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Article: remarks BK updated

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......@@ -37,8 +37,8 @@ The output segment $\mathcal{B}'$ is finally tested according to the
application needs. Too short, too sparse or too fragmented segments
can be rejected. Length, sparsity or fragmentation thresholds are
intuitive parameters left at the end user disposal.
None of these tests are activated for the experimental stage in order
to put forward achievable performance.
%None of these tests are activated for the experimental stage in order
%to put forward achievable performance.
\subsection{Adaptive directional scan}
......@@ -51,36 +51,36 @@ A second search is then run using another directional scan aligned
on the detected segment (\RefFig{fig:escape} b).
In the given example, an outlier added to the initial segment leads to a
wrong orientation value.
But even in case of a correct detection, this estimated orientation
is subject to the numerization rounding, and the longer the real segment
to detect, the higher the probability to fail again on a blurred segment
escape from the directional scan.
But even in case of a correct detection, this estimated orientation is
subject to the numerization rounding, and the longer the real segment is,
the higher the probability gets to fail again on an escape from the scan strip.
\begin{figure}[h]
\center
\begin{tabular}{c@{\hspace{0.2cm}}c}
\includegraphics[width=0.48\textwidth]{Fig_notions/escapeFirst_zoom.png} &
\includegraphics[width=0.48\textwidth]{Fig_notions/escapeSecond_zoom.png} \\
\includegraphics[width=0.48\textwidth]{Fig_notions/escapeLightFirst_zoom.png} &
\includegraphics[width=0.48\textwidth]{Fig_notions/escapeLightSecond_zoom.png} \\
\multicolumn{2}{c}{
\includegraphics[width=0.62\textwidth]{Fig_notions/escapeThird_zoom.png}}
\includegraphics[width=0.62\textwidth]{Fig_notions/escapeLightThird_zoom.png}}
\begin{picture}(1,1)(0,0)
{\color{dwhite}{
\put(-260,87.5){\circle*{8}}
\put(-86,87.5){\circle*{8}}
\put(-172,7.5){\circle*{8}}
\put(-260,78.5){\circle*{8}}
\put(-86,78.5){\circle*{8}}
\put(-172,4.5){\circle*{8}}
}}
\put(-263,85){a}
\put(-89,85){b}
\put(-175,5){c}
\put(-262.5,76){a}
\put(-89,75.5){b}
\put(-174.5,2){c}
\end{picture}
\end{tabular}
\caption{Aborted detections on side escapes of static directional scans
and successful detection using an adaptive directional scan.
The last points added to the left of the blurred segment during
initial detection (a) lead to a bad estimation of its
orientation, and thus to an incomplete fine detection with a
classical directional scan (b). An adaptive directional scan
can continue the segment expansion as far as necessary (c).
orientation, and thus to an incomplete fine tracking with a
classical directional scan (b). An adaptive directional scan at
the place of the static one allows to continue the segment
expansion as far as necessary (c).
On the pictures, the input selection is drawn in red color,
the scan strip bounds
in blue and the detected blurred segment in green.}
......@@ -108,22 +108,26 @@ ADS = \left\{
S_i = \mathcal{D}_i \cap \mathcal{N}_i \cap \mathcal{I}
\left| \begin{array}{l}
\delta(\mathcal{N}_i) = - \delta^{-1}(\mathcal{D}_0) \\
\wedge~ h(\mathcal{N}_i) = h(\mathcal{N}_{i-1}) + p(\mathcal{D}) \\
\wedge~ \mathcal{D}_{i} = \mathcal{D} (C_{i-1}, \vec{D}_{i-1}, w_{i-1}), i > 1
\wedge~ h(\mathcal{N}_i) = h(\mathcal{N}_{i-1}) + p(\mathcal{D}_0) \\
\wedge~ \mathcal{D}_{i} = \mathcal{D} (C_{i-1}, \vec{D}_{i-1}, w_{i-1}),
i > \lambda
\end{array} \right. \right\}
\end{equation}
where $C_{i-1}$, $\vec{D}_{i-1}$ and $w_{i-1}$ are a position, a director
vector and a width observed at iteration $i-1$.
where $C_{i}$, $\vec{D}_{i}$ and $w_{i}$ are respectively a position,
a director vector and a width observed at iteration $i$.
In the scope of the present detector, $C_{i-1}$ is the intersection of
the input selection and the medial axis of $\mathcal{B}_{i-1}$,
$\vec{D}_{i-1}$ the support vector of the enclosing digital segment
$E(\mathcal{B}_{i-1})$, and $w_{i-1}$ a value slightly greater than the
minimal width of $\mathcal{B}_{i-1}$.
So the last clause expresses the update of the scan bounds at iteration $i$.
Compared to static directional scans, the scan strip moves while
Compared to static directional scans where the scan strip remains fixed to
the initial line $\mathcal{D}_0$, here the scan strip moves while
scan lines remain fixed.
This behavior ensures a complete detection of the blurred segment even
when the orientation is badly estimated (\RefFig{fig:escape} c).
This behavior ensures a complete detection of the blurred segment even when
the orientation of $\mathcal{D}_0$ is badly estimated (\RefFig{fig:escape} c).
In practice, it is started after $\lambda = 20$ iterations when the observed
direction becomes more stable.
\subsection{Control of the assigned width}
......@@ -131,15 +135,15 @@ The assigned width $\varepsilon$ to the blurred segment recognition algorithm
is initially set to a large value $\varepsilon_0$ in order to allow the
detection of large blurred segments.
Then, when no more augmentation of the minimal width is observed after
$\lambda$ iterations ($\mu_{i+\lambda} = \mu_i$), it is set to a much
$\tau$ iterations ($\mu_{i+\tau} = \mu_i$), it is set to a much
stricter value able to circumscribe the possible interpretations of the
segment, that take into account the digitization margins:
\begin{equation}
\varepsilon = \mu_{i+\lambda} + \frac{\textstyle 1}{\textstyle 2}
\varepsilon = \mu_{i+\tau} + \frac{\textstyle 1}{\textstyle 2}
\end{equation}
This strategy aims at preventing the incorporation of spurious outliers in
further parts of the segment.
Setting the observation distance to a constant value $\lambda = 20$ seems
Setting the observation distance to a constant value $\tau = 20$ seems
appropriate in most experimented situations.
\subsection{Supervised blurred segment detection}
......@@ -221,7 +225,7 @@ $2~\varepsilon_{ini}$, and $M_j$ is used as start point of the blurred
segment;
\item the occupancy mask is filled in with the points of the dilated blurred
segments $\mathcal{B}_j''$ at the end of each successful detection
(a 21 pixels bowl is used);
(a 21 pixels neighborhood is used);
\item points marked as occupied are rejected when selecting candidates for the
blurred segment extension in the fine tracking step.
\end{enumerate}
......@@ -240,8 +244,8 @@ the borders. At each position, the multi-detection algorithm is run
to collect all the segments found under the stroke.
In the present work, the stroke sweeping step $\delta$ is set to 10 pixels.
The automatic detection of blurred segments in a whole image is left
available for testing in an online demonstration at the following address: \\
The automatic detection of blurred segments in a whole image is left available
for testing from an online demonstration at the following address: \\
\href{http://ipol-geometry.loria.fr/~kerautre/ipol_demo/AdaptDirBS_IPOLDemo}{
\small{\url{
http://ipol-geometry.loria.fr/~kerautre/ipol_demo/AdaptDirBS_IPOLDemo}}}
......
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