<s>
A	O
vanishing	B-General_Concept
point	I-General_Concept
is	O
a	O
point	O
on	O
the	O
image	O
plane	O
of	O
a	O
perspective	B-Architecture
rendering	I-Architecture
where	O
the	O
two-dimensional	O
perspective	B-Architecture
projections	I-Architecture
of	O
mutually	O
parallel	O
lines	O
in	O
three-dimensional	O
space	O
appear	O
to	O
converge	O
.	O
</s>
<s>
When	O
the	O
set	O
of	O
parallel	O
lines	O
is	O
perpendicular	O
to	O
a	O
picture	O
plane	O
,	O
the	O
construction	O
is	O
known	O
as	O
one-point	O
perspective	O
,	O
and	O
their	O
vanishing	B-General_Concept
point	I-General_Concept
corresponds	O
to	O
the	O
oculus	O
,	O
or	O
"	O
eye	O
point	O
"	O
,	O
from	O
which	O
the	O
image	O
should	O
be	O
viewed	O
for	O
correct	O
perspective	B-Architecture
geometry	I-Architecture
.	O
</s>
<s>
Traditional	O
linear	O
drawings	O
use	O
objects	O
with	O
one	O
to	O
three	O
sets	O
of	O
parallels	O
,	O
defining	O
one	O
to	O
three	O
vanishing	B-General_Concept
points	I-General_Concept
.	O
</s>
<s>
Italian	O
humanist	O
polymath	O
and	O
architect	O
Leon	O
Battista	O
Alberti	O
first	O
introduced	O
the	O
concept	O
in	O
his	O
treatise	O
on	O
perspective	B-Architecture
in	I-Architecture
art	I-Architecture
,	O
De	O
pictura	O
,	O
written	O
in	O
1435	O
.	O
</s>
<s>
The	O
vanishing	B-General_Concept
point	I-General_Concept
may	O
also	O
be	O
referred	O
to	O
as	O
the	O
"	O
direction	O
point	O
"	O
,	O
as	O
lines	O
having	O
the	O
same	O
directional	O
vector	O
,	O
say	O
D	O
,	O
will	O
have	O
the	O
same	O
vanishing	B-General_Concept
point	I-General_Concept
.	O
</s>
<s>
If	O
we	O
consider	O
a	O
straight	O
line	O
in	O
space	O
with	O
the	O
unit	O
vector	O
and	O
its	O
vanishing	B-General_Concept
point	I-General_Concept
,	O
the	O
unit	O
vector	O
associated	O
with	O
is	O
equal	O
to	O
,	O
assuming	O
both	O
point	O
towards	O
the	O
image	O
plane	O
.	O
</s>
<s>
When	O
the	O
image	O
plane	O
is	O
parallel	O
to	O
two	O
world-coordinate	O
axes	O
,	O
lines	O
parallel	O
to	O
the	O
axis	O
that	O
is	O
cut	O
by	O
this	O
image	O
plane	O
will	O
have	O
images	O
that	O
meet	O
at	O
a	O
single	O
vanishing	B-General_Concept
point	I-General_Concept
.	O
</s>
<s>
Lines	O
parallel	O
to	O
the	O
other	O
two	O
axes	O
will	O
not	O
form	O
vanishing	B-General_Concept
points	I-General_Concept
as	O
they	O
are	O
parallel	O
to	O
the	O
image	O
plane	O
.	O
</s>
<s>
Similarly	O
,	O
when	O
the	O
image	O
plane	O
intersects	O
two	O
world-coordinate	O
axes	O
,	O
lines	O
parallel	O
to	O
those	O
planes	O
will	O
meet	O
form	O
two	O
vanishing	B-General_Concept
points	I-General_Concept
in	O
the	O
picture	O
plane	O
.	O
</s>
<s>
In	O
three-point	O
perspective	O
the	O
image	O
plane	O
intersects	O
the	O
,	O
,	O
and	O
axes	O
and	O
therefore	O
lines	O
parallel	O
to	O
these	O
axes	O
intersect	O
,	O
resulting	O
in	O
three	O
different	O
vanishing	B-General_Concept
points	I-General_Concept
.	O
</s>
<s>
The	O
vanishing	B-General_Concept
point	I-General_Concept
theorem	O
is	O
the	O
principal	O
theorem	O
in	O
the	O
science	O
of	O
perspective	O
.	O
</s>
<s>
It	O
says	O
that	O
the	O
image	O
in	O
a	O
picture	O
plane	O
of	O
a	O
line	O
in	O
space	O
,	O
not	O
parallel	O
to	O
the	O
picture	O
,	O
is	O
determined	O
by	O
its	O
intersection	O
with	O
and	O
its	O
vanishing	B-General_Concept
point	I-General_Concept
.	O
</s>
<s>
Some	O
authors	O
have	O
used	O
the	O
phrase	O
,	O
"	O
the	O
image	O
of	O
a	O
line	O
includes	O
its	O
vanishing	B-General_Concept
point	I-General_Concept
"	O
.	O
</s>
<s>
Brook	O
Taylor	O
wrote	O
the	O
first	O
book	O
in	O
English	O
on	O
perspective	O
in	O
1714	O
,	O
which	O
introduced	O
the	O
term	O
"	O
vanishing	B-General_Concept
point	I-General_Concept
"	O
and	O
was	O
the	O
first	O
to	O
fully	O
explain	O
the	O
geometry	O
of	O
multipoint	O
perspective	O
,	O
and	O
historian	O
Kirsti	O
Andersen	O
compiled	O
these	O
observations	O
.	O
</s>
<s>
She	O
notes	O
,	O
in	O
terms	O
of	O
projective	O
geometry	O
,	O
the	O
vanishing	B-General_Concept
point	I-General_Concept
is	O
the	O
image	O
of	O
the	O
point	O
at	O
infinity	O
associated	O
with	O
,	O
as	O
the	O
sightline	O
from	O
through	O
the	O
vanishing	B-General_Concept
point	I-General_Concept
is	O
parallel	O
to	O
.	O
</s>
<s>
As	O
a	O
vanishing	B-General_Concept
point	I-General_Concept
originates	O
in	O
a	O
line	O
,	O
so	O
a	O
vanishing	O
line	O
originates	O
in	O
a	O
plane	O
that	O
is	O
not	O
parallel	O
to	O
the	O
picture	O
.	O
</s>
<s>
For	O
different	O
sets	O
of	O
lines	O
parallel	O
to	O
this	O
plane	O
,	O
their	O
respective	O
vanishing	B-General_Concept
points	I-General_Concept
will	O
lie	O
on	O
this	O
vanishing	O
line	O
.	O
</s>
<s>
the	O
vanishing	B-General_Concept
point	I-General_Concept
associated	O
with	O
that	O
pair	O
,	O
on	O
a	O
horizon	O
line	O
,	O
or	O
vanishing	O
line	O
formed	O
by	O
the	O
intersection	O
of	O
the	O
image	O
plane	O
with	O
the	O
plane	O
parallel	O
to	O
and	O
passing	O
through	O
the	O
pinhole	O
.	O
</s>
<s>
This	O
is	O
the	O
vanishing	B-General_Concept
point	I-General_Concept
corresponding	O
to	O
all	O
parallel	O
lines	O
with	O
slope	O
in	O
the	O
plane	O
.	O
</s>
<s>
All	O
vanishing	B-General_Concept
points	I-General_Concept
associated	O
with	O
different	O
lines	O
with	O
different	O
slopes	O
belonging	O
to	O
plane	O
will	O
lie	O
on	O
the	O
axis	O
,	O
which	O
in	O
this	O
case	O
is	O
the	O
horizon	O
line	O
.	O
</s>
<s>
Let	O
,	O
,	O
and	O
be	O
three	O
mutually	O
orthogonal	O
straight	O
lines	O
in	O
space	O
and	O
,	O
,	O
be	O
the	O
three	O
corresponding	O
vanishing	B-General_Concept
points	I-General_Concept
respectively	O
.	O
</s>
<s>
Let	O
,	O
,	O
and	O
be	O
three	O
mutually	O
orthogonal	O
straight	O
lines	O
in	O
space	O
and	O
,	O
,	O
be	O
the	O
three	O
corresponding	O
vanishing	B-General_Concept
points	I-General_Concept
respectively	O
.	O
</s>
<s>
The	O
orthocenter	O
of	O
the	O
triangle	O
with	O
vertices	O
in	O
the	O
three	O
vanishing	B-General_Concept
points	I-General_Concept
is	O
the	O
intersection	O
of	O
the	O
optical	O
axis	O
and	O
the	O
image	O
plane	O
.	O
</s>
<s>
A	O
curvilinear	O
perspective	O
is	O
a	O
drawing	O
with	O
either	O
4	O
or	O
5	O
vanishing	B-General_Concept
points	I-General_Concept
.	O
</s>
<s>
In	O
5-point	O
perspective	O
the	O
vanishing	B-General_Concept
points	I-General_Concept
are	O
mapped	O
into	O
a	O
circle	O
with	O
4	O
vanishing	B-General_Concept
points	I-General_Concept
at	O
the	O
cardinal	O
headings	O
N	O
,	O
W	O
,	O
S	O
,	O
E	O
and	O
one	O
at	O
the	O
circle	O
's	O
origin	O
.	O
</s>
<s>
A	O
reverse	O
perspective	O
is	O
a	O
drawing	O
with	O
vanishing	B-General_Concept
points	I-General_Concept
that	O
are	O
placed	O
outside	O
the	O
painting	O
with	O
the	O
illusion	O
that	O
they	O
are	O
"	O
in	O
front	O
of	O
"	O
the	O
painting	O
.	O
</s>
<s>
Several	O
methods	O
for	O
vanishing	B-General_Concept
point	I-General_Concept
detection	O
make	O
use	O
of	O
the	O
line	O
segments	O
detected	O
in	O
images	O
.	O
</s>
<s>
There	O
are	O
significantly	O
large	O
numbers	O
of	O
vanishing	B-General_Concept
points	I-General_Concept
present	O
in	O
an	O
image	O
.	O
</s>
<s>
Therefore	O
,	O
the	O
aim	O
is	O
to	O
detect	O
the	O
vanishing	B-General_Concept
points	I-General_Concept
that	O
correspond	O
to	O
the	O
principal	O
directions	O
of	O
a	O
scene	O
.	O
</s>
<s>
The	O
first	O
step	O
,	O
called	O
the	O
accumulation	O
step	O
,	O
as	O
the	O
name	O
suggests	O
,	O
clusters	O
the	O
line	O
segments	O
with	O
the	O
assumption	O
that	O
a	O
cluster	O
will	O
have	O
a	O
common	O
vanishing	B-General_Concept
point	I-General_Concept
.	O
</s>
<s>
A	O
line	O
segment	O
on	O
the	O
image	O
corresponds	O
to	O
a	O
great	O
circle	O
on	O
this	O
sphere	O
,	O
and	O
the	O
vanishing	B-General_Concept
point	I-General_Concept
in	O
the	O
image	O
is	O
mapped	O
to	O
a	O
point	O
.	O
</s>
<s>
in	O
the	O
image	O
a	O
line	O
segment	O
intersects	O
the	O
vanishing	B-General_Concept
point	I-General_Concept
.	O
</s>
<s>
Several	O
modifications	O
have	O
been	O
made	O
since	O
,	O
but	O
one	O
of	O
the	O
most	O
efficient	O
techniques	O
was	O
using	O
the	O
Hough	B-Algorithm
Transform	I-Algorithm
,	O
mapping	O
the	O
parameters	O
of	O
the	O
line	O
segment	O
to	O
the	O
bounded	O
space	O
.	O
</s>
<s>
Cascaded	O
Hough	B-Algorithm
Transforms	I-Algorithm
have	O
been	O
applied	O
for	O
multiple	O
vanishing	B-General_Concept
points	I-General_Concept
.	O
</s>
<s>
Camera	O
calibration	O
:	O
The	O
vanishing	B-General_Concept
points	I-General_Concept
of	O
an	O
image	O
contain	O
important	O
information	O
for	O
camera	O
calibration	O
.	O
</s>
<s>
Various	O
calibration	O
techniques	O
have	O
been	O
introduced	O
using	O
the	O
properties	O
of	O
vanishing	B-General_Concept
points	I-General_Concept
to	O
find	O
intrinsic	O
and	O
extrinsic	O
calibration	O
parameters	O
.	O
</s>
<s>
3D	B-Algorithm
reconstruction	I-Algorithm
:	O
A	O
man-made	O
environment	O
has	O
two	O
main	O
characteristics	O
–	O
several	O
lines	O
in	O
the	O
scene	O
are	O
parallel	O
,	O
and	O
a	O
number	O
of	O
edges	O
present	O
are	O
orthogonal	O
.	O
</s>
<s>
Vanishing	B-General_Concept
points	I-General_Concept
aid	O
in	O
comprehending	O
the	O
environment	O
.	O
</s>
<s>
Using	O
sets	O
of	O
parallel	O
lines	O
in	O
the	O
plane	O
,	O
the	O
orientation	O
of	O
the	O
plane	O
can	O
be	O
calculated	O
using	O
vanishing	B-General_Concept
points	I-General_Concept
.	O
</s>
<s>
Torre	O
and	O
Coelho	O
performed	O
extensive	O
investigation	O
in	O
the	O
use	O
of	O
vanishing	B-General_Concept
points	I-General_Concept
to	O
implement	O
a	O
full	O
system	O
.	O
</s>
<s>
With	O
the	O
assumption	O
that	O
the	O
environment	O
consists	O
of	O
objects	O
with	O
only	O
parallel	O
or	O
perpendicular	O
sides	O
,	O
also	O
called	O
Lego-land	O
,	O
using	O
vanishing	B-General_Concept
points	I-General_Concept
constructed	O
in	O
a	O
single	O
image	O
of	O
the	O
scene	O
they	O
recovered	O
the	O
3D	O
geometry	O
of	O
the	O
scene	O
.	O
</s>
<s>
Similar	O
ideas	O
are	O
also	O
used	O
in	O
the	O
field	O
of	O
robotics	O
,	O
mainly	O
in	O
navigation	O
and	O
autonomous	O
vehicles	O
,	O
and	O
in	O
areas	O
concerned	O
with	O
object	B-General_Concept
detection	I-General_Concept
.	O
</s>
