diff --git a/Article/Expe_auto/compTable.tex b/Article/Expe_auto/compTable.tex
index 619e13c170573b8911e5d615ef50457bdd5b6f06..9b9bf130f16833d0304272e751fd4b10028d9e60 100644
--- a/Article/Expe_auto/compTable.tex
+++ b/Article/Expe_auto/compTable.tex
@@ -1,6 +1,6 @@
\begin{tabular}{|l||r@{~$\pm~$}r|r@{~$\pm$~}r|r@{~$\pm$~}r|r@{~$\pm$~}r|r@{~$\pm$~}r|}
\hline
-Measure $M$ & \multicolumn{2}{c|}{$T$ (ms)} & \multicolumn{2}{c|}{$C$ (\%)}
+Measure & \multicolumn{2}{c|}{$T$ (ms)} & \multicolumn{2}{c|}{$C$ (\%)}
& \multicolumn{2}{c|}{$N$}
& \multicolumn{2}{c|}{$L$ (pixels)} & \multicolumn{2}{c|}{$L/N$} \\
\hline
diff --git a/Article/Fig_synth/statsTable.tex b/Article/Fig_synth/statsTable.tex
index 526fdb75d9d494dc3331f8762f6f7d84bfeaae3d..82008032b8e69c1a8fac45a37b9ccff03f99f829 100644
--- a/Article/Fig_synth/statsTable.tex
+++ b/Article/Fig_synth/statsTable.tex
@@ -4,8 +4,8 @@ Detector : & \multicolumn{3}{c|}{old} & \multicolumn{3}{c|}{new} \\
\hline
Detected blurred segments per image
& 17.06 & $\pm$ & 3.22 & 16.83 & $\pm$ & 3.11 \\
-Detected long (> 40 pixels) blurred segments per image
-& 11.24 & $\pm$ & 1.94 & 11.36 & $\pm$ & 1.97 \\
+%Detected long (> 40 pixels) blurred segments per image
+%& 11.24 & $\pm$ & 1.94 & 11.36 & $\pm$ & 1.97 \\
Undetected input segments per image
& 0.152 & $\pm$ & 0.43 & \textbf{0.003} & $\pm$ & \textbf{0.05} \\
Precision (\%) : $P = \#(D\cap S)/\#D$
diff --git a/Article/biblio.bib b/Article/biblio.bib
index 0a35efc4d3c0f8ab68b2fcef759add5c914c1ad9..e52e2c3fd398d038d58c646ad908571153dc0290 100755
--- a/Article/biblio.bib
+++ b/Article/biblio.bib
@@ -212,3 +212,15 @@ in urban imagery},
year = {2010},
pages = {1086--1091}
}
+
+
+@book{DesolneuxAl08,
+ author = {Desolneux, Agn\`es and Moisan, Lionel and Morel, Jean-Michel},
+ year = {2008},
+ month = {January},
+ pages = {273},
+ title = {From {G}estalt Theory to Image Analysis: A Probabilistic Approach},
+ series= {Interdisciplinary Applied Mathematics},
+ volume = {34},
+ doi = {10.1007/978-0-387-74378-3}
+}
diff --git a/Article/expeV2.tex b/Article/expeV2.tex
index c4f8cd6cec8fcace4c6ba2b42c5664ca61130d16..03a2f3652c6694f2f4603eed8ee71aab6f6ff50e 100755
--- a/Article/expeV2.tex
+++ b/Article/expeV2.tex
@@ -24,27 +24,26 @@
%The segment minimal size is set to 5 pixels, except where precised.
In the experimental stage, the proposed approach is validated through
-comparisons with other recent line detectors.
-However only one of them, LSD \cite{GioiAl10}, provides a thickness value
-of output lines, based on the width of regions with same gradient direction.
-Unfortunately, this information does not really match the line sharpness
-or scattering quality, that is addressed in this work, and can not be
-actually compared to the thickness value output by the new detector.
+comparisons with other recent line detectors: LSD \cite{GioiAl10},
+ED-Lines \cite{AkinlarTopal12} and CannyLines \cite{LuAl15}.
+Only LSD provides a thickness value
+based on the width of regions with same gradient direction.
+This information does not match the line sharpness or scattering quality
+addressed in this work, so that it can not be actually compared to the
+thickness value output by the new detector.
Moreover, we did not find any data base with ground truth including
line thickness.
Therefore we proceed in two steps :
-(i) evaluation of the benefits brought by the new concepts to measure
-the lines orientation and thickness on synthetic images;
-(ii) evaluation of more global performance of the unsupervised detector
-compared to other approaches.
-For all these experiments, the stroke sweeping step is set to 15 pixels.
+(i) evaluation on synthetic images of the new concepts enhancements
+on line orientation and thickness estimation;
+(ii) evaluation of more global performance of the proposed approach
+compared to other detectors.
+For all these experiments in unsupervised mode, the stroke sweeping step
+is set to 15 pixels.
-At first, the benefits of introduced concepts are evaluated through a
-comparison of the performance of both versions of the detector
-(with and without the concepts).
-The test is performed on a set of 1000 synthesized images
-containing 10 randomly
-placed input segments with random thickness between 2 and 5 pixels.
+At first, the performance of both versions of the detector (with and without
+the concepts) is tested on a set of 1000 synthesized images containing 10
+randomly placed input segments with random thickness between 2 and 5 pixels.
%Such controlled images can be considered as ground truths.
The initial assigned thickness $\varepsilon_0$ was set to 7 pixels
to detect all the lines in unsupervised mode.
@@ -105,31 +104,26 @@ $D$ the set of all the detected blurred segments.}
\label{tab:synth}
\end{table}
-Next experiments aim at comparing the achieved performance of the new
-detector with those of other line detectors : LSD \cite{GioiAl10},
-ED-Lines \cite{AkinlarTopal12} and CannyLines \cite{LuAl15}.
-The tests are run on the York Urban database \cite{DenisAl08} composed
+Next experiments aim at comparing the new approach with recent line detectors.
+Tests are run on the York Urban database \cite{DenisAl08} composed
of 102 images with their ground truth lines.
-As this database was set in the scope of Manhattan-world environments,
+As it was set in the scope of Manhattan-world environments,
only lines in the three main directions are provided.
-Initial assigned thickness $\varepsilon_0$ is set to 3 pixels, and
-final length threshold to 10 points to suit the stroke sweeping step
-value.
-Results on one image are displayed in \RefFig{fig:york}.
-
-Compared measures $M$ are execution time $T$, covering ratio $C$,
+For these experiments, initial assigned thickness $\varepsilon_0$ is set
+to 3 pixels, and final length threshold to 10 points to suit the stroke
+sweeping step value.
+Output lines smaller than 10 pixels are discarded for all the detectors.
+Compared measures are execution time $T$, covering ratio $C$,
detected lines amount $N$, cumulated length of detected lines $L$ and
mean length ratio $L/N$.
-On each image of the database we measure the execution time of 100 repetitions
-of a complete detection, gradient extraction included, for each line detector;
-$T$ is the mean value computed on the whole image set.
-Tests are run on Intel Core i5 processor.
-Assuming that a pixel of a ground truth line is identified
-if there is a detected line in its 8-neighborhood, then the measure $C$ is
+On each image of the database and for each line detector, the execution time
+of 100 repetitions of a complete detection, gradient extraction included, was
+measured using Intel Core i5 processor; $T$ is the mean value found per image.
+Then, assuming that a pixel of a ground truth line is identified
+if there is a detected line in its 8-neighborhood, measure $C$ is
the mean ratio of the length of ground truth line pixels identified on the
total amount of ground truth line pixels.
-Detected lines smaller than 10 pixels are discarded for all the detectors.
-Found measures are given in \RefTab{tab:comp}.
+Results are given in \RefTab{tab:comp}.
\begin{figure}[h]
\center
@@ -158,7 +152,7 @@ Found measures are given in \RefTab{tab:comp}.
\caption{Comparison of line detectors on one of the 102 ground truth
images of the York Urban database : a) input image, % P1020928
b) ground truth lines, c) LSD output, d) ED-Lines output,
- e) CannyLines output, f) thick lines of the new detector.}
+ e) CannyLines output, f) thick lines of the new detector. }
\label{fig:york}
\end{figure}
@@ -167,12 +161,18 @@ Found measures are given in \RefTab{tab:comp}.
\input{Expe_auto/compTable}
\caption{Measured performance of recent line detectors and of our detector
-on the York Urban Database \cite{DenisAl08}.}
+on the York Urban Database \cite{DenisAl08}. }
\label{tab:comp}
\end{table}
-On these images, CannyLines provides longer lines and ED-Lines is much faster.
-Globally, the performance of the new detector is pretty similar and
-competitive to the other ones, and
-furthermore, our detector provides an indication
+Results displayed on the example of \RefFig{fig:york} indicate that
+the new detector produces many small segments, that could be considered as
+visually non-meaningful. The other detectors eliminates them by a
+validation test based on Helmholtz principle \cite{DesolneuxAl08}.
+Such test is not yet integrated into the new detector.
+But even so, the mean length of output lines is greater.
+Except for execution time for ED-Lines performs best,
+global performance of the new detector is pretty similar and
+competitive to the other ones.
+Furthermore, it provides additional information
on the detected line quality through the estimated thickness.
diff --git a/Article/methodV2.tex b/Article/methodV2.tex
index e82c7a41577701690995b97b646f8bc0d5113a59..58c621796303136354c48f85e71cdb16d1947303 100755
--- a/Article/methodV2.tex
+++ b/Article/methodV2.tex
@@ -263,7 +263,7 @@ An option, called {\it multi-detection} (Algorithm 1), allows the
detection of all the segments crossed by the input stroke $AB$.
In order to avoid multiple detections of the same edge, an occupancy mask,
initially empty, collects the dilated points of all the blurred segments,
-so that these points can not be added to another segment.
+so that these points can not be used any more.
\input{Fig_method/algoMulti}
First the positions $M_j$ of the prominent local maxima of the gradient