\section{Experimental validation}

\label{sec:expe}

The main goal of this work is to provide straight segments with a quality
indication through the associated width parameter.
In lack of available reference tool, the evaluation stage mostly aims
at quantifying the advantages of the new detector compared to the previous
one in unsupervised context.
The process flow of the former method (initial detection followed by two
refinement steps) is integrated as an option into the code of the new
detector, so that both methods rely on the same optimized basic routines.
During all these experiments, only the blurred segment size and its
orientation compared to the initial stroke are tested at the end of
the initial detection, and only the segment size is tested at the end
of the fine tracking stage.
All other tests, sparsity or fragmentation, are disabled.
The segment minimal size is set to 5 pixels, except where precised.

The first test compares the performance of both
detectors on a set of 1000 synthesized images containing 10 randomly
placed input segments with random width between 2 and 5 pixels.
The absolute value of the difference of each found segment to its
matched input segment is measured.
On these ground-truth image, the numerical error on the gradient extraction
biases the line width measures. This bias was first estimated using 1000
images containing only one input segment (no possible interaction)
and the found value (1.4 pixel) was taken into account in the test.
\RefTab{tab:synth} shows
slightly better width and angle measurements for the new detector.
The new detector shows more precise, with a smaller amount of false
detections and succeeds in finding most of the input segments.

%\begin{figure}[h]
%\center
%  \begin{tabular}{
%      c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}c@{\hspace{0.1cm}}c}
%    \includegraphics[width=0.19\textwidth]{Fig_synth/statsExample.png} &
%    \includegraphics[width=0.19\textwidth]{Fig_synth/statsoldPoints.png} &
%    \includegraphics[width=0.19\textwidth]{Fig_synth/statsoldBounds.png} &
%    \includegraphics[width=0.19\textwidth]{Fig_synth/statsnewPoints.png} &
%    \includegraphics[width=0.19\textwidth]{Fig_synth/statsnewBounds.png}
%    \begin{picture}(1,1)
%      \put(-310,0){a)}
%      \put(-240,0){b)}
%      \put(-170,0){c)}
%      \put(-100,0){d)}
%      \put(-30,0){e)}
%    \end{picture}
%  \end{tabular}
%  \caption{Evaluation on synthesized images:
%           a) one of the test images,
%           b) output blurred segments from the old detector and
%           c) their enclosing digital segments,
%           d) output blurred segments from the new detector and
%           e) their enclosing digital segments.}
%  \label{fig:synth}
%\end{figure}
\begin{table}
\centering
\input{Fig_synth/statsTable}
\caption{Measured performance of both detectors on a set of synthesized images.
$S$ is the set of all the input segments,
$D$ the set of all the detected blurred segments.}
\label{tab:synth}
\end{table}

\input{expeAuto}

%\input{expeHard}
