Article: typos and style correction

Article/conclusion.tex

@@ -2,7 +2,7 @@
 
 \label{sec:conclusion}
 
-In this paper we introduced a new edge detector based on a local analysis of
+This paper introduced a new edge detector based on a local analysis of
 the image gradient and on the use of blurred segments to vehiculate an
 estimation of the edge thickness.
 It relies on directional scans of the image around maximal values of the
@@ -15,10 +15,10 @@ is biased.
 Then the scan direction is derived from a bounded blurred segment, that
 inevitably restricts its value to a finite set, so that long edges may be
 not completely detected.
-We solved these limitations through two new concepts:
-first the adaptive directional scans continuously that adjust the scan strip
+These limitations were solved through the integration of two new concepts:
+adaptive directional scans that continuously adjust the scan strip
 to the detected blurred segment direction;
-then the control of the assigned width based on the observation of the
+the control of the assigned width based on the observation of the
 blurred segment thickenning in the early stage of its expansion.
 
 Expected gains in execution time linked to the suppression of a useless

Article/intro.tex

@@ -23,16 +23,16 @@ from the real world by the mean of a width parameter.
 Efficient algorithms were designed to recognize these digital objects in
 binary images.
 
-Our work aims at designing a flexible tool to detect blurred segments
+The present work aims at designing a flexible tool to detect blurred segments
 with optimal width and orientation in gray-level images for as well
 supervised as unsupervised contexts.
-We seek for user-friendly solutions with ideally no parameter to set,
+User-friendly solutions are sought, with ideally no parameter to set,
 or at least quite few values with intuitive meaning to an end user.
 
 \subsection{Previous work}
 
-In a former paper \cite{KerautretEven09}, we already introduced an efficient
-tool to detect blurred segments of fixed width in gray-level images. 
+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 area
 of the image either defined by the user in supervised context or blindly
 explored in automatic mode. The goal is to disclose the presence of an edge.
@@ -46,7 +46,7 @@ untill a correct candidate with an acceptable gradient orientation is found.
 
 Only the gradient information is processed as it provides a good information
 on the image dynamics, and hence the presence of edges.
-Trials to also use the intensity signal were made though costly correlation
+Trials to also use the intensity signal were made through costly correlation
 techniques, but they were mostly successful for detecting objects with
 stable appearance such as metallic pipes \cite{AubryAl17}.
 
@@ -56,16 +56,18 @@ First, the blurred segment width is not measured, but initially set by the
 user to meet the application requirements, so that no quality information
 can be derived from the computed segment.
 Moreover, the blurred segment hull is left free to shift sidewards, or worst,
-to rotate around a thin edge in the image, so that the produced orientation
+to rotate around a thin edge in the image, and the produced orientation
 value can be largely biased.
 
 Then, two refinement steps are systematically run to cope with most of the
 tested data, although this is useless when the first detection is successfull.
 Beyond, there is no guarantee that this could treat all kinds of data.
-The search direction is fixed by the detected direction at the former step,
-and there is necessarily a limit on this direction accuracy - at least
-linked to the restricted directions encoded in a limited grid - so that
-other steps would have been necessary to deal with high resolution images.
+The search direction is fixed by the support vector of the blurred segment
+detected at the former step, and because the set of vectors in a bounded
+discrete space is finite, there is necessarily a limit on this direction
+accuracy.
+It results that more steps would be necessary to process higher resolution
+images.
 
 \subsection{Main contritions}
 
@@ -76,8 +78,8 @@ to the unpredictable orientation problem;
 the control of the assigned width to the blurred segment recognition algorithm,
 intended to derive more reliable information on the edge orientation and
 quality.
-As a side effect, this two major evolutions led to a noticeable improvement
-of the execution time.
+As a side effect, these two major evolutions also led to a noticeable
+improvement of the time performance of the detector.
 
 In the next section, the main theoretical notions this work relies on are
 introduced, with a specific focus on the new concept of adaptive directional