<s>
Camera	B-Algorithm
auto-calibration	I-Algorithm
is	O
the	O
process	O
of	O
determining	O
internal	O
camera	B-Algorithm
parameters	O
directly	O
from	O
multiple	O
uncalibrated	O
images	O
of	O
unstructured	O
scenes	O
.	O
</s>
<s>
In	O
contrast	O
to	O
classic	B-Algorithm
camera	I-Algorithm
calibration	I-Algorithm
,	O
auto-calibration	O
does	O
not	O
require	O
any	O
special	O
calibration	O
objects	O
in	O
the	O
scene	O
.	O
</s>
<s>
In	O
the	O
visual	O
effects	O
industry	O
,	O
camera	B-Algorithm
auto-calibration	I-Algorithm
is	O
often	O
part	O
of	O
the	O
"	O
Match	O
Moving	O
"	O
process	O
where	O
a	O
synthetic	O
camera	B-Algorithm
trajectory	O
and	O
intrinsic	O
projection	O
model	O
are	O
solved	O
to	O
reproject	O
synthetic	O
content	O
into	O
video	O
.	O
</s>
<s>
Camera	B-Algorithm
auto-calibration	I-Algorithm
is	O
a	O
form	O
of	O
sensor	O
ego-structure	B-Algorithm
discovery	I-Algorithm
;	O
the	O
subjective	O
effects	O
of	O
the	O
sensor	O
are	O
separated	O
from	O
the	O
objective	O
effects	O
of	O
the	O
environment	O
leading	O
to	O
a	O
reconstruction	O
of	O
the	O
perceived	O
world	O
without	O
the	O
bias	O
applied	O
by	O
the	O
measurement	O
device	O
.	O
</s>
<s>
This	O
is	O
achieved	O
via	O
the	O
fundamental	O
assumption	O
that	O
images	O
are	O
projected	O
from	O
a	O
Euclidean	O
space	O
through	O
a	O
linear	O
,	O
5	O
degree	O
of	O
freedom	O
(	O
in	O
the	O
simplest	O
case	O
)	O
,	O
pinhole	B-Algorithm
camera	I-Algorithm
model	I-Algorithm
with	O
non-linear	O
optical	O
distortion	O
.	O
</s>
<s>
The	O
linear	O
pinhole	O
parameters	O
are	O
the	O
focal	B-Algorithm
length	I-Algorithm
,	O
the	O
aspect	O
ratio	O
,	O
the	O
skew	O
,	O
and	O
the	O
2D	O
principal	O
point	O
.	O
</s>
<s>
A	O
mathematical	O
theory	O
for	O
general	O
multi-view	O
camera	B-Algorithm
self-calibration	O
was	O
originally	O
demonstrated	O
in	O
1992	O
by	O
Olivier	O
Faugeras	O
,	O
QT	O
Luong	O
,	O
and	O
Stephen	O
J	O
.	O
Maybank	O
.	O
</s>
<s>
Quality	O
modern	O
imaging	B-Architecture
sensors	I-Architecture
and	O
optics	O
may	O
also	O
provide	O
further	O
prior	O
constraints	O
on	O
the	O
calibration	O
such	O
as	O
zero	O
skew	O
(	O
orthogonal	O
pixel	O
grid	O
)	O
and	O
unity	O
aspect	O
ratio	O
(	O
square	O
pixels	O
)	O
.	O
</s>
<s>
Given	O
set	O
of	O
cameras	O
and	O
3D	O
points	O
reconstructed	O
up	O
to	O
projective	O
ambiguity	O
(	O
using	O
,	O
for	O
example	O
,	O
bundle	B-General_Concept
adjustment	I-General_Concept
method	O
)	O
we	O
wish	O
to	O
define	O
rectifying	O
homography	O
such	O
that	O
is	O
a	O
metric	O
reconstruction	O
.	O
</s>
<s>
After	O
that	O
internal	O
camera	B-Algorithm
parameters	O
can	O
be	O
easily	O
calculated	O
using	O
camera	B-General_Concept
matrix	I-General_Concept
factorization	O
.	O
</s>
