<s>
In	O
computer	B-Application
vision	I-Application
,	O
the	O
trifocal	B-Algorithm
tensor	I-Algorithm
(	O
also	O
tritensor	O
)	O
is	O
a	O
3×3×3	O
array	O
of	O
numbers	O
(	O
i.e.	O
,	O
a	O
tensor	B-Device
)	O
that	O
incorporates	O
all	O
projective	O
geometric	O
relationships	O
among	O
three	O
views	O
.	O
</s>
<s>
It	O
relates	O
the	O
coordinates	O
of	O
corresponding	O
points	O
or	O
lines	O
in	O
three	O
views	O
,	O
being	O
independent	O
of	O
the	O
scene	O
structure	O
and	O
depending	O
only	O
on	O
the	O
relative	O
motion	O
(	O
i.e.	O
,	O
pose	B-Architecture
)	O
among	O
the	O
three	O
views	O
and	O
their	O
intrinsic	O
calibration	O
parameters	O
.	O
</s>
<s>
Hence	O
,	O
the	O
trifocal	B-Algorithm
tensor	I-Algorithm
can	O
be	O
considered	O
as	O
the	O
generalization	O
of	O
the	O
fundamental	B-General_Concept
matrix	I-General_Concept
in	O
three	O
views	O
.	O
</s>
<s>
It	O
is	O
noted	O
that	O
despite	O
the	O
tensor	B-Device
being	O
made	O
up	O
of	O
27	O
elements	O
,	O
only	O
18	O
of	O
them	O
are	O
actually	O
independent	O
.	O
</s>
<s>
There	O
is	O
also	O
a	O
so-called	O
calibrated	O
trifocal	B-Algorithm
tensor	I-Algorithm
,	O
which	O
relates	O
the	O
coordinates	O
of	O
points	O
and	O
lines	O
in	O
three	O
views	O
given	O
their	O
intrinsic	O
parameters	O
and	O
encodes	O
the	O
relative	O
pose	B-Architecture
of	O
the	O
cameras	O
up	O
to	O
global	O
scale	O
,	O
totalling	O
11	O
independent	O
elements	O
or	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
The	O
tensor	B-Device
can	O
also	O
be	O
seen	O
as	O
a	O
collection	O
of	O
three	O
rank-two	O
3	O
x	O
3	O
matrices	O
known	O
as	O
its	O
correlation	O
slices	O
.	O
</s>
<s>
Assuming	O
that	O
the	O
projection	B-General_Concept
matrices	I-General_Concept
of	O
three	O
views	O
are	O
,	O
and	O
,	O
the	O
correlation	O
slices	O
of	O
the	O
corresponding	O
tensor	B-Device
can	O
be	O
expressed	O
in	O
closed	O
form	O
as	O
,	O
where	O
are	O
respectively	O
the	O
ith	O
columns	O
of	O
the	O
camera	O
matrices	O
.	O
</s>
<s>
In	O
practice	O
,	O
however	O
,	O
the	O
tensor	B-Device
is	O
estimated	O
from	O
point	O
and	O
line	O
matches	O
across	O
the	O
three	O
views	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
important	O
properties	O
of	O
the	O
trifocal	B-Algorithm
tensor	I-Algorithm
is	O
that	O
it	O
gives	O
rise	O
to	O
linear	O
relationships	O
between	O
lines	O
and	O
points	O
in	O
three	O
images	O
.	O
</s>
<s>
Given	O
the	O
trifocal	B-Algorithm
tensor	I-Algorithm
of	O
three	O
views	O
and	O
a	O
pair	O
of	O
matched	O
points	O
in	O
two	O
views	O
,	O
it	O
is	O
possible	O
to	O
determine	O
the	O
location	O
of	O
the	O
point	O
in	O
the	O
third	O
view	O
without	O
any	O
further	O
information	O
.	O
</s>
<s>
The	O
transfer	O
of	O
third-order	O
models	O
reflecting	O
space	O
torsion	O
using	O
calibrated	O
trifocal	B-Algorithm
tensors	I-Algorithm
have	O
been	O
studied	O
,	O
but	O
remains	O
an	O
open	O
problem	O
for	O
uncalibrated	O
trifocal	B-Algorithm
tensors	I-Algorithm
.	O
</s>
<s>
The	O
case	O
estimating	O
the	O
trifocal	B-Algorithm
tensor	I-Algorithm
from	O
9	O
line	O
correspondences	O
has	O
only	O
recently	O
been	O
solved	O
.	O
</s>
<s>
Estimating	O
the	O
calibrated	O
trifocal	B-Algorithm
tensor	I-Algorithm
has	O
been	O
cited	O
as	O
notoriously	O
difficult	O
,	O
and	O
requires	O
4	O
point	O
correspondences	O
.	O
</s>
