Experiments first revisitation

Article/Expe_auto/cannyTable.tex

+\begin{tabular}{|l||r|r|r|r|r|}
+\hline
+Measure $M$ & \multicolumn{1}{c|}{$T$ (ms)} & \multicolumn{1}{c|}{$C$}
+& \multicolumn{1}{c|}{$N$}
+& \multicolumn{1}{c|}{$L$} & \multicolumn{1}{c|}{$L/N$} \\
+\hline
+Canny
+& 75.4 $\pm$ 11.7 & 60.6 $\pm$ 10.6
+& 466 $\pm$ 138 & 17678 $\pm$ 4419 & 39.5 $\pm$ 10.2 \\
+Ours
+& 83.2 $\pm$ 20.1 & 61.5 $\pm$ 10.8
+& 613 $\pm$ 140 & 20769 $\pm$ 4000 & 34.6 $\pm$ 5.4 \\
+\hline
+\end{tabular}

Article/abstract.tex

-  This paper introduces a new straight line detector in gray-level images,
+  This paper introduces a fully discrete framework for a new straight line
+detector in gray-level images,
 where line segments are enriched with a thickness parameter
 intended to provide a quality criterion on the extracted feature.
 This study enhances previous works on interactive
 line detection with a better estimation of the segment width and
 orientation through two main improvements: adaptive directional scans and
 the control of the assigned width to the detection algorithm.
-A new contribution to the detection of all the segments in a single image
-is also proposed and left available in an online demonstration.
+A new contribution to the automatic detection of all the segments in a single
+image is also proposed and left available in an online demonstration.

Article/biblio.bib

@@ -187,3 +187,28 @@ in urban imagery},
   year = {2013},
   pages = {1578--1583}
 }
+
+
+@article{HuertasMedioni86,
+  title = {Detection of intensity changes with subpixel accuracy using
+           {L}aplacian--{G}aussian masks},
+  author = {Huertas, Andres and Medioni, Gerard},
+  journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
+  volume = {8},
+  number = {5},
+  month = {September},
+  year = {1986},
+  pages = {651--664}
+}
+
+
+@article{KekreGharge10,
+  title = {Image segmentation using extended edge operator for mammographic
+           images},
+  author = {Kekre, H.B. and Gharge, S.M.},
+  journal = {International Journal on Computer Science and Engineering},
+  volume = {2},
+  number = {4},
+  year = {2010},
+  pages = {1086--1091}
+}

Article/conclusion.tex

@@ -20,8 +20,10 @@ adaptive directional scans that continuously adjust the scan strip
 to the detected edge direction;
 the control of the assigned width based on the observation of the
 blurred segment growth.
-Expected gains in accuracy and execution time were confirmed by
-held experiments.
+Experiments on synthetic ground truth images show improved accuracy
+brought be the new concepts, and a reliable extraction of the line width.
+Moreover reached performance are quite comparable to a recent well
+established edge detector in the literature.
 
 A residual weakness of the approach is the sensitivity to the initial
 conditions.

Article/expeV2.tex

+\section{Experimental validation}
+
+\label{sec:expe}
+
+The main goal of this work is to detect straight segments enriched with a
+quality measure through the associated width parameter.
+In lack of available reference tool, the evaluation stage first aims
+at quantifying the benefits of the new detector compared to the previous
+one in unsupervised context on synthetic data considered as a ground truth.
+Then comparisons are made with a well established recent detector
+\cite{LuAl15} in order to check that global performance (processing time,
+ground truth covering, detected lines count and mean length) are not
+degraded.
+
+%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 images, 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.
+Other experiments, also available at the {\it GitHub} repository, show
+that the new detector is faster and finds more edges than the previous one.
+
+
+%\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}
+
+The next experiments aim at evaluating the performance of the new
+detector with respect to CannyLines detector \cite{LuAl15}
+on the 102 annotated ground truth images of the York Urban data base
+\cite{DenisAl08}.
+%One of them is displayed on \RefFig{fig:auto}.
+Compared measures $M$ are execution time $T$, covering ratio $C$,
+Detected lines amount $N$, total lines length $L$ and ratio $L/N$.
+To compare the execution times, for each image of the data base we measure
+the execution time of 100 detections, gradient extraction included.
+The covering ratio compares the length of ground truth lines covered
+by the detected lines wrt the total length of ground truth lines.
+A eight neighborhood of 8 pixels is added to lines provided by CannyLines.
+
+\RefTab{tab:canny} gives the achieved results.
+\begin{table}
+\centering
+\input{Expe_auto/cannyTable}
+\caption{Measured performance of the proposed detector and CannyLines
+on standard images.}
+\label{tab:canny}
+\end{table}
+
+The new detector shows equivalent performance in terms of ground trouth lines
+coverture. CannyLines is faster and finds less but longer lines, but these
+results remain quite comparble so that we can arg that the global performance
+is not degraded. And most of all, our detector provides an indication on the
+detected lines quality through the additional thickness parameter.

Article/introV2.tex

@@ -12,7 +12,7 @@ orientation. They are also used to detect structured features to help a
 Therefore, straight line detection is always an active research topic
 centered on the quest of still faster, more accurate or more robust-to-noise
 methods \cite{AkinlarTopal12,GioiAl10,LuAl15,MatasAl00}.
-Most of the times, they are based on the extraction of an edge map based
+Most of the times, they rely on the extraction of an edge map based
 on gradient magnitude. Gradient orientation is often used to discriminate
 candidates and thus provide better efficiency.
 However, they seldom provide an exploitable measure of the output line
@@ -29,10 +29,10 @@ complementary measures to reprojection errors for local accuracy evaluation.
 
 In digital geometry, new mathematical definitions of classical
 geometric objects, such as lines or circles, have been developed
-to better fit to the discrete nature of most of todays data to process.
+to better fit to the discrete nature of most of today's data to process.
 In particular, the notion of blurred segment \cite{Buzer07,DebledAl05} was
 introduced to cope with the image noise or other sources of imperfections
-from the real world by the mean of a width parameter.
+from the real world using a width parameter.
 Efficient algorithms have already been designed to recognize
 these digital objects in binary images \cite{DebledAl06}.
 Blurred segments seem well suited to reflect the required line quality

Article/main.tex

@@ -57,7 +57,7 @@
 	
 	\input{methodV2}
 	
-	\input{expe}
+	\input{expeV2}
 	
 	\input{conclusion}
   

Article/methodV2.tex

@@ -11,8 +11,8 @@ stable appearance such as metallic tubular objects \cite{AubryAl17}.
 Contrarily to most detectors, no edge map is built here, but gradient
 magnitude and orientation are examined in privileged directions to track
 edge traces.
-Therefore we use a Sobel operator with a 5x5 pixels mask \cite{GuptaMazumdar13}
-to get a high quality gradient information.
+Therefore we use a Sobel operator with a 5x5 pixels mask
+\cite{KekreGharge10} to get a high quality gradient information.
 
 \subsection{Previous work}
 
@@ -42,8 +42,10 @@ The search direction relies on the support vector of the blurred segment
 detected at the former step.
 Because the numerization rounding fixes a limit on this estimated orientation
 accuracy, more steps are inevitably necessary to process larger images.
+In the following, we present the improvements in the new detector to
+overcome these limitations.
 
-\subsection{Workflow of the detection process}
+\subsection{Workflow of the new detection process}
 
 The workflow of the detection process is summerized in the following figure.
 
@@ -68,11 +70,11 @@ In the fine tracking step, another blurred segment $\mathcal{B}'$ is built
 and extended with points that correspond to local maxima of the
 image gradient, ranked by magnitude order, and with gradient direction
 close to start point gradient direction.
-At this refinement step, a control of the assigned width is applied
-and an adaptive directional scan based on the found position $C$ and
+At this refinement step, a {\it control of the assigned width} is applied
+and an {\it adaptive directional scan} based on the found position $C$ and
 direction $\vec{D}$ is used in order to extends the segment in the
 appropriate direction. These two improvements are described in the
-following sections.
+following sections (\ref{subsec:ads} and \ref{subsec:caw}).
 
 The output segment $\mathcal{B}'$ is finally tested according to the
 application needs. Too short, too sparse or too fragmented segments
@@ -82,6 +84,7 @@ intuitive parameters left at the end user disposal.
 %to put forward achievable performance.
 
 \subsection{Adaptive directional scan}
+\label{subsec:ads}
 
 The blurred segment is searched within a directional scan with a position
 and an orientation approximately provided by the user, or blindly defined
@@ -169,6 +172,7 @@ In practice, it is started after $\lambda = 20$ iterations when the observed
 direction becomes more stable.
 
 \subsection{Control of the assigned width}
+\label{subsec:caw}
 
 The assigned width $\varepsilon$ to the blurred segment recognition algorithm
 is initially set to a large value $\varepsilon_0$ in order to allow the