\section{Experimental validation}

\label{sec:expe}

The evaluation stage aims at quantifying the advantages of the new detector
compared to the former one.
For a fair comparison, the process flow of the former method (the 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.

\input{expeSynthese}

\input{expeHard}

The first test compares the computation times of both detectors on a
selection of input strokes (\RefFig{fig:buro}). Results are displayed
in \RefTab{tab:cmpOldNew}.

\begin{figure}[h]
\center
  \begin{tabular}{c@{\hspace{0.2cm}}c}
    \includegraphics[width=0.49\textwidth]{Fig_expe/buroOld.png} &
    \includegraphics[width=0.49\textwidth]{Fig_expe/buroNew.png}
    \begin{picture}(1,1)
      \put(-158,46){\circle{8}}
      \put(-162,42){\makebox(8,8){\scriptsize 0}}
      \put(-18,30){\circle{8}}
      \put(-22,26){\makebox(8,8){\scriptsize 1}}
      \put(-57,92){\circle{8}}
      \put(-61,88){\makebox(8,8){\scriptsize 2}}
      \put(-53,104){\circle{8}}
      \put(-57,100){\makebox(8,8){\scriptsize 3}}
      \put(-90,71){\circle{8}}
      \put(-94,67){\makebox(8,8){\scriptsize 4}}
      \put(-92,23){\circle{8}}
      \put(-96,19){\makebox(8,8){\scriptsize 5}}
      \put(-134,9){\circle{8}}
      \put(-138,5){\makebox(8,8){\scriptsize 6}}
      \put(-156,27){\circle{8}}
      \put(-160,23){\makebox(8,8){\scriptsize 7}}
      \put(-150,84){\circle{8}}
      \put(-154,80){\makebox(8,8){\scriptsize 8}}
      \put(-39,110){\circle{8}}
      \put(-43,106){\makebox(8,8){\scriptsize 9}}
    \end{picture}
  \end{tabular}
  \caption{Outputs of both former (on left) and new (on right) detectors
           using a selection of input strokes.}
  \label{fig:buro}
\end{figure}

\begin{table}
\centering
\begin{tabular}{|l||l|l|l|l|l|l|l|l|l|l|}
\hline \multicolumn{1}{|r||}{Stroke \hspace{0.4cm}} &
       \multicolumn{1}{c|}{1} & \multicolumn{1}{c|}{2} &
       \multicolumn{1}{c|}{3} & \multicolumn{1}{c|}{4} &
       \multicolumn{1}{c|}{5} & \multicolumn{1}{c|}{6} &
       \multicolumn{1}{c|}{7} & \multicolumn{1}{c|}{8} &
       \multicolumn{1}{c|}{9} & \multicolumn{1}{c|}{10} \\ \hline \hline
with the former detector: \hspace{0.4cm}
& 18.2 & 18.2 & 18.2 & 18.2 & 18.2 & 18.2 & 18.2 & 18.2 & 18.2 & 18.2 \\ \hline
with the new detector: & & & & & & & & & & \\ \hline
\end{tabular}
\caption{Compared execution time in milliseconds between former and new
detectors with the input strokes of \RefFig{fig:buro}.}
\label{tab:cmpOldNew}
\end{table}

In the second series of tests, the execution times of both detectors were
compared on the automatic detection of edges on a set of test images.
Results are displayed for one of them (\RefFig{fig:evalAuto}).
998 (resp. 822) blurred segments are extracted with the former
(resp. new) detector on all images.
The average blurred segment width is 5.06 pixels for the former detector,
and 2.62 pixels for the new detector.
The average execution time is 206 ms for the former detector,
and 96 ms for the new detector.

\begin{figure}[h]
\center
  \begin{tabular}{c@{\hspace{0.2cm}}c}
    \includegraphics[width=0.49\textwidth]{Fig_expe/autoOld.png} &
    \includegraphics[width=0.49\textwidth]{Fig_expe/autoNew.png}
  \end{tabular}
  \caption{Automatic edge detections on one of the test images with the
former detector on the left, and the new detector on the right.}
  \label{fig:evalAuto}
\end{figure}

The former detector does not estimate the edge width, but just circumscribes
the edge with a blurred segment of assigned width.
If the edge is very thin, the blurred segment is free to rotate around the
extracted edge and the provided orientation is biased.
Moreover it lets some space to incorporate additional spurious outliers,
as illustrated in \RefFig{fig:outliers}.
With the new appoach, a real estimation of the edge width is provided.
The main risk of outlier incorporation remains at the beginning of the
blurred segment expansion as long as the minimal width continues to grow
and the assigned width has not been set to the detected segment minimal width.

\begin{figure}[h]
\center
  \begin{tabular}{c@{\hspace{0.2cm}}c}
    \includegraphics[width=0.49\textwidth]{Fig_expe/outliersOld_zoom.png} &
    \includegraphics[width=0.49\textwidth]{Fig_expe/outliersNew_zoom.png}
  \end{tabular}
  \caption{Potential insertion of outliers for both detectors:
On the left, the fixed width of the former detector always lets opportunities
of outlier insertions. On the right, the new detector restricts these
opportunities to the blurred segment early analysis stage.}
  \label{fig:outliers}
\end{figure}