<s>
Georeferencing	B-General_Concept
or	O
georegistration	B-General_Concept
is	O
a	O
type	O
of	O
coordinate	O
transformation	O
that	O
binds	O
a	O
digital	O
raster	O
image	O
or	O
vector	O
database	O
that	O
represents	O
a	O
geographic	O
space	O
(	O
usually	O
a	O
scanned	O
map	O
or	O
aerial	O
photograph	O
)	O
to	O
a	O
spatial	O
reference	O
system	O
,	O
thus	O
locating	O
the	O
digital	O
data	O
in	O
the	O
real	O
world	O
.	O
</s>
<s>
It	O
is	O
thus	O
the	O
geographic	O
form	O
of	O
image	B-Algorithm
registration	I-Algorithm
.	O
</s>
<s>
The	O
most	O
common	O
result	O
is	O
that	O
the	O
image	O
can	O
be	O
visually	O
and	O
analytically	O
integrated	O
with	O
other	O
geographic	O
data	O
in	O
geographic	B-Application
information	I-Application
systems	I-Application
and	O
remote	B-Application
sensing	I-Application
software	O
.	O
</s>
<s>
A	O
number	O
of	O
mathematical	O
methods	O
are	O
available	O
,	O
but	O
the	O
process	O
typically	O
involves	O
identifying	O
several	O
sample	O
ground	O
control	O
points	O
with	O
known	O
locations	O
on	O
the	O
image	O
and	O
the	O
ground	O
,	O
then	O
using	O
curve	B-Algorithm
fitting	I-Algorithm
techniques	O
to	O
generate	O
a	O
parametric	O
(	O
or	O
piecewise	O
parametric	O
)	O
formula	O
to	O
transform	O
the	O
rest	O
of	O
the	O
image	O
.	O
</s>
<s>
Once	O
the	O
parameters	O
of	O
the	O
formula	O
are	O
stored	O
,	O
the	O
image	O
may	O
be	O
transformed	O
dynamically	O
at	O
drawing	O
time	O
,	O
or	O
resampled	O
to	O
generate	O
a	O
georeferenced	O
raster	O
GIS	B-Application
file	O
or	O
orthophoto	B-General_Concept
.	O
</s>
<s>
The	O
term	O
georeferencing	B-General_Concept
has	O
also	O
been	O
used	O
to	O
refer	O
to	O
other	O
types	O
of	O
transformation	O
from	O
general	O
expressions	O
of	O
geographic	O
location	O
(	O
geocodes	O
)	O
to	O
coordinate	O
measurements	O
,	O
but	O
most	O
of	O
these	O
other	O
methods	O
are	O
more	O
commonly	O
called	O
geocoding	B-Application
.	O
</s>
<s>
Because	O
of	O
this	O
ambiguity	O
,	O
Georegistration	B-General_Concept
is	O
preferred	O
by	O
some	O
to	O
refer	O
to	O
the	O
image	O
transformation	O
.	O
</s>
<s>
Occasionally	O
,	O
this	O
process	O
has	O
been	O
called	O
rubbersheeting	B-Application
,	O
but	O
that	O
term	O
is	O
more	O
commonly	O
applied	O
to	O
a	O
very	O
similar	O
process	O
applied	O
to	O
vector	O
GIS	B-Application
data	O
.	O
</s>
<s>
Georeferencing	B-General_Concept
is	O
crucial	O
to	O
make	O
aerial	O
and	O
satellite	O
imagery	O
,	O
usually	O
raster	O
images	O
,	O
useful	O
for	O
mapping	O
as	O
it	O
explains	O
how	O
other	O
data	O
,	O
such	O
as	O
the	O
above	O
GPS	O
points	O
,	O
relate	O
to	O
the	O
imagery	O
.	O
</s>
<s>
Georeferencing	B-General_Concept
tools	O
contain	O
methods	O
to	O
combine	O
and	O
overlay	O
these	O
maps	O
with	O
minimum	O
distortion	O
.	O
</s>
<s>
It	O
is	O
thus	O
the	O
extension	O
of	O
the	O
typical	O
task	O
of	O
curve	B-Algorithm
fitting	I-Algorithm
a	O
relationship	O
between	O
two	O
variables	O
to	O
four	O
dimensions	O
.	O
</s>
<s>
Several	O
types	O
of	O
functions	O
are	O
available	O
in	O
most	O
GIS	B-Application
and	O
remote	B-Application
sensing	I-Application
software	O
for	O
georeferencing	B-General_Concept
.	O
</s>
<s>
As	O
the	O
simplest	O
type	O
of	O
two-dimensional	O
curve	O
is	O
a	O
straight	O
line	O
,	O
so	O
the	O
simplest	O
form	O
of	O
coordinate	O
transformation	O
is	O
a	O
linear	O
transformation	O
,	O
the	O
most	O
common	O
type	O
being	O
the	O
affine	B-Algorithm
transformation	I-Algorithm
:	O
</s>
<s>
The	O
world	O
file	O
developed	O
by	O
Esri	O
is	O
a	O
commonly	O
used	O
sidecar	O
file	O
that	O
specifies	O
these	O
six	O
coefficients	O
for	O
image	O
georeferencing	B-General_Concept
.	O
</s>
<s>
A	O
common	O
example	O
is	O
a	O
Thin	B-Algorithm
plate	I-Algorithm
spline	I-Algorithm
transformation	O
.	O
</s>
<s>
Instead	O
,	O
most	O
GIS	B-Application
and	O
remote	B-Application
sensing	I-Application
software	O
provides	O
an	O
interactive	O
environment	O
for	O
visually	O
aligning	O
the	O
image	O
to	O
the	O
destination	O
coordinate	O
system	O
.	O
</s>
<s>
In	O
most	O
software	O
,	O
these	O
are	O
entered	O
by	O
pointing	O
at	O
the	O
location	O
on	O
the	O
image	O
,	O
then	O
pointing	O
at	O
the	O
same	O
location	O
on	O
a	O
vector	O
base	O
map	O
or	O
orthophoto	B-General_Concept
that	O
is	O
already	O
in	O
the	O
desired	O
coordinate	O
system	O
.	O
</s>
<s>
With	O
a	O
minimal	O
set	O
of	O
GCPs	O
,	O
the	O
known	O
coordinates	O
can	O
be	O
entered	O
into	O
the	O
mathematical	O
equations	O
for	O
the	O
desired	O
type	O
of	O
transformation	O
,	O
which	O
can	O
then	O
be	O
solved	O
using	O
linear	B-Language
algebra	I-Language
to	O
determine	O
the	O
coefficients	O
and	O
derive	O
the	O
formulas	O
to	O
use	O
for	O
the	O
entire	O
grid	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
linear	O
affine	B-Algorithm
transformation	I-Algorithm
above	O
has	O
six	O
unknown	O
coefficients	O
,	O
so	O
six	O
equations	O
with	O
known	O
<>	O
are	O
needed	O
to	O
derive	O
them	O
,	O
which	O
will	O
require	O
three	O
ground	O
control	O
points	O
.	O
</s>
<s>
To	O
avoid	O
this	O
,	O
it	O
is	O
common	O
to	O
create	O
many	O
more	O
than	O
the	O
minimal	O
required	O
set	O
(	O
creating	O
an	O
overdetermined	O
system	O
)	O
,	O
and	O
use	O
least	B-Algorithm
squares	I-Algorithm
regression	O
to	O
derive	O
a	O
set	O
of	O
function	O
parameters	O
that	O
most	O
closely	O
matches	O
the	O
points	O
.	O
</s>
<s>
This	O
is	O
almost	O
never	O
a	O
perfect	O
match	O
,	O
so	O
the	O
variance	O
between	O
each	O
GCP	O
location	O
and	O
the	O
location	O
predicted	O
by	O
the	O
functions	O
can	O
be	O
measured	O
and	O
summarized	O
as	O
a	O
Root-mean-square	B-General_Concept
error	I-General_Concept
(	O
RMSE	B-General_Concept
)	O
.	O
</s>
<s>
A	O
lower	O
RMSE	B-General_Concept
thus	O
means	O
that	O
the	O
transformation	O
formulas	O
closely	O
match	O
the	O
GCPs	O
.	O
</s>
<s>
One	O
option	O
is	O
to	O
save	O
the	O
parameters	O
themselves	O
as	O
a	O
form	O
of	O
metadata	O
,	O
either	O
in	O
the	O
header	O
of	O
the	O
image	O
file	O
itself	O
(	O
e.g.	O
,	O
GeoTIFF	B-Application
)	O
,	O
or	O
in	O
a	O
sidecar	O
file	O
stored	O
alongside	O
the	O
image	O
file	O
(	O
e.g.	O
,	O
a	O
world	O
file	O
)	O
.	O
</s>
<s>
Esri	O
GIS	B-Application
software	I-Application
has	O
had	O
this	O
capability	O
for	O
many	O
years	O
,	O
including	O
the	O
Georeferencing	B-General_Concept
tool	O
in	O
ArcGIS	O
Pro	O
.	O
</s>
<s>
QGIS	B-Application
has	O
a	O
Georeferencer	O
tool	O
,	O
originally	O
developed	O
as	O
an	O
add-on	O
but	O
now	O
integrated	O
into	O
the	O
software	O
.	O
</s>
