<s>
The	O
collinearity	B-General_Concept
equations	I-General_Concept
are	O
a	O
set	O
of	O
two	O
equations	O
,	O
used	O
in	O
photogrammetry	B-Application
and	O
computer	B-Algorithm
stereo	I-Algorithm
vision	I-Algorithm
,	O
to	O
relate	O
coordinates	O
in	O
a	O
sensor	O
plane	O
(	O
in	O
two	O
dimensions	O
)	O
to	O
object	O
coordinates	O
(	O
in	O
three	O
dimensions	O
)	O
.	O
</s>
<s>
The	O
equations	O
originate	O
from	O
the	O
central	O
projection	O
of	O
a	O
point	O
of	O
the	O
object	O
through	O
the	O
optical	O
centre	O
of	O
the	O
camera	B-Algorithm
to	O
the	O
image	O
on	O
the	O
sensor	O
plane	O
.	O
</s>
<s>
The	O
point	O
P	O
is	O
normally	O
given	O
in	O
some	O
coordinate	O
system	O
"	O
outside	O
"	O
the	O
camera	B-Algorithm
by	O
the	O
coordinates	O
X	O
,	O
Y	O
and	O
Z	O
,	O
and	O
the	O
projection	O
centre	O
by	O
.	O
</s>
<s>
These	O
coordinates	O
may	O
be	O
transformed	O
through	O
a	O
rotation	B-General_Concept
and	O
a	O
translation	O
to	O
the	O
system	O
on	O
the	O
camera	B-Algorithm
.	O
</s>
<s>
The	O
translation	O
does	O
n't	O
influence	O
the	O
differences	O
of	O
the	O
coordinates	O
,	O
and	O
the	O
rotation	B-General_Concept
,	O
often	O
called	O
camera	B-Algorithm
transform	O
,	O
is	O
given	O
by	O
a	O
3×	O
3-matrix	O
R	O
,	O
transforming	O
into	O
:	O
</s>
<s>
Substitution	O
of	O
these	O
expressions	O
,	O
leads	O
to	O
a	O
set	O
of	O
two	O
equations	O
,	O
known	O
as	O
the	O
collinearity	B-General_Concept
equations	I-General_Concept
:	O
</s>
<s>
The	O
most	O
obvious	O
use	O
of	O
these	O
equations	O
is	O
for	O
images	O
recorded	O
by	O
a	O
camera	B-Algorithm
.	O
</s>
<s>
It	O
forms	O
the	O
basis	O
for	O
the	O
equations	O
used	O
in	O
bundle	B-General_Concept
adjustment	I-General_Concept
.	O
</s>
<s>
They	O
indicate	O
that	O
the	O
image	O
point	O
(	O
on	O
the	O
sensor	O
plate	O
of	O
the	O
camera	B-Algorithm
)	O
,	O
the	O
observed	O
point	O
(	O
on	O
the	O
object	O
)	O
and	O
the	O
projection	O
center	O
of	O
the	O
camera	B-Algorithm
were	O
aligned	O
when	O
the	O
picture	O
was	O
taken	O
.	O
</s>
