edit section 2

Article/Fig_notions/bswidth.tex

 \begin{picture}(220,60)
   \multiput(0,6)(2,-6){2}{\line(3,1){150}}
-  \multiput(0,8)(30,6){8}{\line(5,1){10}}
-  \multiput(0,18)(30,6){8}{\line(5,1){10}}
+  \multiput(0,8)(30,6){8}{\color{red}{\line(5,1){10}}}
+  \multiput(0,18)(30,6){8}{\color{red}{\line(5,1){10}}}
   \put(45,21){\circle*{3}}
   \put(55,21){\circle*{3}}
   \put(65,21){\circle*{3}}
@@ -15,7 +15,8 @@
   \put(140,36){\vector(0,1){10}}
   \put(140,62.66){\vector(0,-1){10}}
   \put(120,58){$\mu_{i-1}$}
-  \put(160,30){\vector(0,1){10}}
-  \put(160,60){\vector(0,-1){10}}
-  \put(164,36){$\mu_i$}
+  \put(160,30){\color{red}{\vector(0,1){10}}}
+  \put(160,60){\color{red}{\vector(0,-1){10}}}
+  \put(164,36){\color{red}{$\mu_i$}}
+  \put(180,60){\color{red}{$\mathcal{B}_{i}$}}
 \end{picture}

Article/main.tex

@@ -12,6 +12,7 @@
 \usepackage{graphicx}
 \usepackage{color}
 \definecolor{dwhite}{rgb}{1,1,1}
+\definecolor{dgreen}{rgb}{0.2,0.7,0.2}
 %\graphicspath{{./Fignotions/}{./Figmethod}}
 
 \usepackage[ruled,vlined]{algorithm2e}

Article/notions.tex

@@ -53,6 +53,9 @@ the assigned width $\varepsilon$, then the new input point is rejected.}
   \label{fig:bs}
 \end{figure}
 
+Associated to this primitive, the following definition of directional
+scan will also be used in the following.
+
 \subsection{Directional scan}
 
 A directional scan $DS$ is an ordered partition restricted to the image
@@ -104,12 +107,12 @@ At each iteration $i$, the scans $S_i$ and $S_{-i}$ are successively processed.
      \put(-185,112){$A$}
      \put(-88,14){$B$}
      \put(-20,98){$\mathcal{D}$}
-     \put(-137,64){$S_0$}
-     \put(-77,94){$S_8$}
-     \put(-183,64){$S_{-5}$}
-     \put(-123,8){$\mathcal{N}_0$}
-     \put(-60,30){$\mathcal{N}_8$}
-     \put(-169,8){$\mathcal{N}_{-5}$}
+     \put(-137,64){\color{blue}{$S_0$}}
+     \put(-77,94){\color{red}{$S_8$}}
+     \put(-183,64){\color{dgreen}{$S_{-5}$}}
+     \put(-123,8){\color{blue}{$\mathcal{N}_0$}}
+     \put(-60,30){\color{red}{$\mathcal{N}_8$}}
+     \put(-169,8){\color{dgreen}{$\mathcal{N}_{-5}$}}
      \end{picture}
   \caption{A directional scan.
            The start scan $S_0$ is drawn in blue, odd scans in green,