<s>
Radar	B-Algorithm
geo-warping	I-Algorithm
is	O
the	O
adjustment	O
of	O
geo-referenced	B-General_Concept
radar	B-Application
images	O
and	O
video	O
data	O
to	O
be	O
consistent	O
with	O
a	O
geographical	O
projection	B-Application
.	O
</s>
<s>
This	O
image	B-Algorithm
warping	I-Algorithm
avoids	O
any	O
restrictions	O
when	O
displaying	O
it	O
together	O
with	O
video	O
from	O
multiple	O
radar	B-Application
sources	O
or	O
with	O
other	O
geographical	O
data	O
including	O
scanned	O
maps	O
and	O
satellite	O
images	O
which	O
may	O
be	O
provided	O
in	O
a	O
particular	O
projection	B-Application
.	O
</s>
<s>
There	O
are	O
many	O
areas	O
where	O
geo	B-Algorithm
warping	I-Algorithm
has	O
unique	O
benefits	O
:	O
</s>
<s>
Single	O
radar	B-Application
video	O
signal	O
displayed	O
together	O
with	O
maps	O
of	O
different	O
geographical	O
projections	B-Application
.	O
</s>
<s>
Multiple	O
radar	B-Application
video	O
signals	O
displayed	O
simultaneously	O
:	O
</s>
<s>
Adapting	O
the	O
projection	B-Application
of	O
all	O
radar	B-Application
signals	O
allowing	O
the	O
geographically	O
correct	O
display	O
and	O
accurate	O
superimposition	O
of	O
those	O
videos	O
.	O
</s>
<s>
Slant	O
range	O
correction	O
:	O
a	O
modern	O
3D	O
radar	B-Application
system	I-Application
can	O
measure	O
the	O
height	O
of	O
a	O
target	O
and	O
hence	O
it	O
is	O
possible	O
to	O
correct	O
the	O
radar	B-Application
video	O
by	O
the	O
real	O
corrected	O
range	O
of	O
the	O
target	O
.	O
</s>
<s>
Slant	O
Range	O
Correction	O
also	O
allows	O
to	O
compensate	O
the	O
radar	B-Application
tower	O
height	O
e.g.	O
</s>
<s>
for	O
maritime	O
surveillance	O
radars	B-Application
.	O
</s>
<s>
Radar	B-Application
video	O
presents	O
the	O
echoes	O
of	O
electromagnetic	O
waves	O
a	O
radar	B-Application
system	I-Application
has	O
emitted	O
and	O
received	O
as	O
reflections	O
afterwards	O
.	O
</s>
<s>
The	O
first	O
problem	O
arises	O
from	O
the	O
fact	O
that	O
typically	O
the	O
radar	B-Application
antenna	O
turns	O
around	O
its	O
position	O
and	O
measures	O
the	O
reflection	O
echo	O
distances	O
from	O
its	O
position	O
in	O
one	O
direction	O
.	O
</s>
<s>
This	O
effectively	O
means	O
that	O
the	O
radar	B-Application
video	O
data	O
are	O
present	O
in	O
polar	O
coordinates	O
.	O
</s>
<s>
In	O
older	O
systems	O
the	O
polar	O
oriented	O
picture	O
has	O
been	O
displayed	O
in	O
so	O
called	O
plan	B-Algorithm
position	I-Algorithm
indicators	I-Algorithm
(	O
PPI	O
)	O
.	O
</s>
<s>
This	O
results	O
in	O
a	O
map-like	O
picture	O
of	O
the	O
area	O
covered	O
by	O
the	O
radar	B-Application
beam	O
.	O
</s>
<s>
This	O
process	O
called	O
radar	B-Application
scan	O
conversion	O
is	O
presented	O
with	O
more	O
detail	O
in	O
the	O
next	O
section	O
.	O
</s>
<s>
The	O
second	O
problem	O
to	O
solve	O
arises	O
from	O
the	O
fact	O
that	O
a	O
radar	B-Application
system	I-Application
is	O
placed	O
in	O
the	O
real	O
world	O
and	O
measures	O
real	O
world	O
echo	O
positions	O
.	O
</s>
<s>
Building	O
a	O
link	O
from	O
real	O
world	O
earth	O
positions	O
to	O
display	O
pixels	O
is	O
commonly	O
called	O
geographical	O
referencing	O
or	O
in	O
short	O
geo-referencing	B-General_Concept
.	O
</s>
<s>
Part	O
of	O
the	O
geo-referencing	B-General_Concept
process	O
is	O
to	O
map	O
the	O
3D	O
earth	O
surface	O
onto	O
a	O
2D	O
display	O
.	O
</s>
<s>
This	O
process	O
of	O
a	O
geographical	O
projection	B-Application
can	O
be	O
performed	O
in	O
many	O
ways	O
,	O
but	O
different	O
data	O
sources	O
have	O
their	O
own	O
'	O
natural	O
 '	O
projection	B-Application
.	O
</s>
<s>
Cartesian	O
radar	B-Application
video	O
data	O
from	O
a	O
radar	B-Application
source	O
on	O
the	O
earth	O
surface	O
are	O
geo-referenced	B-General_Concept
by	O
a	O
so-called	O
radar	B-Application
projection	B-Application
.	O
</s>
<s>
When	O
using	O
this	O
radar	B-Application
projection	B-Application
the	O
Cartesian	O
radar	B-Application
video	O
pixels	O
can	O
directly	O
displayed	O
on	O
a	O
computer	O
screen	O
(	O
only	O
being	O
linearly	O
transformed	O
according	O
to	O
the	O
current	O
position	O
on	O
the	O
screen	O
and	O
e.g.	O
</s>
<s>
also	O
a	O
satellite	O
map	O
shall	O
be	O
shown	O
together	O
with	O
the	O
radar	B-Application
video	O
data	O
.	O
</s>
<s>
The	O
'	O
natural	O
 '	O
geographical	O
projection	B-Application
of	O
a	O
satellite	O
image	O
would	O
be	O
a	O
satellite	O
projection	B-Application
which	O
depends	O
on	O
the	O
satellite	O
orbit	O
,	O
position	O
and	O
further	O
parameters	O
.	O
</s>
<s>
Now	O
either	O
the	O
satellite	O
image	O
has	O
to	O
be	O
reprojected	O
to	O
a	O
radar	B-Application
projection	B-Application
or	O
the	O
radar	B-Application
video	O
has	O
to	O
use	O
the	O
satellite	O
projection	B-Application
.	O
</s>
<s>
This	O
geographical	O
re-projection	O
is	O
also	O
called	O
geographical	O
warping	O
or	O
Geo	B-Algorithm
Warping	I-Algorithm
where	O
each	O
image	O
pixel	O
has	O
to	O
be	O
transformed	O
from	O
one	O
projection	B-Application
into	O
another	O
.	O
</s>
<s>
This	O
article	O
describes	O
in	O
further	O
detail	O
the	O
Geo	B-Algorithm
Warping	I-Algorithm
of	O
radar	B-Application
video	O
images	O
in	O
real	O
time	O
.	O
</s>
<s>
It	O
will	O
also	O
show	O
that	O
radar	B-Application
video	O
Geo	B-Algorithm
Warping	I-Algorithm
is	O
done	O
most	O
efficiently	O
when	O
it	O
is	O
integrated	O
with	O
the	O
radar	B-Application
scan	O
conversion	O
process	O
.	O
</s>
<s>
This	O
section	O
describes	O
the	O
principles	O
of	O
the	O
radar-scan	O
conversion	O
(	O
RSC	O
)	O
process	O
.	O
</s>
<s>
The	O
radar	B-Application
supplies	O
its	O
measured	O
data	O
in	O
polar	O
coordinates	O
( ρ	O
,	O
θ	O
)	O
directly	O
from	O
the	O
rotating	O
antenna	O
.	O
</s>
<s>
As	O
detailed	O
later	O
the	O
RSC	O
process	O
also	O
takes	O
the	O
currently	O
used	O
geographical	O
projection	B-Application
into	O
account	O
when	O
the	O
radar	B-Application
video	O
images	O
are	O
Geo	O
Warped	O
.	O
</s>
<s>
The	O
OpenGL	B-Application
RSC	O
is	O
implemented	O
using	O
a	O
reverse	O
scan	O
conversion	O
approach	O
which	O
calculates	O
for	O
every	O
image	O
pixel	O
the	O
most	O
appropriate	O
radar	B-Application
amplitude	O
value	O
in	O
the	O
polar	O
store	O
.	O
</s>
<s>
By	O
applying	O
bi-linear	O
filtering	O
between	O
adjacent	O
pixels	O
in	O
the	O
polar	O
store	O
during	O
the	O
conversion	O
process	O
the	O
OpenGL	B-Application
RSC	O
finally	O
achieves	O
a	O
very	O
high	O
visual	O
quality	O
radar	B-Application
display	O
image	O
for	O
every	O
zoom	O
level	O
,	O
creating	O
smooth	O
images	O
of	O
the	O
radar	B-Application
echoes	O
.	O
</s>
<s>
This	O
section	O
illustrates	O
how	O
radar	B-Application
video	O
data	O
are	O
geo	O
referenced	O
and	O
displayed	O
on	O
a	O
computer	O
screen	O
.	O
</s>
<s>
The	O
radar	B-Application
sensor	O
is	O
positioned	O
on	O
the	O
earth	O
surface	O
with	O
a	O
height	O
h	O
above	O
the	O
ground	O
.	O
</s>
<s>
the	O
distance	O
the	O
target	O
is	O
away	O
from	O
the	O
radar	B-Application
if	O
one	O
would	O
move	O
on	O
the	O
earth	O
surface	O
)	O
.	O
</s>
<s>
This	O
distance	O
is	O
then	O
used	O
in	O
the	O
display	O
plane	O
after	O
adjustment	O
to	O
the	O
current	O
display	O
zoom	O
level	O
by	O
the	O
radar	B-Application
scan	O
converter	O
(	O
RSC	O
)	O
.	O
</s>
<s>
Now	O
it	O
has	O
to	O
be	O
clarified	O
how	O
the	O
radar	B-Application
video	O
data	O
is	O
geo	O
referenced	O
.	O
</s>
<s>
a	O
light	O
house	O
)	O
which	O
is	O
at	O
the	O
same	O
real	O
world	O
position	O
as	O
the	O
radar	B-Application
target	O
,	O
that	O
it	O
also	O
shall	O
appear	O
at	O
the	O
same	O
position	O
in	O
the	O
display	O
plane	O
.	O
</s>
<s>
This	O
is	O
realized	O
by	O
calculating	O
the	O
distance	O
from	O
the	O
radar	B-Application
sensor	O
to	O
the	O
respective	O
real	O
world	O
object	O
and	O
use	O
that	O
distance	O
in	O
the	O
display	O
plane	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
using	O
a	O
radar	B-Application
projection	B-Application
with	O
geographical	O
data	O
is	O
done	O
by	O
simulating	O
a	O
radar	B-Application
measurement	O
process	O
with	O
the	O
real	O
world	O
objects	O
and	O
use	O
the	O
resulting	O
range	O
and	O
azimuth	O
in	O
the	O
display	O
plane	O
.	O
</s>
<s>
The	O
second	O
picture	O
to	O
the	O
right	O
shows	O
an	O
example	O
radar	B-Application
projection	B-Application
with	O
the	O
center	O
of	O
projection	B-Application
(	O
COP	O
)	O
at	O
latitude	O
50.0	O
°	O
and	O
longitude	O
0.0	O
°	O
which	O
is	O
also	O
the	O
radar	B-Application
position	O
.	O
</s>
<s>
The	O
solid	O
lines	O
show	O
equal-range	O
and	O
equal-azimuth	O
with	O
the	O
respect	O
to	O
the	O
radar	B-Application
position	O
.	O
</s>
<s>
It	O
is	O
a	O
feature	O
of	O
the	O
radar	B-Application
projection	B-Application
that	O
equal-range	O
lines	O
are	O
circles	O
and	O
equal-azimuth	O
lines	O
are	O
straight	O
lines	O
.	O
</s>
<s>
This	O
is	O
necessary	O
to	O
display	O
radar	B-Application
video	O
consistently	O
with	O
other	O
map	O
data	O
when	O
using	O
a	O
radar	B-Application
projection	B-Application
where	O
the	O
projection	B-Application
center	O
has	O
to	O
be	O
the	O
radar	B-Application
position	O
.	O
</s>
<s>
This	O
section	O
explains	O
the	O
actual	O
geo	B-Algorithm
warping	I-Algorithm
or	O
re-projection	O
process	O
when	O
applied	O
to	O
radar	B-Application
video	O
in	O
real	O
time	O
.	O
</s>
<s>
Assume	O
we	O
want	O
to	O
display	O
radar	B-Application
video	O
on	O
top	O
of	O
a	O
satellite	O
image	O
.	O
</s>
<s>
As	O
an	O
example	O
we	O
use	O
the	O
CIB	O
projection	B-Application
which	O
is	O
used	O
to	O
display	O
satellite	O
data	O
in	O
CIB	O
(	O
Controlled	O
Image	O
Base	O
)	O
format	O
.	O
</s>
<s>
The	O
Figure	O
Geo	B-Algorithm
Warping	I-Algorithm
Radar	B-Application
to	O
CIB	O
Projection	B-Application
shows	O
dashed	O
the	O
maximal	O
range	O
circle	O
for	O
a	O
range	O
of	O
111km	O
or	O
60	O
miles	O
using	O
the	O
radar	B-Application
projection	B-Application
.	O
</s>
<s>
Such	O
a	O
range	O
is	O
typical	O
for	O
long	O
range	O
coastal	O
surveillance	O
radars	B-Application
.	O
</s>
<s>
The	O
solid	O
line	O
ellipse	O
shows	O
the	O
same	O
range	O
circle	O
for	O
the	O
CIB	O
projection	B-Application
.	O
</s>
<s>
Typically	O
the	O
errors	O
occurring	O
without	O
Geo	B-Algorithm
Warping	I-Algorithm
are	O
smallest	O
near	O
the	O
radar	B-Application
position	O
if	O
at	O
least	O
the	O
projection	B-Application
center	O
(	O
COP	O
)	O
coincides	O
with	O
the	O
radar	B-Application
position	O
,	O
as	O
realized	O
in	O
our	O
example	O
.	O
</s>
<s>
Otherwise	O
the	O
error	O
distribution	O
depends	O
both	O
on	O
the	O
used	O
projection	B-Application
and	O
also	O
on	O
the	O
projection	B-Application
parameters	O
.	O
</s>
<s>
Thus	O
,	O
in	O
our	O
case	O
the	O
errors	O
are	O
most	O
significant	O
near	O
the	O
maximum	O
radar	B-Application
range	O
.	O
</s>
<s>
The	O
CIB	O
projection	B-Application
error	O
corrected	O
in	O
east	O
–	O
west	O
direction	O
at	O
half	O
the	O
radar	B-Application
range	O
is	O
2.6km	O
and	O
is	O
5.3km	O
at	O
the	O
full	O
radar	B-Application
range	O
of	O
111km	O
.	O
</s>
<s>
An	O
error	O
of	O
5.3km	O
is	O
quite	O
significant	O
compared	O
to	O
a	O
typical	O
radial	O
radar	B-Application
measurement	O
resolution	O
of	O
15m	O
.	O
</s>
<s>
The	O
Figure	O
Coordinate	O
re-projection	O
explains	O
how	O
the	O
radar	B-Application
coordinates	O
have	O
to	O
be	O
transformed	O
to	O
match	O
the	O
CIB	O
projection	B-Application
coordinates	O
.	O
</s>
<s>
The	O
radar	B-Application
world	O
coordinates	O
correspond	O
to	O
the	O
Cartesian	O
version	O
of	O
the	O
data	O
measured	O
by	O
the	O
radar	B-Application
sensor	O
.	O
</s>
<s>
Using	O
an	O
inverse	O
radar	B-Application
projection	B-Application
these	O
coordinates	O
are	O
converted	O
into	O
geographic	O
coordinates	O
which	O
represent	O
the	O
radar	B-Application
data	O
posi-tions	O
on	O
the	O
earth	O
surface	O
.	O
</s>
<s>
These	O
coordinates	O
are	O
then	O
finally	O
projected	O
by	O
the	O
CIB	O
(	O
or	O
any	O
other	O
)	O
projection	B-Application
for	O
displaying	O
on	O
the	O
computer	O
screen	O
.	O
</s>
<s>
A	O
problem	O
which	O
arises	O
is	O
that	O
geo	B-Algorithm
warping	I-Algorithm
all	O
measured	O
radar	B-Application
video	O
pixels	O
is	O
far	O
too	O
computing	O
resource	O
consuming	O
as	O
to	O
be	O
performed	O
in	O
real	O
time	O
.	O
</s>
<s>
a	O
display	O
zoom	O
operation	O
still	O
causes	O
a	O
noticeable	O
delay	O
for	O
radar	B-Application
video	O
visualization	O
.	O
</s>
<s>
The	O
Figure	O
Geo	B-Algorithm
warping	I-Algorithm
grid	O
depicts	O
the	O
solution	O
to	O
the	O
problem	O
.	O
</s>
<s>
The	O
circular	O
radar	B-Application
coverage	O
area	O
is	O
divided	O
into	O
a	O
circular	O
grid	O
.	O
</s>
<s>
As	O
geographical	O
projections	B-Application
are	O
typically	O
non-linear	O
functions	O
this	O
introduces	O
a	O
certain	O
error	O
for	O
the	O
radar	B-Application
video	O
display	O
position	O
.	O
</s>
<s>
Keeping	O
this	O
error	O
sufficiently	O
below	O
the	O
radar	B-Application
measurement	O
resolution	O
makes	O
sure	O
that	O
this	O
is	O
no	O
restriction	O
for	O
the	O
radar	B-Application
video	O
display	O
quality	O
.	O
</s>
<s>
The	O
grid	O
tile	O
size	O
has	O
to	O
be	O
computed	O
once	O
for	O
a	O
radar	B-Application
position	O
and	O
a	O
given	O
projection	B-Application
.	O
</s>
<s>
Thus	O
,	O
the	O
grid	O
is	O
typically	O
computed	O
once	O
for	O
a	O
static	O
radar	B-Application
and	O
only	O
more	O
often	O
for	O
moving	O
radars	B-Application
such	O
as	O
on	O
ships	O
.	O
</s>
<s>
The	O
OpenGL	B-Application
radar-scan	O
converter	O
does	O
its	O
scan	O
conversion	O
computations	O
on	O
the	O
graphics	B-Architecture
processing	I-Architecture
unit	I-Architecture
to	O
achieve	O
high	O
performance	O
and	O
visual	O
quality	O
.	O
</s>
<s>
The	O
bi-linear	O
coordinate	O
interpolation	O
mentioned	O
above	O
is	O
done	O
in	O
dedicated	O
hardware	O
on	O
the	O
GPU	B-Architecture
and	O
therefore	O
causes	O
no	O
overhead	O
for	O
the	O
scan	O
converter	O
.	O
</s>
<s>
This	O
example	O
demonstrates	O
how	O
geo	B-Algorithm
warping	I-Algorithm
helps	O
to	O
consistently	O
display	O
multiple	O
radar	B-Application
videos	O
.	O
</s>
<s>
This	O
figure	O
shows	O
the	O
visual	O
effects	O
on	O
the	O
right	O
side	O
without	O
geo	B-Algorithm
warping	I-Algorithm
that	O
targets	O
seen	O
by	O
two	O
radars	B-Application
cannot	O
be	O
correctly	O
displayed	O
and	O
it	O
is	O
unclear	O
where	O
the	O
target	O
is	O
actually	O
positioned	O
.	O
</s>
<s>
The	O
red	O
and	O
yellow	O
target	O
echoes	O
are	O
seen	O
be	O
radars	B-Application
which	O
are	O
about	O
50km	O
away	O
.	O
</s>
<s>
The	O
radars	B-Application
are	O
also	O
about	O
50km	O
away	O
from	O
each	O
other	O
.	O
</s>
<s>
In	O
this	O
scenario	O
even	O
a	O
radar	B-Application
projection	B-Application
is	O
used	O
but	O
of	O
course	O
the	O
radar	B-Application
projection	B-Application
center	O
(	O
COP	O
)	O
can	O
be	O
only	O
at	O
the	O
position	O
of	O
one	O
of	O
the	O
radars	B-Application
.	O
</s>
<s>
Even	O
larger	O
inconsistencies	O
can	O
arise	O
if	O
a	O
projection	B-Application
different	O
from	O
a	O
radar	B-Application
projection	B-Application
is	O
used	O
.	O
</s>
<s>
The	O
geo	O
warped	O
view	O
on	O
the	O
left	O
side	O
shows	O
the	O
consistently	O
displayed	O
radar	B-Application
echoes	O
where	O
both	O
radar	B-Application
echoes	O
are	O
exactly	O
at	O
the	O
real	O
target	O
's	O
position	O
.	O
</s>
