<s>
Camera	B-Algorithm
resectioning	I-Algorithm
is	O
the	O
process	O
of	O
estimating	O
the	O
parameters	O
of	O
a	O
pinhole	B-Algorithm
camera	I-Algorithm
model	I-Algorithm
approximating	O
the	O
camera	O
that	O
produced	O
a	O
given	O
photograph	O
or	O
video	O
;	O
it	O
determines	O
which	O
incoming	O
light	B-Device
ray	I-Device
is	O
associated	O
with	O
each	O
pixel	B-Algorithm
on	O
the	O
resulting	O
image	O
.	O
</s>
<s>
Basically	O
,	O
the	O
process	O
determines	O
the	O
pose	B-Architecture
of	O
the	O
pinhole	O
camera	O
.	O
</s>
<s>
Usually	O
,	O
the	O
camera	O
parameters	O
are	O
represented	O
in	O
a	O
34	O
projection	O
matrix	O
called	O
the	O
camera	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
The	O
extrinsic	O
parameters	O
define	O
the	O
camera	B-Architecture
pose	I-Architecture
(	O
position	O
and	O
orientation	O
)	O
while	O
the	O
intrinsic	O
parameters	O
specify	O
the	O
camera	O
image	O
format	O
(	O
focal	B-Algorithm
length	I-Algorithm
,	O
pixel	B-Algorithm
size	O
,	O
and	O
image	O
origin	O
)	O
.	O
</s>
<s>
This	O
process	O
is	O
often	O
called	O
geometric	B-Algorithm
camera	I-Algorithm
calibration	I-Algorithm
or	O
simply	O
camera	O
calibration	O
,	O
although	O
that	O
term	O
may	O
also	O
refer	O
to	O
photometric	B-Algorithm
camera	I-Algorithm
calibration	I-Algorithm
or	O
be	O
restricted	O
for	O
the	O
estimation	O
of	O
the	O
intrinsic	O
parameters	O
only	O
.	O
</s>
<s>
Exterior	B-Algorithm
orientation	I-Algorithm
and	O
interior	B-Algorithm
orientation	I-Algorithm
refer	O
to	O
the	O
determination	O
of	O
only	O
the	O
extrinsic	O
and	O
intrinsic	O
parameters	O
,	O
respectively	O
.	O
</s>
<s>
The	O
classic	O
camera	O
calibration	O
requires	O
special	O
objects	O
in	O
the	O
scene	O
,	O
which	O
is	O
not	O
required	O
in	O
camera	B-Algorithm
auto-calibration	I-Algorithm
.	O
</s>
<s>
Camera	B-Algorithm
resectioning	I-Algorithm
is	O
often	O
used	O
in	O
the	O
application	O
of	O
stereo	B-Algorithm
vision	I-Algorithm
where	O
the	O
camera	O
projection	O
matrices	O
of	O
two	O
cameras	O
are	O
used	O
to	O
calculate	O
the	O
3D	O
world	O
coordinates	O
of	O
a	O
point	O
viewed	O
by	O
both	O
cameras	O
.	O
</s>
<s>
The	O
camera	O
projection	O
matrix	O
is	O
derived	O
from	O
the	O
intrinsic	O
and	O
extrinsic	O
parameters	O
of	O
the	O
camera	O
,	O
and	O
is	O
often	O
represented	O
by	O
the	O
series	O
of	O
transformations	O
;	O
e.g.	O
,	O
a	O
matrix	O
of	O
camera	O
intrinsic	O
parameters	O
,	O
a	O
33	O
rotation	B-Algorithm
matrix	I-Algorithm
,	O
and	O
a	O
translation	O
vector	O
.	O
</s>
<s>
In	O
this	O
context	O
,	O
we	O
use	O
to	O
represent	O
a	O
2D	O
point	O
position	O
in	O
pixel	B-Algorithm
coordinates	O
and	O
is	O
used	O
to	O
represent	O
a	O
3D	O
point	O
position	O
in	O
world	O
coordinates	O
.	O
</s>
<s>
Referring	O
to	O
the	O
pinhole	B-Algorithm
camera	I-Algorithm
model	I-Algorithm
,	O
a	O
camera	B-General_Concept
matrix	I-General_Concept
is	O
used	O
to	O
denote	O
a	O
projective	O
mapping	O
from	O
world	O
coordinates	O
to	O
pixel	B-Algorithm
coordinates	O
.	O
</s>
<s>
by	O
convention	O
are	O
the	O
x	O
and	O
y	O
coordinates	O
of	O
the	O
pixel	B-Algorithm
in	O
the	O
camera	O
,	O
is	O
the	O
intrinsic	O
matrix	O
as	O
described	O
below	O
,	O
and	O
form	O
the	O
extrinsic	O
matrix	O
as	O
described	O
below	O
.	O
</s>
<s>
are	O
the	O
coordinates	O
of	O
the	O
source	O
of	O
the	O
light	B-Device
ray	I-Device
which	O
hits	O
the	O
camera	O
sensor	O
in	O
world	O
coordinates	O
,	O
relative	O
to	O
the	O
origin	O
of	O
the	O
world	O
.	O
</s>
<s>
By	O
dividing	O
the	O
matrix	O
product	O
by	O
,	O
the	O
z-coordinate	O
of	O
the	O
camera	O
relative	O
to	O
the	O
world	O
origin	O
,	O
the	O
theoretical	O
value	O
for	O
the	O
pixel	B-Algorithm
coordinates	O
can	O
be	O
found	O
.	O
</s>
<s>
These	O
parameters	O
encompass	O
focal	B-Algorithm
length	I-Algorithm
,	O
image	B-Algorithm
sensor	I-Algorithm
format	I-Algorithm
,	O
and	O
camera	O
principal	O
point	O
.	O
</s>
<s>
The	O
parameters	O
and	O
represent	O
focal	B-Algorithm
length	I-Algorithm
in	O
terms	O
of	O
pixels	B-Algorithm
,	O
where	O
and	O
are	O
the	O
inverses	O
of	O
the	O
width	O
and	O
height	O
of	O
a	O
pixel	B-Algorithm
on	O
the	O
projection	O
plane	O
and	O
is	O
the	O
focal	B-Algorithm
length	I-Algorithm
in	O
terms	O
of	O
distance	O
.	O
</s>
<s>
This	O
is	O
done	O
in	O
the	O
form	O
of	O
optimising	O
the	O
camera	O
and	O
distortion	O
parameters	O
in	O
the	O
form	O
of	O
what	O
is	O
generally	O
known	O
as	O
bundle	B-General_Concept
adjustment	I-General_Concept
.	O
</s>
<s>
The	O
position	O
,	O
,	O
of	O
the	O
camera	O
expressed	O
in	O
world	O
coordinates	O
is	O
(	O
since	O
is	O
a	O
rotation	B-Algorithm
matrix	I-Algorithm
)	O
.	O
</s>
<s>
Camera	O
calibration	O
is	O
often	O
used	O
as	O
an	O
early	O
stage	O
in	O
computer	B-Application
vision	I-Application
.	O
</s>
<s>
Each	O
pixel	B-Algorithm
on	O
the	O
image	O
plane	O
therefore	O
corresponds	O
to	O
a	O
shaft	O
of	O
light	O
from	O
the	O
original	O
scene	O
.	O
</s>
<s>
The	O
main	O
contribution	O
of	O
Zhang	O
method	O
is	O
how	O
to	O
extract	O
a	O
constrained	O
instrinsic	O
and	O
numbers	O
of	O
and	O
calibration	O
parameters	O
from	O
pose	B-Architecture
of	O
the	O
calibration	O
target	O
.	O
</s>
<s>
Assume	O
we	O
have	O
a	O
homography	B-Algorithm
that	O
maps	O
points	O
on	O
a	O
"	O
probe	O
plane	O
"	O
to	O
points	O
on	O
the	O
image	O
.	O
</s>
<s>
It	O
is	O
a	O
2-stage	O
algorithm	O
,	O
calculating	O
the	O
pose	B-Architecture
(	O
3D	O
Orientation	O
,	O
and	O
x-axis	O
and	O
y-axis	O
translation	O
)	O
in	O
first	O
stage	O
.	O
</s>
<s>
In	O
second	O
stage	O
it	O
computes	O
the	O
focal	B-Algorithm
length	I-Algorithm
,	O
distortion	O
coefficients	O
and	O
the	O
z-axis	O
translation	O
.	O
</s>
