Article: remarks PN updated

Article/Expe_perf/perf_iut_scc2.txt

+100
+768
+512
+6.24317
+2752
+903
+160
+25.5535
+2.25717
+2.21315
+7.27919
+2667
+850
+168
+27.4307
+2.56642
+2.51868

Article/Expe_perf/perf_iut_scc3.txt

+100
+768
+512
+4.41504
+1852
+692
+122
+24.3828
+2.10468
+2.10685
+5.22814
+1822
+652
+133
+25.929
+2.50248
+2.4839

Article/Expe_perf/perf_loria_indoor1.txt

+100
+768
+512
+5.86233
+2790
+921
+110
+20.7075
+2.26903
+2.14334
+6.88069
+2673
+909
+110
+21.8659
+2.52832
+2.39787

Article/Expe_perf/perf_loria_indoor2.txt

+100
+768
+512
+4.91989
+2184
+779
+123
+22.4072
+2.13355
+2.09208
+5.75351
+2077
+716
+127
+24.7289
+2.48592
+2.39442

Article/Expe_perf/perf_loria_indoor3.txt

+100
+768
+512
+5.01374
+1625
+649
+195
+40.2443
+1.9953
+1.93206
+6.06808
+1659
+561
+178
+45.238
+2.40001
+2.38361

Article/Expe_perf/perf_loria_office1.txt

+100
+768
+512
+5.88139
+2690
+914
+137
+22.5576
+2.12867
+1.95291
+6.94068
+2660
+891
+139
+23.289
+2.41498
+2.22931

Article/Expe_perf/perf_loria_outdoor1.txt

+100
+768
+512
+5.80022
+2678
+839
+87
+20.24
+2.43775
+2.57967
+6.60938
+2584
+825
+104
+21.8391
+2.66773
+2.72427

Article/Expe_perf/perf_vosges_castle1.txt

+100
+768
+512
+5.80337
+3169
+865
+75
+15.3847
+2.21368
+2.12883
+6.33414
+3009
+919
+80
+15.4394
+2.51226
+2.43735

Article/Expe_perf/perf_vosges_castle2.txt

+100
+768
+512
+2.85011
+1404
+415
+55
+22.5612
+2.25116
+2.39249
+3.21413
+1363
+403
+61
+23.2159
+2.45696
+2.50577

Article/Expe_perf/perf_vosges_corridor1.txt

+100
+512
+341
+1.14078
+342
+160
+50
+37.3961
+2.00629
+2.01085
+1.3908
+343
+142
+47
+41.1792
+2.36076
+2.33786

Article/Expe_perf/perf_vosges_detail1.txt

+100
+735
+570
+12.9189
+7209
+2108
+50
+11.4931
+2.84108
+3.21585
+14.1981
+6802
+2101
+56
+12.2208
+3.00296
+3.21142

Article/Expe_perf/perf_vosges_detail2.txt

+100
+458
+325
+3.12422
+1653
+478
+49
+16.9293
+2.66354
+2.70177
+3.56203
+1623
+496
+41
+16.3789
+2.85431
+2.73118

Article/Expe_perf/perf_vosges_detail3.txt

+100
+314
+508
+3.16186
+1637
+453
+64
+23.1678
+2.60882
+2.83866
+3.65571
+1619
+464
+71
+22.5974
+2.8246
+2.94086

Article/conclusion.tex

@@ -4,8 +4,8 @@
 
 This paper introduced a new straight edge detector based on a local analysis of
 the image gradient and on the use of blurred segments to embed an
-estimation of the edge thickness.
-It relies on directional scans of the image around maximal values of the
+estimation of the detected edge thickness.
+It relies on directional scans of the input image around maximal values of the
 gradient magnitude, that have previously been presented in
 \cite{KerautretEven09}.
 %Despite of good performances achieved, the former approach suffers of two

Article/expe.tex

@@ -6,7 +6,7 @@ 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
-detector in unsupervised context.
+one in unsupervised context.
 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

Article/intro.tex

@@ -36,7 +36,7 @@ In a former paper \cite{KerautretEven09}, an efficient tool to detect
 blurred segments of fixed width in gray-level images was already introduced.
 It is based on a first rough detection in a local image area
 defined by the user. The goal is to disclose the presence of a straight edge.
-Therefore an as simple test as the gradient maximal value is performed.
+Therefore as simple a test as the gradient maximal value is performed.
 In case of success, refinement steps are run through an exploration of
 the image in the direction of the detected edge.
 In order to prevent local disturbances such as the presence of a sharper
@@ -56,7 +56,7 @@ on the edge quality is rather poor, and especially when the edge is thin,
 the risk to incorporate outlier points is quite high, thus producing a
 biased estimation of the edge orientation.
 Then, two refinement steps are systematically run.
-On one hand, this is useless when the first detection is successfull.
+On the one hand, this is useless when the first detection is successfull.
 On the other hand, there is no guarantee that this approach is able to
 process larger images.
 The search direction relies on the support vector of the blurred segment
@@ -78,8 +78,7 @@ improvement of the time performance of the detector.
 They are also put forward within a global line extraction algorithm
 which can be evaluated through an online demonstration.
 
-In the next section, the main theoretical notions this work relies on are
-introduced.
+In the next section, the main theoretical notions are introduced.
 The new detector workflow, the adaptive directional scan, the control
 of the assigned with and their integration into both supervised and
 unsupervised contexts are then presented in \RefSec{sec:method}.

Article/method.tex

@@ -224,7 +224,7 @@ $\vec{AB}_\perp$ to the stroke as input to build a static scan of fixed width
 $2~\varepsilon_{ini}$, and $M_j$ is used as start point of the blurred
 segment;
 \item the occupancy mask is filled in with the points of the dilated blurred
-segments $\mathcal{B}_j''$ at the end of each successful detection
+segments $\mathcal{B}_j'$ at the end of each successful detection
 (a 21 pixels neighborhood is used);
 \item points marked as occupied are rejected when selecting candidates for the
 blurred segment extension in the fine tracking step.
@@ -239,14 +239,14 @@ in opposite edge selection mode.
 An unsupervised mode is also proposed to automatically detect all the
 straight edges in the image. The principle of this automatic detection
 is described in Algorithm 2. A stroke that crosses the whole image, is
-swept in both direction, vertical then horizontal, from the center to
+swept in both directions, vertical then horizontal, from the center to
 the borders. At each position, the multi-detection algorithm is run
 to collect all the segments found under the stroke.
 In the present work, the stroke sweeping step $\delta$ is set to 10 pixels.
 
-
-The automatic detection of blurred segments in a whole image is left available
-for testing from an online demonstration and  \textit{GitHub} source code at this address: \\
+The automatic detection of blurred segments in a whole image is available
+for testing from an online demonstration
+and \textit{GitHub} source code at this address: \\
 \href{http://ipol-geometry.loria.fr/~kerautre/ipol_demo/AdaptDirBS_IPOLDemo}{
 \small{\url{http://ipol-geometry.loria.fr/~kerautre/ipol_demo/AdaptDirBS_IPOLDemo}}}
 

Article/notions.tex

@@ -9,7 +9,8 @@ defined in the digital geometry literature \cite{KletteRosenfeld04}.
 Only the 2D case is considered here.
 
 \begin{definition}
-A digital line $\mathcal{L}(a,b,c,\nu)$, with $(a,b,c,\nu) \in \mathbb{Z}^4$,
+A \textbf{digital straight line} $\mathcal{L}(a,b,c,\nu)$,
+with $(a,b,c,\nu) \in \mathbb{Z}^4$,
 is the set of points $P(x,y)$ of $\mathbb{Z}^2$ that satisfy :
 $0 \leq ax + by - c < \nu$.
 \end{definition}
@@ -19,12 +20,12 @@ digital line $\mathcal{L}$, $w(\mathcal{L}) = \nu$ its arithmetical width,
 $h(\mathcal{L}) = c$ its shift to origin, and $p(\mathcal{L}) = max(|a|,|b|)$
 its period (i.e. the length of its periodic pattern).
 When $\nu = p(\mathcal{L})$, then $\mathcal{L}$ is the narrowest 8-connected
-line and is called a naive line.
+line and is called a {\it naive line}.
 
 \begin{definition}
-A blurred segment $\mathcal{B}$ of assigned width $\varepsilon$ is a set
-of points in $\mathbb{Z}^2$ that all belong to a digital line $\mathcal{L}$
-of arithmetical width $w(\mathcal{L}) = \varepsilon$.
+A \textbf{blurred segment} $\mathcal{B}$ of assigned width $\varepsilon$ is
+a set of points in $\mathbb{Z}^2$ that all belong to a digital straight line
+$\mathcal{L}$ of arithmetical width $w(\mathcal{L}) = \varepsilon$.
 \end{definition}
 
 A linear-time algorithm to recognize a blurred segment of assigned width
@@ -55,7 +56,7 @@ and $\mathcal{B}_i = \mathcal{B}_{i-1}$.}
 \end{figure}
 
 Associated to this primitive, the following definition of a directional scan
-also based on digital straight lines is also used in this work.
+also based on digital straight lines is used in this work.
 
 \subsection{Directional scan}