<s>
In	O
computer	B-Application
vision	I-Application
,	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
is	O
a	O
3×3	O
matrix	B-Architecture
which	O
relates	O
corresponding	B-Algorithm
points	I-Algorithm
in	O
stereo	O
images	O
.	O
</s>
<s>
In	O
epipolar	B-Algorithm
geometry	I-Algorithm
,	O
with	O
homogeneous	O
image	O
coordinates	O
,	O
x	O
and	O
x′	O
,	O
of	O
corresponding	B-Algorithm
points	I-Algorithm
in	O
a	O
stereo	B-Algorithm
image	I-Algorithm
pair	O
,	O
Fx	O
describes	O
a	O
line	O
(	O
an	O
epipolar	B-Algorithm
line	O
)	O
on	O
which	O
the	O
corresponding	B-Algorithm
point	I-Algorithm
x′	O
on	O
the	O
other	O
image	O
must	O
lie	O
.	O
</s>
<s>
Being	O
of	O
rank	O
two	O
and	O
determined	O
only	O
up	O
to	O
scale	O
,	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
can	O
be	O
estimated	O
given	O
at	O
least	O
seven	O
point	B-Algorithm
correspondences	I-Algorithm
.	O
</s>
<s>
Its	O
seven	O
parameters	O
represent	O
the	O
only	O
geometric	O
information	O
about	O
cameras	O
that	O
can	O
be	O
obtained	O
through	O
point	B-Algorithm
correspondences	I-Algorithm
alone	O
.	O
</s>
<s>
The	O
term	O
"	O
fundamental	B-General_Concept
matrix	I-General_Concept
"	O
was	O
coined	O
by	O
QT	O
Luong	O
in	O
his	O
influential	O
PhD	O
thesis	O
.	O
</s>
<s>
It	O
is	O
sometimes	O
also	O
referred	O
to	O
as	O
the	O
"	O
bifocal	B-General_Concept
tensor	I-General_Concept
"	O
.	O
</s>
<s>
The	O
above	O
relation	O
which	O
defines	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
was	O
published	O
in	O
1992	O
by	O
both	O
Olivier	O
Faugeras	O
and	O
Richard	O
Hartley	O
.	O
</s>
<s>
Although	O
H	O
.	O
Christopher	O
Longuet-Higgins	O
'	O
essential	B-General_Concept
matrix	I-General_Concept
satisfies	O
a	O
similar	O
relationship	O
,	O
the	O
essential	B-General_Concept
matrix	I-General_Concept
is	O
a	O
metric	O
object	O
pertaining	O
to	O
calibrated	O
cameras	O
,	O
while	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
describes	O
the	O
correspondence	O
in	O
more	O
general	O
and	O
fundamental	O
terms	O
of	O
projective	O
geometry	O
.	O
</s>
<s>
and	O
its	O
corresponding	O
essential	B-General_Concept
matrix	I-General_Concept
,	O
</s>
<s>
The	O
fundamental	B-General_Concept
matrix	I-General_Concept
is	O
a	O
relationship	O
between	O
any	O
two	O
images	O
of	O
the	O
same	O
scene	O
that	O
constrains	O
where	O
the	O
projection	O
of	O
points	O
from	O
the	O
scene	O
can	O
occur	O
in	O
both	O
images	O
.	O
</s>
<s>
Given	O
the	O
projection	O
of	O
a	O
scene	O
point	O
into	O
one	O
of	O
the	O
images	O
the	O
corresponding	B-Algorithm
point	I-Algorithm
in	O
the	O
other	O
image	O
is	O
constrained	O
to	O
a	O
line	O
,	O
helping	O
the	O
search	O
,	O
and	O
allowing	O
for	O
the	O
detection	O
of	O
wrong	O
correspondences	O
.	O
</s>
<s>
The	O
relation	O
between	O
corresponding	B-Algorithm
points	I-Algorithm
,	O
which	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
represents	O
,	O
is	O
referred	O
to	O
as	O
epipolar	B-Algorithm
constraint	I-Algorithm
,	O
matching	O
constraint	O
,	O
discrete	O
matching	O
constraint	O
,	O
or	O
incidence	O
relation	O
.	O
</s>
<s>
The	O
fundamental	B-General_Concept
matrix	I-General_Concept
can	O
be	O
determined	O
by	O
a	O
set	O
of	O
point	B-Algorithm
correspondences	I-Algorithm
.	O
</s>
<s>
Additionally	O
,	O
these	O
corresponding	O
image	O
points	O
may	O
be	O
triangulated	O
to	O
world	O
points	O
with	O
the	O
help	O
of	O
camera	O
matrices	O
derived	O
directly	O
from	O
this	O
fundamental	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
The	O
scene	O
composed	O
of	O
these	O
world	O
points	O
is	O
within	O
a	O
projective	B-Algorithm
transformation	I-Algorithm
of	O
the	O
true	O
scene	O
.	O
</s>
<s>
Say	O
we	O
transform	O
space	O
by	O
a	O
general	O
homography	B-Algorithm
matrix	B-Architecture
such	O
that	O
.	O
</s>
<s>
The	O
fundamental	B-General_Concept
matrix	I-General_Concept
can	O
also	O
be	O
derived	O
using	O
the	O
coplanarity	O
condition	O
.	O
</s>
<s>
The	O
fundamental	B-General_Concept
matrix	I-General_Concept
expresses	O
the	O
epipolar	B-Algorithm
geometry	I-Algorithm
in	O
stereo	O
images	O
.	O
</s>
<s>
The	O
epipolar	B-Algorithm
geometry	I-Algorithm
in	O
images	O
taken	O
with	O
perspective	O
cameras	O
appears	O
as	O
straight	O
lines	O
.	O
</s>
<s>
Therefore	O
,	O
there	O
are	O
multiple	O
projection	O
centers	O
for	O
one	O
image	O
scene	O
and	O
the	O
epipolar	B-Algorithm
line	O
is	O
formed	O
as	O
an	O
epipolar	B-Algorithm
curve	O
.	O
</s>
<s>
However	O
,	O
in	O
special	O
conditions	O
such	O
as	O
small	O
image	O
tiles	O
,	O
the	O
satellite	O
images	O
could	O
be	O
rectified	O
using	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
.	O
</s>
<s>
The	O
fundamental	B-General_Concept
matrix	I-General_Concept
is	O
of	O
rank	O
2	O
.	O
</s>
<s>
Its	O
kernel	B-Algorithm
defines	O
the	O
epipole	O
.	O
</s>
