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Kerautret Bertrand
2019 FBSD
Commits
77c65c58
Commit
77c65c58
authored
6 years ago
by
even
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Article: ours hunting and eq numbering
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Article/expe.tex
+10
-9
10 additions, 9 deletions
Article/expe.tex
Article/method.tex
+1
-1
1 addition, 1 deletion
Article/method.tex
Article/notions.tex
+41
-33
41 additions, 33 deletions
Article/notions.tex
with
52 additions
and
43 deletions
Article/expe.tex
+
10
−
9
View file @
77c65c58
...
...
@@ -12,8 +12,8 @@ For instance, the new directional scanners are encoded as an iterator so that
only required scan lines are provided when required, whereas with the former
code, all the scan lines were computed and returned, whenever they were used
or not.
We just checked that the o
utputs of the new coding of the former detector
are equivalent to those of the old release
.
O
utputs of the new coding of the former detector
were compared to those of
the old release, to ensure an equivalent behaviour
.
\begin{figure}
[h]
\center
...
...
@@ -42,7 +42,7 @@ are equivalent to those of the old release.
\end{picture}
\end{tabular}
\caption
{
Outputs of both former (on left) and new (on right) detectors
using a selec
tionof input strokes.
}
using a selection
of input strokes.
}
\label
{
fig:buro
}
\end{figure}
...
...
@@ -68,12 +68,13 @@ detectors with the input strokes of \RefFig{fig:buro}.}
\label
{
tab:cmpOldNew
}
\end{table}
In the second series of tests, we compare the execution times of both detectors
for the automatic detection of edges on a set of test images. We display the
results for one of them (
\RefFig
{
fig:evalAuto
}
). X (resp. Y) blurred segments
are extracted with the former (resp. new) detector on all images. The
average execution time is X ms for the former detector, and Y ms for the
new detector.
In the second series of tests, the execution times of both detectors were
compared on the automatic detection of edges on a set of test images.
Results are displayed for one of them (
\RefFig
{
fig:evalAuto
}
).
X (resp. Y) blurred segments are extracted with the former
(resp. new) detector on all images.
The average execution time is X ms for the former detector,
and Y ms for the new detector.
\begin{figure}
[h]
\center
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...
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Article/method.tex
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−
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77c65c58
...
...
@@ -159,7 +159,7 @@ directions, so that in the exemple of figure (\RefFig{fig:edgeDir} b)),
both edges (in different colours) are highlighted.
These two thin blurred segments are much shorter, probably because the
tiles are not perfectly aligned.
This example illustrates
our detector versatility
.
This example illustrates
the versatility of the new detector
.
\subsection
{
Automatic blurred segment detection
}
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Article/notions.tex
+
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−
33
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@@ -4,9 +4,9 @@
\subsection
{
Blurred segment
}
Our
work relies on the notion of digital straight line as classically
This
work relies on the notion of digital straight line as classically
defined in the digital geometry literature
\cite
{
KletteRosenfeld04
}
.
Only the 2
-dimensional
case is considered here.
Only the 2
D
case is considered here.
\begin{definition}
A digital line
$
\mathcal
{
L
}
(
a,b,c,
\nu
)
$
, with
$
(
a,b,c,
\nu
)
\in
\mathbb
{
Z
}^
4
$
,
...
...
@@ -25,8 +25,8 @@ of points in $\mathbb{Z}^2$ that all belong to a digital line of
arithmetical width
$
\varepsilon
$
.
\end{definition}
In this work, we use a
linear-time algorithm t
hat was developed to recognize
a blurred segment of assigned width
$
\varepsilon
$
\cite
{
DebledAl05
}
.
A
linear-time algorithm t
o recognize a blurred segment of assigned width
$
\varepsilon
$
\cite
{
DebledAl05
}
is used in the work
.
It is based on an incremental growth of the convex hull of the blurred
segment when adding each point successively.
The minimal width
$
\mu
$
of the blurred segment
$
\mathcal
{
B
}$
is the
...
...
@@ -59,34 +59,36 @@ avoid the incorporation of spurious outliers in further parts of the segment.
A directional scan is a partition of a digital straight line
$
\mathcal
{
D
}$
,
called the
{
\it
scan strip
}
, into scans
$
S
_
i
$
, each of them being a
segment of a naive line
$
\mathcal
{
S
}_
i
$
orthogonal to
$
\mathcal
{
D
}$
.
\[
S
_
i
=
\mathcal
{
D
}
\cap
\mathcal
{
S
}_
i,
\mathcal
{
S
}_
i
\perp
\mathcal
{
D
}
\]
\begin{equation}
S
_
i =
\mathcal
{
D
}
\cap
\mathcal
{
S
}_
i,
\mathcal
{
S
}_
i
\perp
\mathcal
{
D
}
\end{equation}
The scans
$
S
_
i
$
are developed on each side of a central scan
$
S
_
0
$
,
and labelled with their manhattan distance (
$
d
_
1
=
|d
_
x|
+
|d
_
y|
$
) to
the central line
$
\mathcal
{
S
}_
0
$
and a positive (resp. negative) sign
if the
ir
are on the left (resp. right) of
$
\mathcal
{
S
}_
0
$
.
if the
y
are on the left (resp. right)
side
of
$
\mathcal
{
S
}_
0
$
.
\begin{figure}
[h]
\center
%\begin{picture}(300,40)
%\end{picture}
\input
{
Fig
_
notions/fig
}
\caption
{
Example of directional scan.
}
\label
{
fig:ds
}
\end{figure}
The
directional scan can be defined by its central scan
$
S
_
0
$
.
A
directional scan can be defined by its central scan
$
S
_
0
$
.
If
$
A
(
x
_
A,y
_
A
)
$
and
$
B
(
x
_
B,y
_
B
)
$
are the end points of
$
S
_
0
$
,
the scan strip is defined by :
\[
\mathcal
{
D
}
(
A,B
)
=
\mathcal
{
L
}
(
\delta
_
x,
\delta
_
y, min
(
c
1
,c
2
)
,
1
+
|c
_
1
-
c
_
2
|
)
\]
\begin{equation}
\mathcal
{
D
}
(A,B) =
\mathcal
{
L
}
(
\delta
_
x,
\delta
_
y, min (c1,c2), 1 + |c
_
1-c
_
2|)
\end{equation}
\noindent
where
$
\delta
_
x
=
x
_
B
-
x
_
A,
\delta
_
y
=
y
_
B
-
y
_
A,
c
_
1
=
a
\cdot
x
_
A
+
b
\cdot
y
_
A
$
and
$
c
_
2
=
a
\cdot
x
_
B
+
b
\cdot
y
_
B
$
.
The scan line
$
\mathcal
{
S
}_
i
$
is then defined by :
\[
\mathcal
{
S
}_
i
(
A,B
)
=
\mathcal
{
L
}
(
\delta
_
y,
-
\delta
_
x,
\delta
_
y
\cdot
x
_
A
-
\delta
_
X
\cdot
y
_
A
+
i
\cdot
\nu
_{
AB
}
,
\nu
_{
AB
}
)
\]
\begin{equation}
\mathcal
{
S
}_
i(A,B) =
\mathcal
{
L
}
(
\delta
_
y, -
\delta
_
x,
\delta
_
y
\cdot
x
_
A -
\delta
_
X
\cdot
y
_
A + i
\cdot
\nu
_{
AB
}
,
\nu
_{
AB
}
)
\end{equation}
where
$
\nu
_{
AB
}
=
max
(
|
\delta
_
x|, |
\delta
_
y|
)
$
The scan lines length is
$
d
_
\infty
(
AB
)
$
or
$
d
_
\infty
(
AB
)-
1
$
, where
$
d
_
\infty
$
...
...
@@ -94,29 +96,32 @@ 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
(
x
_
C,y
_
C
)
$
,
A
directional scan can also be defined by its central point
$
C
(
x
_
C,y
_
C
)
$
,
its direction
$
\vec
{
D
}
(
x
_
D,y
_
D
)
$
and its width
$
w
$
. The scan strip is :
\[
\mathcal
{
D
}
(
C,
\vec
{
D
}
,w
)
=
\mathcal
{
L
}
(
y
_
D,
-
x
_
D, x
_
C
\cdot
y
_
D
-
y
_
C
\cdot
x
_
D
-
w
/
2
, w
)
\]
\begin{equation}
\mathcal
{
D
}
(C,
\vec
{
D
}
,w)
=
\mathcal
{
L
}
(y
_
D, -x
_
D, x
_
C
\cdot
y
_
D - y
_
C
\cdot
x
_
D - w / 2, w)
\end{equation}
\noindent
and the scan line
$
\mathcal
{
S
}_
i
(
C,
\vec
{
D
}
,w
)
$
:
\
[
\mathcal
{
S
}_
i
(
C,
\vec
{
D
}
,w
)
=
\mathcal
{
L
}
(
x
_
D, y
_
D,
x
_
D
\cdot
x
_
C
+
y
_
D
\cdot
y
_
C
-
w
/
2
+
i
\cdot
w,
max
(
|x
_
D|,|y
_
D|
)
\]
\
begin{equation}
\mathcal
{
S
}_
i(C,
\vec
{
D
}
,w)
=
\mathcal
{
L
}
(x
_
D, y
_
D,
x
_
D
\cdot
x
_
C + y
_
D
\cdot
y
_
C - w / 2 + i
\cdot
w,
max (|x
_
D|,|y
_
D|)
\end{equation}
\subsection
{
Adaptive directional scan
}
We try to detect a
blurred segment inside a directional scan which position
The
blurred segment
is searched
inside a directional scan which position
and orientation are given by the user, or defined in arbitrary direction in
unsupervised mode.
Most of the times, the detection stops where the segment escapes sideways
froms the scan strip.
Therefore a second search is run again using an other directional scan aligned
on the detected segment.
But
we
only
have
an estimation of this blurred segment direction
, and the
longer the real segment, the higher the probability to fail again
on a
blurred segment escape from the directional scan.
But only an estimation of this blurred segment direction
is provided,
and the
longer the real segment, the higher the probability to fail again
on a
blurred segment escape from the directional scan.
\begin{figure}
[h]
\center
...
...
@@ -136,8 +141,8 @@ rather a conic shape to take into account the blurred segment preimage.
% Of course this problem is amplified when ideal BS are considered.
% -> FAUX : c'est relativement plus penalisant sur 1 BS reduit a 2 pts
% que sur un BS qu'on n'autorise pas a s'elargir.
This side shift is amplified
when we let
the blurred segment
the capacity
to get thicker in order to capture possible noisy features.
This side shift is amplified
in situations where
the blurred segment
is
left free
to get thicker in order to capture possible noisy features.
The assigned width is then still greater than the detected minimal width,
so that the segment can move within the directional scan.
Knowing the detected blurred segment shape and the image size, it is
...
...
@@ -172,10 +177,13 @@ but also of the multiple detection of the same segment start points.
\label
{
fig:adaptiveScan
}
\end{figure}
The solution we propose here is to dynamically adapt the scan direction
on the detection result. At each position
$
i
$
, the scan strip is updated
using the direction and minimal width of the blurred segment computed
at the former position
$
i
-
1
$
, that is :
\[
S
_
i
=
\mathcal
{
D
}
\cap
\mathcal
{
S
}_{
i
-
1
}
\]
Compared to static directional scans, the scan strip varies while the
The proposed solution is to dynamically adapt the scan direction on the
detection result.
At each position
$
i
$
, the scan strip is updated using the direction and
minimal width of the blurred segment computed at the former position
$
i
-
1
$
,
that is :
\begin{equation}
S
_
i =
\mathcal
{
D
}_{
i-1
}
\cap
\mathcal
{
S
}_
i
\end{equation}
Compared to static directional scans, the scan strip is variable while the
scan lines remain fixed.
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