Article structure

Article/Makefile

+all:
+	@echo "ps pdf release"
+	make release
+
+ps:
+	pdflatex main
+
+
+pdf:
+	pdflatex main 
+	bibtex main
+	pdflatex main
+	pdflatex main
+
+
+
+release:
+	pdflatex main
+	bibtex main
+	pdflatex main
+	pdflatex main
+
+
+clean:
+	rm -f main.pdf main.ps main.dvi main.log main.bbl main.blg main.aux *~

Article/abstract.tex

+\begin{abstract}
+  Penser \`a prendre du beurre sal\'e \`a la biocoop.
+\end{abstract}

Article/biblio.bib

+@inproceedings{KerautretEven09,
+  title = {Blurred segments in gray level images for
+           interactive line extraction},
+  volume = {5852},
+  booktitle = {Proceedings of the 13th {IWCIA}},
+  publisher = {Springer},
+  author = {Kerautret, Bertrand and Even, Philippe},
+  editor = {Wiederhold, P. and Barneva, R. P.},
+  month = nov,
+  year = {2009},
+  series = {{LNCS}},
+  pages = {176--186}
+}
+
+
+
+@inproceedings{Debled05,
+  title = {Blurred Segments Decomposition in Linear Time},
+  author = {Debled-Rennesson, Isabelle and Feschet, Fabien and
+            Rouyer-Degli, Jocelyne},
+  booktitle = {Proc. of Int. Conf. on DGCI},
+  year = {2005},
+  editor = {Andres, E. and Damiand, G. and Lienhardt, P.},
+  volume = {3429},
+  series = {LNCS},
+  pages = {371-382},
+  optaddress = {Poitiers, France},
+  month = {April},
+  publisher = {Springer}
+}
+
+
+
+@article{Buzer07,
+  title = "A simple algorithm for digital line recognition
+           in the general case",
+  author = "Buzer, Lilian",
+  journal = "Pattern Recognition",
+  volume = "40",
+  number = "6",
+  pages = "1675--1684",
+  year = "2007",
+  doi = "DOI: 10.1016/j.patcog.2006.10.005"
+}
+
+
+
+@article{EvenMalavaud00,
+  author = {Even, Philippe and Malavaud, Anne},
+  title = {Semi-automated edge segment specification for an interactive
+           modelling system of robot environments},
+  journal = {International Archives of Photogrammetry and Remote Sensing},
+  year = {2000},
+  number = {B5},
+  pages = {222-229},
+  volume = {33}
+}
+
+
+
+@article{AubryAl17,
+  author = {Aubry, Nicolas and Kerautret, Bertrand and Even, Philippe
+            and Debled-Rennesson, Isabelle},
+  title = {Photometric intensity profiles analysis for thick segment
+           recognition and geometric measures},
+  journal = {Mathematical Morphology: Theory and Applications},
+  year = {2017},
+  number = {2},
+  pages = {35-54}
+}
+
+
+@article{Melkman87,
+  author="Melkman, Avraham A.",
+  title="On-line construction of the convex hull of a simple polyline.",
+  journal="Information Processing Letters",
+  volume="25",
+  number="1",
+  year="1987",
+  month="April",
+  pages="11--12"
+}

Article/conclusion.tex

+\section{Conclusion and perspectives}
+
+Gains importants en efficacit\'e.
+
+Tentative d'estimation de la largeur du segment, qui fiabilise
+l'estimation de l'orientation (plus de segments en travers).
+
+Scans directionnels adaptatifs : une solution au probl\`eme de
+la non pr\'edictibilit\'e de l'orientation.
+
+D\'efauts persistants :
+\begin{itemize}
+\item L'\'epaisseur trouv\'ee n'est pas certifi\'ee.
+\item Le r\'esultat d\'epend des conditions initiales.
+Ca reste une m\'ethode instable, m\^eme si la duplication de la premi\`ere
+\'etape a permis de gagner en stabilit\'e.
+\item On n'est pas \`a l'abri d'un contour voisin qui vient perturber
+la d\'etection initiale ou l'affinement.
+Les filtres en fin de tracking sont l\`a pour soigner, pas pour gu\'erir.
+\end{itemize}
+
+Perspectives : validation sur contextes applicatifs.
+
+\section*{Acknowledgements}
+This work was supported by La Cabane au Darou.

Article/expe.tex

+\section{Experiments}
+
+Mettre en valeur les gains obtenus par rapport \`a la version pr\'ec\'edente
+avec des comparatifs en temps d'ex\'ecution et en qualit\'e de d\'etection
+avec notamment une meilleure estimation de l'orientation.
+
+D\'efauts persistants :
+\begin{itemize}
+\item L'\'epaisseur trouv\'ee n'est pas certifi\'ee.
+\item Le r\'esultat d\'epend des conditions initiales.
+Ca reste une m\'ethode instable, m\^eme si la duplication de la premi\`ere
+\'etape a permis de gagner en stabilit\'e.
+\item On n'est pas \`a l'abri d'un contour voisin qui vient perturber
+la d\'etection initiale ou l'affinement.
+Les filtres en fin de tracking sont l\`a pour soigner, pas pour gu\'erir.
+\end{itemize}

Article/intro.tex

+\section{Introduction}
+
+\subsection{Motivations}
+
+Straight edge detection is a preliminary step of many image analysis
+processes. Therefore it is always an active reasearch topic centered
+on the quest of still faster, more accurate or more robust-to-noise
+methods.
+
+{\it TOWRITE : petit \'etat de l'art en r\'esumant IWCIA'09 et en ajoutant
+quelques id\'ees perso (Hough, local, ...).
+Parameter-space-based methods : robust to noise, well suited to
+supervided context \cite{EvenMalavaud00}.
+Most of works aim at reducing their time complexity. }
+
+These methods rarely provide a direct measure of the quality of the output
+edge, such as sharpness, connectivity or scattering. Some information may
+often be drawn from their specific context, for example through
+an analysis of the peak in a Hough transform accumulator, or ...
+
+In digital geometry, the notion of blurred segment \cite{Debled05,Buzer07}
+was introduced to cope with the image noise or other sources of
+imperfections from the real world.
+
+Our work aims at designing a flexible tool to detect such blurred segment
+in gray-level images for as well supervised as unsupervised contexts.
+We seek for user-friendly solutions with ideally no parameter to set,
+or at least quite few values with intuitive meaning to an end user.
+
+\subsection{Method overview and previous work}
+
+The method we propose 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.
+Therefore, a simple 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, for instance the intersection with
+a sharper edge, all the local gradient maxima are successively tested,
+and the gradient orientation consistency is checked.
+
+We already designed and experimented an exploratory detector
+\cite{KerautretEven09}.
+
+Despite of good performances obtained compared
+to other methods from the literature, several drawbacks remained.
+At first, a fixed width value was set by the user according to the
+application requirements, and detected segments were embedded in that
+fixed tolerence whatever their dispersion be. When this dispersion is low,
+the blurred segment is free to shiff sidewards, or worst, to rotate, thus
+degrading the provided position and rotation measures.
+
+Then two refinement steps were arbitrarily run to cope with most of
+the tested data, uselessly when the first one was successfull.
+Beyond, there was 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.
+
+Our study relies only on the use of the image gradient, as it provides a
+good information on the signal dynamics, and hence the presence of edges.
+Trials were made to use also the intensity signal though expensive
+correlation techniques, but it was mostly successful for tracking objects
+with stable appearance such as metallic pipes \cite{AubryAl17}.
+
+Organisation of the paper : TO WRITE.

Article/macros.tex

+\newcommand{\RefFigure}[1]{Fig.\,\ref{#1}}
+\newcommand{\RefSection}[1]{Section\,\ref{#1}}
+\newcommand{\RefTab}[1]{Tab.\,\ref{#1}}

Article/main.tex

+\documentclass[runningheads]{llncs}
+
+%\usepackage[utf8]{inputenc}
+%\usepackage[T1]{fontenc}
+
+\usepackage{graphicx}
+\graphicspath{{./images/}{./images/introduction}}
+
+\usepackage[ruled,vlined]{algorithm2e}
+
+\usepackage{amsmath}
+\usepackage{amssymb}
+
+\input{macros}
+
+\begin{document}	
+  \begin{frontmatter}
+    \title{Straight edge detection
+           based on an adaptive directional tracking of blurred segments}
+
+    \author{Philippe Even\inst{1} \and
+            Phuc Ngo\inst{1} \and
+            Bertrand Kerautret\inst{2}}
+
+    \authorrunning{P. Even et al.}
+
+    \institute{Universit\'e de Lorraine, LORIA, UMR 7503, Nancy, France
+               \email{philippe.even,hoai-diem-phuc.ngo\{at\}loria.fr}
+               \and Universit\'e de Lyon 2, LIRIS, Lyon, France
+               \email{bertrand.kerautret\{at\}univ-lyon2.fr}}
+
+    \maketitle
+
+    \begin{abstract}
+TOWRITE.
+    
+    \keywords{Line detection \and discrete geometry \and TOCOMPLETE.}
+    \end{abstract}
+
+  \end{frontmatter}
+	
+	\input{intro}
+	
+	\input{notions}
+	
+	\input{method}
+	
+	\input{expe}
+	
+	\input{conclusion}
+  
+  %\section*{References}
+    \bibliographystyle{splncs04}
+    \bibliography{biblio}
+    
+\end{document}

Article/method.tex

+\section{The detection method}
+
+\subsection{Workflow of the detection process}
+
+The blurred segment detector workflow is summerized
+in the following figure.
+
+\begin{center}
+\begin{picture}(340,34)(0,-4)
+%\put(0,-2.5){\framebox(340,35)}
+\put(-2,18){\scriptsize $(A,B)$}
+\put(-2,15){\vector(1,0){24}}
+\put(24,0){\framebox(56,30)}
+\put(24,15){\makebox(56,10){Initial}}
+\put(24,3){\makebox(56,10){detection}}
+\put(86,18){\scriptsize $S_{i}$}
+\put(80,15){\vector(1,0){22}}
+%\put(102,0){\framebox(56,30)}
+\multiput(102,15)(28,9){2}{\line(3,-1){28}}
+\multiput(102,15)(28,-9){2}{\line(3,1){28}}
+\put(100,0){\makebox(60,30){Valid ?}}
+\put(133,-2){\scriptsize $0$}
+\put(130,6){\vector(0,-1){10}}
+\put(159,18){\scriptsize $(C,\vec{D})$}
+\put(158,15){\vector(1,0){28}}
+\put(186,0){\framebox(56,30)}
+\put(186,15){\makebox(56,10){Fine}}
+\put(186,3){\makebox(60,10){tracking}}
+\put(250,18){\scriptsize $S_{f}$}
+\put(242,15){\vector(1,0){24}}
+\put(266,0){\framebox(56,30){Filtering}}
+\put(330,18){\scriptsize $S_{o}$}
+\put(322,15){\vector(1,0){22}}
+\end{picture}
+\end{center}
+
+The fast track stage consists in building and extending a blurred segment
+$S_i$ based on the highest gradient points on each line of the directional
+scanner based on an input segment $AB$.
+
+Validity tests based on the length or sparsity of $S_i$ are applied to
+decide of the detection poursuit. In case of positive response, the
+position and direction of this initial blurred segment is extracted.
+
+The fine track stage consists on building and extending a blurred segment
+$S_f$ based on points that correspond to local maxima of the gradient,
+ranked by magnitude order, and with gradient direction close to a reference
+gradient direction at the segment first point.
+During that step a thinning procedure is run :
+the assigned width of the BS is progressively brought to
+the detected BS minimal width.
+
+The fine track output segment is finally filtered to remove artifacts
+and outliers, and a solution blurred segment $S_o$ is provided.
+
+\subsection{Implementation details}
+
+A directional scanner is encoded as an iterator that provides successively
+all the scan lines.
+
+Description de l'interface pour la d\'etection supervis\'ee d'un segment.
+
+Description de la d\'etection multiple.
+
+Description de la d\'etection automatique.

Article/notions.tex

+\section{Base notions}
+
+\subsection{Blurred segment}
+
+Our work relies on the notion of digital straight line
+as classically defined in the digital geometry literature \cite{debled}.
+Only the 2-dimensional case is considered here.
+
+\begin{definition}
+A digital line $\cal D$ with integer parameters $(a,b,c,\nu)$ is the set
+of points $P(x,y)$ of $\mathbb{Z}^2$ that satisfy : $0 \leq ax + by - c < \nu$.
+\end{definition}
+
+The parameter $\nu$ is the width of the digital line.
+If $\nu = max (|a|, |b|)$, $\cal D$ is the narrowest 8-connected line
+and is called a naive line.
+
+\begin{definition}
+A blurred segment of width $\nu$ is a set ${\cal S}_\nu$ of points in
+$\mathbb{Z}^2$ that all belong to a digital line of width $\nu$.
+\end{definition}
+
+\begin{picture}(300,20)
+\framebox(300,20){Exemple de segment flou ? (\c ca va finir par lasser)}
+\end{picture}
+
+To construct a blurred segment we use a liner time algorithm based on the
+incremental growth of the convex hull of the input points using Melkman
+algorithm \cite{Melkman87}. Points are added while the convex hull width
+is less than the blurred segment assigned width.
+
+\subsection{Directional scan}
+
+A directional scan is a partition of a digital straight line ${\cal S}$,
+called the {\it scan strip}, into naive straight line segments ${\cal L}_i$,
+that are orthogonal to ${\cal S}$. The segments, called {\it scan lines}, are
+developed on each side of a central scan line ${\cal S}_0$, and labelled
+with their manhattan distance ($d_1 = |d_x| + |d_y|$) to ${\cal L}_0$ and
+a positive (resp.  negative) sign if their are on the left (resp. right)
+of ${\cal L}_0$.
+
+\begin{picture}(300,20)
+\framebox(300,20){Exemple de directional scan}
+\end{picture}
+
+The directional scan can be defined by its central scan line ${\cal L}_0$.
+If $A(x_A,y_A)$ and $B(x_B,y_B)$ are the end points of this scan line,
+the scan strip is defined by :
+
+\centerline{
+${\cal S}(A,B) = {\cal D}(a, b, c, \nu)$, with
+$\left\{ \begin{array}{l}
+a = x_B - x_A \\
+b = y_B - y_A \\
+\nu = 1 + |c_2 - c_1| \\
+c = min (c_1, c_2)
+\end{array} \right.$
+}
+\noindent
+where $c_1 = a\cdot x_A + b\cdot y_A$ and $c_2 = a\cdot x_B + b\cdot y_B$.
+
+The scan line $\cal{L}_i(A,B)$ is then defined by :
+
+\centerline{
+${\cal L}_i(A,B) = {\cal S}(A,B) \cap {\cal D}(a, b, c, \nu)$, with
+$\left\{ \begin{array}{l}
+a = y_B - y_A \\
+b = x_A - x_B \\
+\nu = max (|a|,|b|) \\
+c = a\cdot x_A + b\cdot y_A + i \cdot \nu
+\end{array} \right.$
+}
+
+The scan lines length is $d_\infty(AB)$ or $d_\infty(AB)-1$, where $d_\infty$
+is the chessboard distance ($d_\infty = max (|d_x|,|d_y|)$).
+In practice, this difference of length between scan lines is not a drawback,
+as the image bounds should also be processed anyway.
+
+The directional scan can also be defined by its central point $C$, its
+direction $\vec{D}$ and its width $w$. TO BE DEVELOPED.
+
+\subsection{Adaptive directional scan}
+
+Notions \`a d\'evelopper :
+\begin{itemize}
+\item Direction de scan
+\item Epaisseur de consigne du SF
+\item Largeur optimale du SF
+\end{itemize}
+
+Poser le pb : la direction est incompl\`etement estim\'ee, d'o\`u un risque
+de sortie de scan.
+\begin{picture}(300,20)
+\framebox(300,20){Illustration d'une sortie de scan avec les diff\'erentes
+\'epaisseurs en jeu}
+\end{picture}
+
+La direction du segment ne peut \^etre connue qu'a posteriori.
+
+La direction d'une droite discr\`ete s'affine au fur et \`a mesure de
+son d\'eveloppement. 
+Ainsi en va t-il des segments flous (a fortiori).
+
+Il faut donc r\'eactualiser la direction du scan.
+
+$N$ scans reste limit\'e.
+
+D'o\`u le scan adaptatif $\rightarrow$ r\'eorientation de $\cal S$.