From 0decc4301591c556560c8b581e53496455668d94 Mon Sep 17 00:00:00 2001
From: even <philippe.even@loria.fr>
Date: Mon, 24 Dec 2018 19:15:17 +0100
Subject: [PATCH] Article: rmk BK integrated
---
Article/Fig_method/workflow.tex | 26 ++++++++++
Article/Fig_method/workflowBK.tex | 27 +++++++++++
Article/Fig_notions/bswidth.tex | 11 +++--
Article/abstract.tex | 12 +++--
Article/biblio.bib | 19 ++++++--
Article/intro.tex | 22 +++++----
Article/main.tex | 13 ++++-
Article/method.tex | 80 +++++++++++++------------------
Article/notions.tex | 15 +++---
9 files changed, 145 insertions(+), 80 deletions(-)
create mode 100755 Article/Fig_method/workflow.tex
create mode 100755 Article/Fig_method/workflowBK.tex
diff --git a/Article/Fig_method/workflow.tex b/Article/Fig_method/workflow.tex
new file mode 100755
index 0000000..77d18c8
--- /dev/null
+++ b/Article/Fig_method/workflow.tex
@@ -0,0 +1,26 @@
+ \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(24,16){\makebox(56,10){Initial}}
+ \put(24,4){\makebox(56,10){detection}}
+ \put(86,18){\scriptsize $\mathcal{B}$}
+ \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 $\emptyset$}
+ \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(186,16){\makebox(56,10){Fine}}
+ \put(186,4){\makebox(60,10){tracking}}
+ \put(250,18){\scriptsize $\mathcal{B}'$}
+ \put(242,15){\vector(1,0){24}}
+ \put(266,0){\framebox(56,30){Filtering}}
+ \put(330,18){\scriptsize $\mathcal{B}''$}
+ \put(322,15){\vector(1,0){22}}
+ \end{picture}
diff --git a/Article/Fig_method/workflowBK.tex b/Article/Fig_method/workflowBK.tex
new file mode 100755
index 0000000..f2844f3
--- /dev/null
+++ b/Article/Fig_method/workflowBK.tex
@@ -0,0 +1,27 @@
+ \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(24,16){\makebox(56,10){Initial}}
+ \put(24,4){\makebox(56,10){detection}}
+ \put(86,18){\scriptsize $\mathcal{B}$}
+ \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 $\emptyset$}
+ \put(130,6){\vector(0,-1){10}}
+ \put(159,18){\scriptsize $(C,\vec{D})$}
+ \put(158,15){\vector(1,0){26}}
+ \put(184,0){\framebox(62,30)}
+ \put(186,18){\makebox(56,10){Fine}}
+ \put(186,8){\makebox(60,10){tracking }}
+ \put(186,0){\makebox(60,10){\scriptsize{\color{gray}{(adapt. dir. scan)}}}}
+ \put(250,18){\scriptsize $\mathcal{B}'$}
+ \put(246,15){\vector(1,0){20}}
+ \put(266,0){\framebox(56,30){Filtering}}
+ \put(330,18){\scriptsize $\mathcal{B}''$}
+ \put(322,15){\vector(1,0){22}}
+ \end{picture}
diff --git a/Article/Fig_notions/bswidth.tex b/Article/Fig_notions/bswidth.tex
index ba010fe..5393c1f 100644
--- a/Article/Fig_notions/bswidth.tex
+++ b/Article/Fig_notions/bswidth.tex
@@ -1,7 +1,7 @@
\begin{picture}(220,60)
\multiput(0,6)(2,-6){2}{\line(3,1){150}}
- \multiput(0,8)(30,6){8}{\line(5,1){10}}
- \multiput(0,18)(30,6){8}{\line(5,1){10}}
+ \multiput(0,8)(30,6){8}{\color{red}{\line(5,1){10}}}
+ \multiput(0,18)(30,6){8}{\color{red}{\line(5,1){10}}}
\put(45,21){\circle*{3}}
\put(55,21){\circle*{3}}
\put(65,21){\circle*{3}}
@@ -15,7 +15,8 @@
\put(140,36){\vector(0,1){10}}
\put(140,62.66){\vector(0,-1){10}}
\put(120,58){$\mu_{i-1}$}
- \put(160,30){\vector(0,1){10}}
- \put(160,60){\vector(0,-1){10}}
- \put(164,36){$\mu_i$}
+ \put(160,30){\color{red}{\vector(0,1){10}}}
+ \put(160,60){\color{red}{\vector(0,-1){10}}}
+ \put(164,36){\color{red}{$\mu_i$}}
+ \put(180,60){\color{red}{$\mathcal{B}_{i}$}}
\end{picture}
diff --git a/Article/abstract.tex b/Article/abstract.tex
index e495d65..3b0b065 100755
--- a/Article/abstract.tex
+++ b/Article/abstract.tex
@@ -1,6 +1,8 @@
This paper introduces a new straight edge detector in gray-level images
-based on blurred segments, digital objects able to imbed quality measurements
-on the extracted features. This study completes previous works with a better
-estimation of the blurred segment width and orientation, with two main
-improvements: adaptive directional scans and the control of the
-assigned width to the detection algorithm.
+based on blurred segments, digital objects able to embed quality measurements
+on the extracted features. This study enhances previous works on interactive
+line detection with a better estimation of the blurred 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.
diff --git a/Article/biblio.bib b/Article/biblio.bib
index 8af3773..62f91c0 100755
--- a/Article/biblio.bib
+++ b/Article/biblio.bib
@@ -1,3 +1,11 @@
+@article{DebledAl06,
+ title = {Optimal Blurred Segments Decomposition of Noisy Shapes
+ in Linear Times},
+ journal = {Computers and Graphics},
+ author = {Debled-Rennesson, I. and Feschet, F. and Rouyer-Degli, J.},
+ year = {2006}
+}
+
@book{KletteRosenfeld04,
title = {Digital geometry -- Geometric methods for digital picture analysis},
author = {Klette, Reinhard and Rosenfeld, Azriel},
@@ -18,7 +26,8 @@
editor = {Wiederhold, P. and Barneva, R. P.},
optmonth = nov,
year = {2009},
- pages = {176--186}
+ pages = {176--186},
+ optdoi = {10.1007/978-3-642-10210-3_14}
}
@@ -47,7 +56,7 @@
number = "6",
pages = "1675--1684",
year = "2007",
- doi = "DOI: 10.1016/j.patcog.2006.10.005"
+ doi = "10.1016/j.patcog.2006.10.005"
}
@@ -71,7 +80,8 @@
journal = {Mathematical Morphology: Theory and Applications},
year = {2017},
number = {2},
- pages = {35-54}
+ pages = {35-54},
+ doi = {10.1016/j.patcog.2006.10.005}
}
@@ -136,7 +146,8 @@
booktitle = {Int. Conf. on Image Processing},
publisher = {IEEE},
year = {2015},
- pages = {507--511}
+ pages = {507--511},
+ doi = {10.1109/ICIP.2015.7350850}
}
diff --git a/Article/intro.tex b/Article/intro.tex
index 53d2923..fb5fa08 100755
--- a/Article/intro.tex
+++ b/Article/intro.tex
@@ -22,7 +22,7 @@ introduced to cope with the image noise or other sources of imperfections
from the real world by the mean of a width parameter.
It is well suited to reflect the required edge quality information.
Moreover efficient algorithms have already been designed to recognize
-these digital objects in binary images.
+these digital objects in binary images \cite{DebledAl06}.
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
@@ -72,20 +72,22 @@ resolution images.
The work presented in this paper aims at solving both former mentioned
drawbacks through two main contributions:
-the concept of adaptive directional scanner designed to get some compliance
-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.
+(i) the concept of adaptive directional scanner designed to get some
+compliance to the unpredictable orientation problem;
+(ii) 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, these two major evolutions also led to a noticeable
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.
-Then the new detector workflow, the adaptive directional scanner, the control
-of the assigned with and their integration into both supervised
-and unsupervised contexts are presented and discussed in \RefSec{sec:method}.
+The new detector workflow, the adaptive directional scanner, the control
+of the assigned with and their integration into both supervised and
+unsupervised contexts are then presented and discussed in \RefSec{sec:method}.
Experiments led to assess the expected increase of performance are decribed
in \RefSec{sec:expe}.
-Finally achieved results are summarized in \RefSec{sec:conclusion},
+Finally, achieved results are summarized in \RefSec{sec:conclusion},
followed by some open perspectives for future works.
diff --git a/Article/main.tex b/Article/main.tex
index f458d99..74fbea3 100755
--- a/Article/main.tex
+++ b/Article/main.tex
@@ -3,9 +3,16 @@
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
+\usepackage{tikzrput}
+\definecolor{dblue}{RGB}{55,55,200}
+
+
+\usepackage[colorlinks=true,citecolor=dblue]{hyperref}
+
\usepackage{graphicx}
\usepackage{color}
\definecolor{dwhite}{rgb}{1,1,1}
+\definecolor{dgreen}{rgb}{0.1,0.5,0.1}
%\graphicspath{{./Fignotions/}{./Figmethod}}
\usepackage[ruled,vlined]{algorithm2e}
@@ -19,7 +26,7 @@
\begin{frontmatter}
% \title{Straight edge detection
% based on adaptive directional tracking of blurred segments}
- \title{Adaptive directional tracking of blurred segments}
+ \title{Adaptive Directional Tracking of Blurred Segments}
\author{Philippe Even\inst{1} \and
Phuc Ngo\inst{1} \and
@@ -37,7 +44,9 @@
\begin{abstract}
\input{abstract}
- \keywords{Line detection \and discrete objects \and image analysis}
+ \keywords{Line/segment detection
+ \and discrete objects
+ \and image analysis}
\end{abstract}
\end{frontmatter}
diff --git a/Article/method.tex b/Article/method.tex
index d38d22d..3ef6d59 100755
--- a/Article/method.tex
+++ b/Article/method.tex
@@ -9,32 +9,7 @@ in the following figure.
\begin{figure}[h]
\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(24,16){\makebox(56,10){Initial}}
- \put(24,4){\makebox(56,10){detection}}
- \put(86,18){\scriptsize $\mathcal{B}$}
- \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 $\emptyset$}
- \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(186,16){\makebox(56,10){Fine}}
- \put(186,4){\makebox(60,10){tracking}}
- \put(250,18){\scriptsize $\mathcal{B}'$}
- \put(242,15){\vector(1,0){24}}
- \put(266,0){\framebox(56,30){Filtering}}
- \put(330,18){\scriptsize $\mathcal{B}''$}
- \put(322,15){\vector(1,0){22}}
- \end{picture}
+ \input{Fig_method/workflow}
\caption{The detection process main workflow.}
\label{fig:workflow}
\end{figure}
@@ -71,10 +46,12 @@ Most of the time, the detection stops where the segment escapes sideways
from the scan strip (\RefFig{fig:escape} a).
A second search is then run using another directional scan aligned
on the detected segment (\RefFig{fig:escape} b).
-However, even in case of a correct detection, the estimated orientation
-of the segment is subject to the numerization rounding,
-and the longer the real segment to detect, the higher the probability to
-fail again on a blurred segment escape from the directional scan.
+In the given example, an outlier added to the initial segment leads to a
+wrong orientation value.
+But even in case of a correct detection, this estimated orientation
+is subject to the numerization rounding, and the longer the real segment
+to detect, the higher the probability to fail again on a blurred segment
+escape from the directional scan.
%Even in ideal situation where the detected segment is a perfect line,
%its width is never null as a result of the discretization process.
@@ -116,8 +93,9 @@ thus producing a useless computational cost.
Here the proposed solution is to dynamically align the scan direction on
the blurred segment one all along the expansion stage.
-At each iteration $i$, the scan strip is aligned on the direction of the
-blurred segment $\mathcal{B}_{i-1}$ computed at previous iteration $i-1$.
+At each iteration $i$ of the expansion, the scan strip is aligned on the
+direction of the blurred segment $\mathcal{B}_{i-1}$ computed at previous
+iteration $i-1$.
More generally, an adaptive directional scan $ADS$ is defined by:
\begin{equation}
%S_i = \mathcal{D}_{i-1} \cap \mathcal{N}_i
@@ -228,19 +206,18 @@ extracting the segment and contributes to notably stabilize the overall
process.
When selecting candidates for the fine detection stage, an option, called
-{\it edge selection mode}, is left to filter the points according to their
-gradient direction.
+{\it edge selection mode}, is left to also filter the points according to
+their gradient direction.
In {\it main edge selection mode}, only the points with a gradient vector
in the same direction as the start point gradient vector are added to the
blurred segment.
In {\it opposite edge selection mode}, only the points with an opposite
gradient vector direction are kept.
-In {\it line selection mode} this filter is not applied, and all the
-candidate points are aggregated into a same blurred segment, whatever the
-direction of their gradient vector.
-This mode allows the detection of the two opposite edges of a thin straight
-object.
-This distinction is illustrated on \RefFig{fig:edgeDir}.
+In {\it line selection mode} this direction-based filter is not applied,
+and all the candidate points are aggregated into a same blurred segment,
+whatever the direction of their gradient vector.
+As illustrated on \RefFig{fig:edgeDir}, this mode allows the detection of
+the two opposite edges of a thin straight object.
\begin{figure}[h]
\center
@@ -256,13 +233,15 @@ This distinction is illustrated on \RefFig{fig:edgeDir}.
\put(-262.5,-20){a}
\put(-89,-20){b}
\end{picture}
- \caption{Blurred segments obtained in line or edge selection mode
- as a result of the gradient direction filtering when adding points.
- In line selection mode (a), a thick blurred segment is built and
- extended all along the brick join.
- In edge selection mode (b), a thin blurred segment is built along
- one of the two join edges.
- Both join edges are detected with the multi-selection option.
+ \caption{Blurred segments obtained in \textit{line} or \textit{edge
+ selection mode} as a result of the gradient direction filtering
+ when adding points.
+ In \textit{line selection mode} (a), a thick blurred segment is
+ built and extended all along the brick join.
+ In \textit{edge selection mode} (b), a thin blurred segment is
+ built along one of the two join edges.
+ Both join edges are detected with the \textit{multi-selection}
+ option.
On that very textured image, they are much shorter than the whole
join detected in line selection mode.
Blurred segment points are drawn in black color, and the enclosing
@@ -276,7 +255,7 @@ Another 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 add to another segment.
+so that these points can not be added to another segment.
First the positions $M_j$ of the prominent local maxima of the gradient
magnitude found under the stroke are sorted from the highest to the lowest.
@@ -391,6 +370,11 @@ of interfering outliers insertion.
\label{fig:noisy}
\end{figure}
+The automatic detection of blurred segments in a whole image is left
+available for testing in an online demonstration at the following address: \\
+{\small \tt
+http://ipol-geometry.loria.fr/\~{}kerautre/ipol\_demo/AdaptDirBS\_IPOLDemo/}
+
%The behavior of the unsupervised detection is depicted through the two
%examples of \RefFig{fig:auto}.
%The example on the left shows the detection of thin straight objects on a
diff --git a/Article/notions.tex b/Article/notions.tex
index cc62fe6..00d917d 100755
--- a/Article/notions.tex
+++ b/Article/notions.tex
@@ -53,6 +53,9 @@ the assigned width $\varepsilon$, then the new input point is rejected.}
\label{fig:bs}
\end{figure}
+Associated to this primitive, the following definition of directional scan
+also based on digital straight lines is also used in the following.
+
\subsection{Directional scan}
A directional scan $DS$ is an ordered partition restricted to the image
@@ -104,12 +107,12 @@ At each iteration $i$, the scans $S_i$ and $S_{-i}$ are successively processed.
\put(-185,112){$A$}
\put(-88,14){$B$}
\put(-20,98){$\mathcal{D}$}
- \put(-137,64){$S_0$}
- \put(-77,94){$S_8$}
- \put(-183,64){$S_{-5}$}
- \put(-123,8){$\mathcal{N}_0$}
- \put(-60,30){$\mathcal{N}_8$}
- \put(-169,8){$\mathcal{N}_{-5}$}
+ \put(-137,64){\color{blue}{$S_0$}}
+ \put(-77,94){\color{red}{$S_8$}}
+ \put(-183,64){\color{dgreen}{$S_{-5}$}}
+ \put(-123,8){\color{blue}{$\mathcal{N}_0$}}
+ \put(-60,30){\color{red}{$\mathcal{N}_8$}}
+ \put(-169,8){\color{dgreen}{$\mathcal{N}_{-5}$}}
\end{picture}
\caption{A directional scan.
The start scan $S_0$ is drawn in blue, odd scans in green,
--
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