<s>
Image	B-Algorithm
Geometry	I-Algorithm
Correction	I-Algorithm
(	O
often	O
referred	O
to	O
as	O
Image	B-Algorithm
Warping	I-Algorithm
)	O
is	O
the	O
process	O
of	O
digitally	O
manipulating	O
image	O
data	O
such	O
that	O
the	O
image	O
’s	O
projection	O
precisely	O
matches	O
a	O
specific	O
projection	O
surface	O
or	O
shape	O
.	O
</s>
<s>
Image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
compensates	O
for	O
the	O
distortion	O
created	O
by	O
off-axis	O
projector	B-Application
or	O
screen	O
placement	O
or	O
non-flat	O
screen	O
surface	O
,	O
by	O
applying	O
a	O
pre-compensating	O
inverse	O
distortion	O
to	O
that	O
image	O
in	O
the	O
digital	O
domain	O
.	O
</s>
<s>
Usually	O
,	O
Image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
is	O
applied	O
such	O
that	O
equal	O
areas	O
of	O
projection	O
surface	O
are	O
perceived	O
by	O
the	O
viewer	O
map	O
to	O
equal	O
areas	O
in	O
the	O
source	O
image	O
.	O
</s>
<s>
Image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
applies	O
to	O
static	O
or	O
dynamic	O
images	O
(	O
i.e.	O
</s>
<s>
Image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
is	O
generally	O
implemented	O
in	O
2	O
different	O
ways	O
:	O
</s>
<s>
Both	O
techniques	O
involve	O
the	O
real	O
time	O
execution	O
of	O
a	O
spatial	O
transformation	O
from	O
the	O
input	O
image	O
to	O
the	O
output	O
image	O
,	O
and	O
both	O
techniques	O
require	O
powerful	O
hardware	B-Architecture
.	O
</s>
<s>
In	O
Graphics	O
Processing	O
,	O
the	O
spatial	O
transformation	O
consists	O
of	O
a	O
polygon	B-Algorithm
mesh	I-Algorithm
(	O
usually	O
triangles	O
)	O
.	O
</s>
<s>
The	O
transformation	O
is	O
executed	O
by	O
texture	O
mapping	O
from	O
the	O
rectilinear	O
mesh	B-Algorithm
of	O
the	O
input	O
image	O
to	O
the	O
transformed	O
shape	O
of	O
the	O
destination	O
image	O
.	O
</s>
<s>
Each	O
polygon	B-General_Concept
on	O
the	O
input	O
image	O
is	O
thus	O
applied	O
to	O
an	O
equivalent	O
(	O
but	O
transformed	O
in	O
shape	O
and	O
location	O
)	O
polygon	B-General_Concept
in	O
the	O
output	O
image	O
.	O
</s>
<s>
Graphics	O
Processing	O
based	O
Image	B-Algorithm
Geometry	I-Algorithm
Correction	I-Algorithm
,	O
may	O
be	O
performed	O
with	O
inexpensive	O
PC-based	O
graphics	O
controllers	O
.	O
</s>
<s>
The	O
sophisticated	O
software	O
that	O
uses	O
the	O
texture	O
mapping	O
hardware	B-Architecture
of	O
a	O
graphics	O
controller	O
is	O
not	O
standard	O
,	O
and	O
is	O
available	O
only	O
through	O
vendors	O
of	O
specialty	O
software	O
(	O
i.e.	O
</s>
<s>
Graphics	O
Processing	O
based	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
is	O
very	O
effective	O
for	O
content	O
that	O
originates	O
in	O
the	O
PC	O
.	O
</s>
<s>
In	O
Signal	O
Processing	O
based	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
,	O
the	O
spatial	O
transformation	O
consists	O
of	O
spatially	O
defined	O
2-dimensional	O
image	O
re-sampling	O
or	O
scaling	O
filter	O
.	O
</s>
<s>
Signal	O
Processing	O
based	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
is	O
implemented	O
by	O
specially	O
designed	O
hardware	B-Architecture
in	O
the	O
projection	O
system	O
(	O
i.e.	O
</s>
<s>
Signal	O
Processing	O
based	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
is	O
the	O
most	O
flexible	O
form	O
of	O
this	O
technology	O
,	O
enabling	O
the	O
correction	O
of	O
images	O
that	O
originate	O
from	O
ANY	O
graphics	O
controller	O
platform	O
.	O
</s>
<s>
The	O
drawback	O
of	O
Signal	O
Processing	O
based	O
Image	B-Algorithm
Geometry	I-Algorithm
Correction	I-Algorithm
is	O
the	O
extra	O
expense	O
of	O
the	O
hardware	B-Architecture
that	O
is	O
used	O
to	O
perform	O
it	O
.	O
</s>
<s>
This	O
extra	O
expense	O
can	O
be	O
mitigated	O
by	O
the	O
inclusion	O
of	O
additional	O
features	O
(	O
such	O
as	O
switching	O
and	O
Edge	O
Blending	O
in	O
the	O
Signal	O
Processing	O
based	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
system	O
)	O
.	O
</s>
<s>
The	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
transformation	O
can	O
be	O
calculated	O
by	O
predictive	O
geometry	O
(	O
i.e.	O
</s>
<s>
The	O
number	O
of	O
points	O
in	O
the	O
2-dimensional	O
array	O
that	O
are	O
required	O
to	O
do	O
an	O
accurate	O
Image	B-Algorithm
Geometry	I-Algorithm
Correction	I-Algorithm
depends	O
on	O
the	O
surface	O
involved	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
Keystone	B-General_Concept
Correction	I-General_Concept
,	O
4	O
points	O
are	O
all	O
that	O
are	O
required	O
to	O
completely	O
describe	O
any	O
projection	O
situation	O
.	O
</s>
<s>
The	O
simplest	O
application	O
of	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
is	O
a	O
specific	O
case	O
known	O
as	O
keystone	O
distortion	O
correction	O
derived	O
from	O
Keystone	B-General_Concept
effect	I-General_Concept
.	O
</s>
<s>
Keystone	O
distortion	O
gets	O
its	O
name	O
from	O
the	O
symmetric	O
trapezoidal	O
distortion	O
resulting	O
from	O
misaligned	O
projector	B-Application
placement	O
in	O
the	O
vertical	O
dimension	O
(	O
although	O
the	O
term	O
is	O
generally	O
applied	O
to	O
the	O
non-symmetric	O
quadrilateral	O
shape	O
that	O
occurs	O
from	O
an	O
off-axis	O
projection	O
in	O
both	O
dimensions	O
)	O
.	O
</s>
<s>
Keystone	B-General_Concept
correction	I-General_Concept
capabilities	O
are	O
now	O
included	O
in	O
most	O
projectors	B-Application
currently	O
available	O
on	O
the	O
market	O
,	O
allowing	O
users	O
to	O
move	O
the	O
image	O
both	O
vertically	O
and	O
horizontally	O
.	O
</s>
<s>
Keystone	B-General_Concept
correction	I-General_Concept
is	O
ideal	O
for	O
simple	O
business	O
(	O
i.e.	O
</s>
<s>
Projector	B-Application
Stacking	O
is	O
an	O
advanced	O
form	O
of	O
keystone	B-General_Concept
correction	I-General_Concept
.	O
</s>
<s>
In	O
this	O
application	O
,	O
two	O
or	O
more	O
projectors	B-Application
are	O
projected	O
onto	O
exactly	O
the	O
same	O
surface	O
.	O
</s>
<s>
Since	O
the	O
two	O
projectors	B-Application
cannot	O
occupy	O
exactly	O
the	O
same	O
space	O
,	O
the	O
output	O
of	O
each	O
must	O
be	O
at	O
least	O
slightly	O
corrected	O
for	O
Keystone	O
Distortion	O
.	O
</s>
<s>
Passive	O
3D	O
Projector	B-Application
Stacking	O
provides	O
precise	O
alignment	O
for	O
2	O
synchronized	O
projectors	B-Application
that	O
are	O
supplying	O
the	O
left	O
eye	O
and	O
right	O
eye	O
of	O
a	O
3D	O
application	O
.	O
</s>
<s>
Image	B-Algorithm
Geometry	I-Algorithm
Correction	I-Algorithm
onto	O
regular	O
surfaces	O
(	O
such	O
as	O
spheres	O
and	O
cylinders	O
)	O
is	O
the	O
next	O
level	O
of	O
complexity	O
.	O
</s>
<s>
Image	B-Algorithm
Geometry	I-Algorithm
Correction	I-Algorithm
onto	O
irregular	O
surfaces	O
is	O
the	O
most	O
advanced	O
form	O
.	O
</s>
<s>
Edge	O
Blending	O
is	O
a	O
companion	O
application	O
to	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
.	O
</s>
<s>
Edge	O
blending	O
enables	O
the	O
seamless	O
projection	O
of	O
a	O
large	O
image	O
using	O
several	O
overlapping	O
projectors	B-Application
.	O
</s>
<s>
Since	O
Keystone	O
Distortion	O
(	O
and	O
frequently	O
the	O
requirement	O
of	O
projection	O
onto	O
a	O
non-flat	O
surface	O
)	O
is	O
a	O
built-in	O
requirement	O
of	O
almost	O
all	O
Edge	O
Blending	O
systems	O
,	O
the	O
pairing	O
of	O
Edge	O
blending	O
and	O
image	B-Algorithm
geometry	I-Algorithm
correction	I-Algorithm
in	O
the	O
same	O
video	O
signal	O
processor	O
is	O
a	O
natural	O
one	O
.	O
</s>
