f-score (computed from the ground truth), f-scores obtained using only Shijian's method and f-scores obtained from our automatic selection.}
+\label{selectionRes}
 {\small
 \hfill{}
 \begin{tabular}{|l|c|c|c|c|c|}
 \hline					
 \end{tabular}}
 \hfill{}
-\label{selectionRes}
+
 \end{table}
 \end{center}