diff --git a/Article/Fig_method/algoMulti.tex b/Article/Fig_method/algoMulti.tex
index 139655e9f39d4bcc9dd349e018c82b5fb3d7cb24..84f36d47a8ce307fe247c8de745a7fefb8a9c7b0 100644
--- a/Article/Fig_method/algoMulti.tex
+++ b/Article/Fig_method/algoMulti.tex
@@ -6,7 +6,7 @@
\SetKwData{lm}{LocMax}
\SetKwData{nullset}{$\emptyset$}
\SetKwData{ortho}{$\vec{AB}_\perp$}
- \SetKwData{eps}{$\varepsilon_{ini}$}
+ \SetKwData{eps}{$2~\varepsilon_{ini}$}
\SetKwData{pta}{$A$}
\SetKwData{ptb}{$B$}
\SetKwData{Result}{Result}
diff --git a/Article/intro.tex b/Article/intro.tex
index 8efbf7fb15c7573e94f71932a6343fbfd1068f20..53d2923913a9d6f04f37c173f74fe3ff6e878ef5 100755
--- a/Article/intro.tex
+++ b/Article/intro.tex
@@ -28,7 +28,7 @@ The present work aims at designing a flexible tool to detect blurred segments
with optimal width and orientation in gray-level images for as well
supervised as unsupervised contexts.
User-friendly solutions are sought, with ideally no parameter to set,
-or at least quite few values with intuitive meaning to an end user.
+or at least quite few values with intuitive meaning.
\subsection{Previous work}
diff --git a/Article/method.tex b/Article/method.tex
index cc263ff80a36202fcc7a0df4e74ccca012c57f2d..d38d22dea545b60d6b82b71a20169930f11b8c4d 100755
--- a/Article/method.tex
+++ b/Article/method.tex
@@ -154,15 +154,15 @@ when the orientation is badly estimated (\RefFig{fig:escape} c).
\includegraphics[width=0.48\textwidth]{Fig_notions/escapeFirst_zoom.png} &
\includegraphics[width=0.48\textwidth]{Fig_notions/escapeSecond_zoom.png} \\
\multicolumn{2}{c}{
- \includegraphics[width=0.78\textwidth]{Fig_notions/escapeThird_zoom.png}}
+ \includegraphics[width=0.72\textwidth]{Fig_notions/escapeThird_zoom.png}}
\begin{picture}(1,1)(0,0)
{\color{dwhite}{
- \put(-260,108.5){\circle*{8}}
- \put(-86,108.5){\circle*{8}}
+ \put(-260,100.5){\circle*{8}}
+ \put(-86,100.5){\circle*{8}}
\put(-172,7.5){\circle*{8}}
}}
- \put(-263,106){a}
- \put(-89,106){b}
+ \put(-263,98){a}
+ \put(-89,98){b}
\put(-175,5){c}
\end{picture}
\end{tabular}
@@ -282,9 +282,10 @@ First the positions $M_j$ of the prominent local maxima of the gradient
magnitude found under the stroke are sorted from the highest to the lowest.
For each of them the main detection process is run with three modifications:
\begin{enumerate}
-\item the initial detection takes $M_j$ and the orthogonal direction $AB_\perp$
-to the stroke as input to build a static scan of fixed width
-$\varepsilon_{ini}$, and $M_j$ is used as start point of the blurred segment;
+\item the initial detection takes $M_j$ and the orthogonal direction
+$\vec{AB}_\perp$ to the stroke as input to build a static scan of fixed width
+$2~\varepsilon_{ini}$, and $M_j$ is used as start point of the blurred
+segment;
\item the occupancy mask is filled in with the points of the detected blurred
segments $\mathcal{B}_j''$ at the end of each successful detection;
\item points marked as occupied are rejected when selecting candidates for the
@@ -357,21 +358,36 @@ to collect all the segments found under the stroke.
\input{Fig_method/algoAuto}
-The performance of the detector is illustrated in \RefFig{fig:evalAuto}b
-or in \RefFig{fig:noisy} where hardly perceptible edges are detected in this
-quite textured image. When the initial value of the assigned width is small,
-short edges are detected edges. Longer edges are detected if the initial
-assigned width is larger, but the found segments incorporate a lot of
-interfering outliers.
+\RefFig{fig:evalAuto}b gives an idea of the automatic detection performance.
+In the example of \RefFig{fig:noisy}, hardly perceptible edges are detected
+despite of a quite textured context.
+Unsurpringly the length of the detected edges is linked to the initial
+value of the assigned width, but a large value also augments the rate
+of interfering outliers insertion.
\begin{figure}[h]
\center
- \begin{tabular}{c@{\hspace{0.2cm}}c@{\hspace{0.2cm}}c}
+ \begin{tabular}{c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}c}
\includegraphics[width=0.32\textwidth]{Fig_method/parpaings.png} &
\includegraphics[width=0.32\textwidth]{Fig_method/parpaings2.png} &
\includegraphics[width=0.32\textwidth]{Fig_method/parpaings3.png}
\end{tabular}
- \caption{Automatic detection of blurred segments on a quite texture image.}
+ \begin{picture}(1,1)(0,0)
+ {\color{dwhite}{
+ \put(-286,-25.5){\circle*{8}}
+ \put(-171,-25.5){\circle*{8}}
+ \put(-58,-25.5){\circle*{8}}
+ }}
+ \put(-288.5,-28){a}
+ \put(-173.5,-28){b}
+ \put(-60.5,-28){c}
+ \end{picture}
+ \caption{Automatic detection of blurred segments on a textured image.
+ a) the input image,
+ b) automatic detection result with initial assigned width set
+ to 3 pixels,
+ c) automatic detection result with initial assigned width set
+ to 8 pixels.}
\label{fig:noisy}
\end{figure}
diff --git a/Article/notions.tex b/Article/notions.tex
index 981465fa9cb99ee066c99200a21adb43cedf1486..cc62fe6442d9f73ca08cc601f4a8e8e1ab3c67b2 100755
--- a/Article/notions.tex
+++ b/Article/notions.tex
@@ -121,21 +121,20 @@ At each iteration $i$, the scans $S_i$ and $S_{-i}$ are successively processed.
A directional scan can be defined by its start scan $S_0$.
If $A(x_A,y_A)$ and $B(x_B,y_B)$ are the end points of $S_0$,
-the scan strip is defined by :
+and if we note $\delta_x = x_B - x_A$, $\delta_y = y_B - y_A$,
+$c_1 = \delta_x\cdot x_A + \delta_y\cdot y_A$,
+$c_2 = \delta_x\cdot x_B + \delta_y\cdot y_B$ and
+$\nu_{AB} = max (|\delta_x|, |\delta_y|)$, it is then defined by
+the following scan strip $\mathcal{D}^{A,B}$ and scan lines
+$\mathcal{N}_i^{A,B}$:
\begin{equation}
-\mathcal{D}(A,B) =
-\mathcal{L}(\delta_x,~ \delta_y,~ min (c1,c2),~ 1 + |c_1-c_2|)
-\end{equation}
-\noindent
-where $\delta_x = x_B - x_A$, $\delta_y = y_B - y_A$,
-$c_1 = \delta_x\cdot x_A + \delta_y\cdot y_A$ and
-$c_2 = \delta_x\cdot x_B + \delta_y\cdot y_B$.
-The scan line $\mathcal{N}_i$ is then defined by :
-\begin{equation}
-\mathcal{N}_i(A,B) = \mathcal{L}(\delta_y,~ -\delta_x,~
+\left\{ \begin{array}{l}
+\mathcal{D}^{A,B} =
+\mathcal{L}(\delta_x,~ \delta_y,~ min (c1,c2),~ 1 + |c_1-c_2|) \\
+\mathcal{N}_i^{A,B} = \mathcal{L}(\delta_y,~ -\delta_x,~
\delta_y\cdot x_A - \delta_x\cdot y_A + i\cdot \nu_{AB},~ \nu_{AB})
+\end{array} \right.
\end{equation}
-where $\nu_{AB} = max (|\delta_x|, |\delta_y|)$
%The scan lines length is $d_\infty(AB)$ or $d_\infty(AB)-1$, where $d_\infty$
%is the chessboard distance ($d_\infty = max (|d_x|,|d_y|)$).
@@ -143,15 +142,16 @@ where $\nu_{AB} = max (|\delta_x|, |\delta_y|)$
%as the image bounds should also be processed anyway.
A 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 $w$. The scan strip is :
-\begin{equation}
-\mathcal{D}(C,\vec{D},w)
-= \mathcal{L}(Y_D,~ -X_D,~ x_C\cdot Y_D - y_C\cdot X_D - w / 2,~ w)
-\end{equation}
-
-\noindent
-and the scan line $\mathcal{N}_i(C,\vec{D},w)$ :
+its direction $\vec{D}(X_D,Y_D)$ and its width $w$. If we note
+$c_3 = x_C\cdot Y_D - y_C\cdot X_D$ and
+$c_4 = X_D\cdot x_C + Y_D\cdot y_C$, it is then defined by
+the following scan strip $\mathcal{D}^{C,\vec{D},w}$ and scan lines
+$\mathcal{N}_i^{C,\vec{D},w}$:
\begin{equation}
-\mathcal{N}_i(C,\vec{D},w) = \mathcal{L}(X_D,~ Y_D,~
- X_D\cdot x_C + Y_D\cdot y_C - w / 2 + i\cdot w,~ max (|X_D|,|Y_D|)
+\left\{ \begin{array}{l}
+\mathcal{D}^{C,\vec{D},w}
+= \mathcal{L}(Y_D,~ -X_D,~ c_3 - w / 2,~ w) \\
+\mathcal{N}_i^{C,\vec{D},w} = \mathcal{L}(X_D,~ Y_D,~
+ c_4 - w / 2 + i\cdot w,~ max (|X_D|,|Y_D|)
+\end{array} \right.
\end{equation}