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Article: adaptive scan

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......@@ -7,18 +7,18 @@ defined in the digital geometry literature \cite{KletteRosenfeld04}.
Only the 2-dimensional case is considered here.
\begin{definition}
A digital line $\mathcal{D}$ with integer parameters $(a,b,c,\nu)$ is the set
A digital line $\mathcal{L}$ 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 arithmetic width of the digital line.
When $\nu = max (|a|, |b|)$, $\mathcal{D}$ is the narrowest 8-connected
When $\nu = max (|a|, |b|)$, $\mathcal{L}$ is the narrowest 8-connected
line and is called a naive line.
\begin{definition}
A blurred segment $\mathcal{B}$ of assigned width $\varepsilon$ is a set
$\mathcal{S}_\varepsilon$ of points in $\mathbb{Z}^2$ that all belong
to a digital line of arithmetical width $\varepsilon$.
of points in $\mathbb{Z}^2$ that all belong to a digital line of
arithmetical width $\varepsilon$.
\end{definition}
Linear time algorithms have been developed to recognize a blurred segment
......@@ -128,28 +128,74 @@ c' = a'\cdot x_C + b'\cdot y_C - w / 2 + i\cdot w
\subsection{Adaptive directional scan}
Notions \`a d\'evelopper :
\begin{itemize}
\item Direction de scan
\item Epaisseur de consigne du SF
\item Largeur optimale du SF
\end{itemize}
We try to detect a blurred segment inside a directional scan which position
and orientation are given by the user, or defined in arbitrary direction in
unsupervised mode.
Most of the times, the detection stops where the segment escapes sideways
froms the scan strip.
Therefore a second search is run again using an other directional scan aligned
on the detected segment.
But we only have an estimation of this blurred segment direction, and the
longer the real segment, the higher the probability to fail again on a
blurred segment escape from the directional scan.
Poser le pb : la direction est incompl\`etement estim\'ee, d'o\`u un risque
de sortie de scan.
\begin{picture}(300,20)
\framebox(300,20){Illustration d'une sortie de scan avec les diff\'erentes
\'epaisseurs en jeu}
\end{picture}
\begin{figure}[h]
\center
\begin{picture}(300,40)
\end{picture}
\caption{Example of early detection failures
on side escapes from the directional scan.}
\label{fig:sideEscapes}
\end{figure}
La direction du segment ne peut \^etre connue qu'a posteriori.
Even in ideal situation where the detected segment is a perfect line,
its width is never null as a result of the discretization process.
The estimated direction accuracy is mostly constrained by the length of
the detected segment.
To avoid these side escapes, the scan should not be a linear strip but
rather a conic shape to take into account the blurred segment preimage.
% Of course this problem is amplified when ideal BS are considered.
% -> FAUX : c'est relativement plus penalisant sur 1 BS reduit a 2 pts
% que sur un BS qu'on n'autorise pas a s'elargir.
This side shift is amplified when we let the blurred segment the capacity
to get thicker in order to capture possible noisy features.
The assigned width is then still greater than the detected minimal width,
so that the segment can move within the directional scan.
Knowing the detected BS shape and the image size, it is possible to
define a conic scan area, but this solution is computationaly expensive
because it leads to useless exploration of large image areas.
\begin{figure}[h]
\center
%\begin{picture}(300,40)
%\end{picture}
\input{Fig_notions/bscone}
\caption{Possible extension area based
on the detected blurred segment preimage.}
\label{fig:cone}
\end{figure}
La direction d'une droite discr\`ete s'affine au fur et \`a mesure de
son d\'eveloppement.
Ainsi en va t-il des segments flous (a fortiori).
The solution implemented in the former work was to let some arbitrary
margin between the scan strip width and the assigned width to the detection,
and to perform two fine detection steps, using for each of them the direction
found at the former step.
This process could be itered as long as the blurred segment escapes from
the directional scanner using as any detection steps as necessary.
But it produces a useless computational coast, because of the margin left,
but also the multiple detection of the same segment start points.
Il faut donc r\'eactualiser la direction du scan.
\begin{figure}[h]
\center
\begin{picture}(300,40)
\end{picture}
\caption{Example of blurred segment detection
using an adaptive directional scan.}
\label{fig:adaptiveScan}
\end{figure}
$N$ scans reste limit\'e.
The solution we propose here is to dynamically adapt the scan direction
on the detection result. At each position, the scan strip is updated
using the BS direction and minimal width computed at the former position,
that is :
\[\mathcal{S}_i = \mathcal{L}_0 \cup \mathcal{D}_{i-1}\]
D'o\`u le scan adaptatif $\rightarrow$ r\'eorientation de $\mathcal{S}$.
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