assigned width in article

Article/Fig_notions/fig.tex

+
+\begin{center}
+\begin{picture}(320,120)(0,0)
+\multiput(-1,119)(8,0){40}{\makebox(2,2){.}}
+\multiput(-1,111)(8,0){40}{\makebox(2,2){.}}
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+\multiput(-1,-1)(8,0){40}{\makebox(2,2){.}}
+
+\put(176,24){\circle*{3}}
+\multiput(168,32)(0,8){3}{\circle*{3}}
+\multiput(160,56)(0,8){2}{\circle*{3}}
+\multiput(152,72)(0,8){3}{\circle*{3}}
+\put(144,96){\circle*{3}}
+
+\put(183,23){\framebox(2,2)}
+\multiput(175,31)(0,8){3}{\framebox(2,2)}
+\multiput(167,55)(0,8){2}{\framebox(2,2)}
+\multiput(159,71)(0,8){3}{\framebox(2,2)}
+\put(151,95){\framebox(2,2)}
+
+\put(192,24){\circle{3}}
+\multiput(184,32)(0,8){3}{\circle{3}}
+\multiput(176,56)(0,8){2}{\circle{3}}
+\multiput(168,72)(0,8){3}{\circle{3}}
+\put(160,96){\circle{3}}
+
+\put(168,24){\makebox(2,2){-1}}
+\multiput(160,32)(0,8){3}{\makebox(2,2){-1}}
+\multiput(152,56)(0,8){2}{\makebox(2,2){-1}}
+\multiput(144,72)(0,8){3}{\makebox(2,2){-1}}
+\put(136,96){\makebox(2,2){-1}}
+
+\end{picture}
+\end{center}
+

Article/biblio.bib

+@book{KletteRosenfeld04,
+  title = {Digital geometry -- Geometric methods for digital picture analysis},
+  author = {Klette, Reinhard and Rosenfeld, Azriel},
+  editor = {Elsevier},
+  publisher = {Morgan Kaufmann},
+  year = {2004}
+}
+
+
 @inproceedings{KerautretEven09,
   title = {Blurred segments in gray level images for
            interactive line extraction},
-  volume = {5852},
+  author = {Kerautret, Bertrand and Even, Philippe},
   booktitle = {Proceedings of the 13th {IWCIA}},
+  series = {LNCS},
+  volume = {5852},
   publisher = {Springer},
-  author = {Kerautret, Bertrand and Even, Philippe},
   editor = {Wiederhold, P. and Barneva, R. P.},
   month = nov,
   year = {2009},
-  series = {{LNCS}},
   pages = {176--186}
 }
 
 
-
-@inproceedings{Debled05,
+@inproceedings{DebledAl05,
   title = {Blurred Segments Decomposition in Linear Time},
   author = {Debled-Rennesson, Isabelle and Feschet, Fabien and
             Rouyer-Degli, Jocelyne},
@@ -30,7 +38,6 @@
 }
 
 
-
 @article{Buzer07,
   title = "A simple algorithm for digital line recognition
            in the general case",
@@ -44,7 +51,6 @@
 }
 
 
-
 @article{EvenMalavaud00,
   author = {Even, Philippe and Malavaud, Anne},
   title = {Semi-automated edge segment specification for an interactive
@@ -57,7 +63,6 @@
 }
 
 
-
 @article{AubryAl17,
   author = {Aubry, Nicolas and Kerautret, Bertrand and Even, Philippe
             and Debled-Rennesson, Isabelle},

Article/method.tex

@@ -5,34 +5,37 @@
 The blurred segment detector workflow is summerized
 in the following figure.
 
-\begin{center}
-\begin{picture}(340,34)(0,-4)
-%\put(0,-2.5){\framebox(340,35)}
-\put(-2,18){\scriptsize $(A,B)$}
-\put(-2,15){\vector(1,0){24}}
-\put(24,0){\framebox(56,30)}
-\put(24,15){\makebox(56,10){Initial}}
-\put(24,3){\makebox(56,10){detection}}
-\put(86,18){\scriptsize $S_{i}$}
-\put(80,15){\vector(1,0){22}}
-%\put(102,0){\framebox(56,30)}
-\multiput(102,15)(28,9){2}{\line(3,-1){28}}
-\multiput(102,15)(28,-9){2}{\line(3,1){28}}
-\put(100,0){\makebox(60,30){Valid ?}}
-\put(133,-2){\scriptsize $0$}
-\put(130,6){\vector(0,-1){10}}
-\put(159,18){\scriptsize $(C,\vec{D})$}
-\put(158,15){\vector(1,0){28}}
-\put(186,0){\framebox(56,30)}
-\put(186,15){\makebox(56,10){Fine}}
-\put(186,3){\makebox(60,10){tracking}}
-\put(250,18){\scriptsize $S_{f}$}
-\put(242,15){\vector(1,0){24}}
-\put(266,0){\framebox(56,30){Filtering}}
-\put(330,18){\scriptsize $S_{o}$}
-\put(322,15){\vector(1,0){22}}
-\end{picture}
-\end{center}
+\begin{figure}[h]
+\center
+  \begin{picture}(340,34)(0,-4)
+    %\put(0,-2.5){\framebox(340,35)}
+    \put(-2,18){\scriptsize $(A,B)$}
+    \put(-2,15){\vector(1,0){24}}
+    \put(24,0){\framebox(56,30)}
+    \put(24,15){\makebox(56,10){Initial}}
+    \put(24,3){\makebox(56,10){detection}}
+    \put(86,18){\scriptsize $S_{i}$}
+    \put(80,15){\vector(1,0){22}}
+    %\put(102,0){\framebox(56,30)}
+    \multiput(102,15)(28,9){2}{\line(3,-1){28}}
+    \multiput(102,15)(28,-9){2}{\line(3,1){28}}
+    \put(100,0){\makebox(60,30){Valid ?}}
+    \put(133,-2){\scriptsize $0$}
+    \put(130,6){\vector(0,-1){10}}
+    \put(159,18){\scriptsize $(C,\vec{D})$}
+    \put(158,15){\vector(1,0){28}}
+    \put(186,0){\framebox(56,30)}
+    \put(186,15){\makebox(56,10){Fine}}
+    \put(186,3){\makebox(60,10){tracking}}
+    \put(250,18){\scriptsize $S_{f}$}
+    \put(242,15){\vector(1,0){24}}
+    \put(266,0){\framebox(56,30){Filtering}}
+    \put(330,18){\scriptsize $S_{o}$}
+    \put(322,15){\vector(1,0){22}}
+  \end{picture}
+  \caption{The detection method work flow.}
+  \label{fig:workflow}
+\end{figure}
 
 The fast track stage consists in building and extending a blurred segment
 $S_i$ based on the highest gradient points on each line of the directional

Article/notions.tex

@@ -2,53 +2,72 @@
 
 \subsection{Blurred segment}
 
-Our work relies on the notion of digital straight line
-as classically defined in the digital geometry literature \cite{debled}.
+Our work relies on the notion of digital straight line as classically
+defined in the digital geometry literature \cite{KletteRosenfeld04}.
 Only the 2-dimensional case is considered here.
 
 \begin{definition}
-A digital line $\cal D$ with integer parameters $(a,b,c,\nu)$ is the set
+A digital line $\mathcal{D}$ with integer parameters $(a,b,c,\nu)$ is the set
 of points $P(x,y)$ of $\mathbb{Z}^2$ that satisfy : $0 \leq ax + by - c < \nu$.
 \end{definition}
 
-The parameter $\nu$ is the width of the digital line.
-If $\nu = max (|a|, |b|)$, $\cal D$ is the narrowest 8-connected line
-and is called a naive line.
+The parameter $\nu$ is the arithmetic width of the digital line.
+When $\nu = max (|a|, |b|)$, $\mathcal{D}$ is the narrowest 8-connected
+line and is called a naive line.
 
 \begin{definition}
-A blurred segment of width $\nu$ is a set ${\cal S}_\nu$ of points in
-$\mathbb{Z}^2$ that all belong to a digital line of width $\nu$.
+A blurred segment of assigned width $\epsilon$ is a set $\mathcal{S}_\epsilon$
+of points in $\mathbb{Z}^2$ that all belong to a digital line of arithmetical
+width $\epsilon$.
 \end{definition}
 
-\begin{picture}(300,20)
-\framebox(300,20){Exemple de segment flou ? (\c ca va finir par lasser)}
-\end{picture}
-
-To construct a blurred segment we use a liner time algorithm based on the
-incremental growth of the convex hull of the input points using Melkman
-algorithm \cite{Melkman87}. Points are added while the convex hull width
-is less than the blurred segment assigned width.
+Linear time algorithms have been developed to recognize a blurred segment
+of assigned width $\epsilon$ \cite{DebledAl05,Buzer07}.
+They are based on an incremental growth of the convex hull of the blurred
+segment when adding each point successively.
+The minimal width $\mu$ of the blurred segment is the minimal width of
+this convex hull as computed by Melkman's algorithm \cite{Melkman87}.
+The extension of the blurred segment with a new input point is controlled
+by the recognition test $\mu < \epsilon$.
+
+\begin{figure}[h]
+\center
+  \begin{picture}(300,40)
+  \end{picture}
+  \caption{Example of blurred segment and recognition problem.}
+  \label{fig:bs}
+\end{figure}
+
+At the beginning, a large width $\epsilon_{ini}$ is assigned to the
+recognition problem to allow the detection of large blurred segments.
+Then, when extending the blurred segment, this assigned width is
+gradually decremented to reach the detected blurred segment minimal width.
 
 \subsection{Directional scan}
 
-A directional scan is a partition of a digital straight line ${\cal S}$,
-called the {\it scan strip}, into naive straight line segments ${\cal L}_i$,
-that are orthogonal to ${\cal S}$. The segments, called {\it scan lines}, are
-developed on each side of a central scan line ${\cal S}_0$, and labelled
-with their manhattan distance ($d_1 = |d_x| + |d_y|$) to ${\cal L}_0$ and
+A directional scan is a partition of a digital straight line $\mathcal{S}$,
+called the {\it scan strip}, into naive straight line segments $\mathcal{L}_i$,
+that are orthogonal to $\mathcal{S}$. The segments, called {\it scan lines},
+are developed on each side of a central scan line $\mathcal{S}_0$, and labelled
+with their manhattan distance ($d_1 = |d_x| + |d_y|$) to $\mathcal{L}_0$ and
 a positive (resp.  negative) sign if their are on the left (resp. right)
-of ${\cal L}_0$.
-
-\begin{picture}(300,20)
-\framebox(300,20){Exemple de directional scan}
-\end{picture}
-
-The directional scan can be defined by its central scan line ${\cal L}_0$.
+of $\mathcal{L}_0$.
+
+\begin{figure}[h]
+\center
+  %\begin{picture}(300,40)
+  %\end{picture}
+  \input{Fig_notions/fig}
+  \caption{Example of directional scan.}
+  \label{fig:ds}
+\end{figure}
+
+The directional scan can be defined by its central scan line $\mathcal{L}_0$.
 If $A(x_A,y_A)$ and $B(x_B,y_B)$ are the end points of this scan line,
 the scan strip is defined by :
 
 \centerline{
-${\cal S}(A,B) = {\cal D}(a, b, c, \nu)$, with
+$\mathcal{S}(A,B) = \mathcal{D}(a, b, c, \nu)$, with
 $\left\{ \begin{array}{l}
 a = x_B - x_A \\
 b = y_B - y_A \\
@@ -59,10 +78,10 @@ c = min (c_1, c_2)
 \noindent
 where $c_1 = a\cdot x_A + b\cdot y_A$ and $c_2 = a\cdot x_B + b\cdot y_B$.
 
-The scan line ${\cal L}_i(A,B)$ is then defined by :
+The scan line $\mathcal{L}_i(A,B)$ is then defined by :
 
 \centerline{
-${\cal L}_i(A,B) = {\cal S}(A,B) \cap {\cal D}(a', b', c', \nu')$, with
+$\mathcal{L}_i(A,B) = \mathcal{S}(A,B) \cap \mathcal{D}(a', b', c', \nu')$, with
 $\left\{ \begin{array}{l}
 a' = y_B - y_A \\
 b' = x_A - x_B \\
@@ -80,7 +99,7 @@ The directional scan can also be defined by its central point $C(x_C,y_C)$,
 its direction $\vec{D}(x_D,y_D)$ and its width $w$ :
 
 \centerline{
-${\cal S}(C,\vec{D},w) = {\cal D}(a, b, c, \nu)$, with
+$\mathcal{S}(C,\vec{D},w) = \mathcal{D}(a, b, c, \nu)$, with
 $\left\{ \begin{array}{l}
 a = y_D \\
 b = -x_D \\
@@ -89,11 +108,11 @@ c = a\cdot x_C + b\cdot y_C - w / 2
 \end{array} \right.$
 }
 
-and the scan line ${\cal L}_i(A,B)$ by :
+and the scan line $\mathcal{L}_i(A,B)$ by :
 
 \centerline{
-${\cal L}_i(C,\vec{D},w) =
-{\cal S}(C,\vec{D},w) \cap {\cal D}(a', b', c', \nu')$, with
+$\mathcal{L}_i(C,\vec{D},w) =
+\mathcal{S}(C,\vec{D},w) \cap \mathcal{D}(a', b', c', \nu')$, with
 $\left\{ \begin{array}{l}
 a' = x_D \\
 b' = y_D \\
@@ -128,4 +147,4 @@ Il faut donc r\'eactualiser la direction du scan.
 
 $N$ scans reste limit\'e.
 
-D'o\`u le scan adaptatif $\rightarrow$ r\'eorientation de $\cal S$.
+D'o\`u le scan adaptatif $\rightarrow$ r\'eorientation de $\mathcal{S}$.