<s>
Image	B-Algorithm
stitching	I-Algorithm
or	O
photo	B-Algorithm
stitching	I-Algorithm
is	O
the	O
process	O
of	O
combining	O
multiple	O
photographic	O
images	O
with	O
overlapping	O
fields	O
of	O
view	O
to	O
produce	O
a	O
segmented	O
panorama	B-Application
or	O
high-resolution	O
image	O
.	O
</s>
<s>
Commonly	O
performed	O
through	O
the	O
use	O
of	O
computer	B-Application
software	I-Application
,	O
most	O
approaches	O
to	O
image	B-Algorithm
stitching	I-Algorithm
require	O
nearly	O
exact	O
overlaps	O
between	O
images	O
and	O
identical	O
exposures	O
to	O
produce	O
seamless	O
results	O
,	O
although	O
some	O
stitching	O
algorithms	O
actually	O
benefit	O
from	O
differently	O
exposed	O
images	O
by	O
doing	O
high-dynamic-range	O
imaging	O
in	O
regions	O
of	O
overlap	O
.	O
</s>
<s>
Some	O
digital	B-Device
cameras	I-Device
can	O
stitch	O
their	O
photos	O
internally	O
.	O
</s>
<s>
Image	B-Algorithm
stitching	I-Algorithm
is	O
widely	O
used	O
in	O
modern	O
applications	O
,	O
such	O
as	O
the	O
following	O
:	O
</s>
<s>
The	O
image	B-Algorithm
stitching	I-Algorithm
process	O
can	O
be	O
divided	O
into	O
three	O
main	O
components	O
:	O
image	B-Algorithm
registration	I-Algorithm
,	O
calibration	O
,	O
and	O
blending	O
.	O
</s>
<s>
Distinctive	O
features	O
can	O
be	O
found	O
in	O
each	O
image	O
and	O
then	O
efficiently	O
matched	O
to	O
rapidly	O
establish	O
correspondences	B-Algorithm
between	O
pairs	O
of	O
images	O
.	O
</s>
<s>
When	O
multiple	O
images	O
exist	O
in	O
a	O
panorama	B-Application
,	O
techniques	O
have	O
been	O
developed	O
to	O
compute	O
a	O
globally	O
consistent	O
set	O
of	O
alignments	O
and	O
to	O
efficiently	O
discover	O
which	O
images	O
overlap	O
one	O
another	O
.	O
</s>
<s>
A	O
final	O
compositing	O
surface	O
onto	O
which	O
to	O
warp	O
or	O
projectively	O
transform	O
and	O
place	O
all	O
of	O
the	O
aligned	O
images	O
is	O
needed	O
,	O
as	O
are	O
algorithms	O
to	O
seamlessly	O
blend	O
the	O
overlapping	O
images	O
,	O
even	O
in	O
the	O
presence	O
of	O
parallax	B-Device
,	O
lens	O
distortion	O
,	O
scene	O
motion	O
,	O
and	O
exposure	O
differences	O
.	O
</s>
<s>
Other	O
major	O
issues	O
to	O
deal	O
with	O
are	O
the	O
presence	O
of	O
parallax	B-Device
,	O
lens	O
distortion	O
,	O
scene	O
motion	O
,	O
and	O
exposure	O
differences	O
.	O
</s>
<s>
Additionally	O
,	O
the	O
aspect	O
ratio	O
of	O
a	O
panorama	B-Application
image	O
needs	O
to	O
be	O
taken	O
into	O
account	O
to	O
create	O
a	O
visually	O
pleasing	O
composite	O
.	O
</s>
<s>
For	O
panoramic	B-Application
stitching	O
,	O
the	O
ideal	O
set	O
of	O
images	O
will	O
have	O
a	O
reasonable	O
amount	O
of	O
overlap	O
(	O
at	O
least	O
15	O
–	O
30%	O
)	O
to	O
overcome	O
lens	O
distortion	O
and	O
have	O
enough	O
detectable	O
features	O
.	O
</s>
<s>
Feature	O
detection	O
is	O
necessary	O
to	O
automatically	O
find	O
correspondences	B-Algorithm
between	O
images	O
.	O
</s>
<s>
Robust	O
correspondences	B-Algorithm
are	O
required	O
in	O
order	O
to	O
estimate	O
the	O
necessary	O
transformation	O
to	O
align	O
an	O
image	O
with	O
the	O
image	O
it	O
is	O
being	O
composited	O
on	O
.	O
</s>
<s>
Corners	O
,	O
blobs	O
,	O
Harris	O
corners	O
,	O
and	O
differences	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
of	O
Harris	O
corners	O
are	O
good	O
features	O
since	O
they	O
are	O
repeatable	O
and	O
distinct	O
.	O
</s>
<s>
Like	O
Moravec	O
,	O
they	O
needed	O
a	O
method	O
to	O
match	O
corresponding	B-Algorithm
points	I-Algorithm
in	O
consecutive	O
image	O
frames	O
,	O
but	O
were	O
interested	O
in	O
tracking	O
both	O
corners	O
and	O
edges	O
between	O
frames	O
.	O
</s>
<s>
SIFT	B-Algorithm
and	O
SURF	B-Algorithm
are	O
recent	O
key-point	O
or	O
interest	O
point	O
detector	O
algorithms	O
but	O
a	O
point	O
to	O
note	O
is	O
that	O
SURF	B-Algorithm
is	O
patented	O
and	O
its	O
commercial	O
usage	O
restricted	O
.	O
</s>
<s>
Once	O
a	O
feature	O
has	O
been	O
detected	O
,	O
a	O
descriptor	O
method	O
like	O
SIFT	B-Algorithm
descriptor	O
can	O
be	O
applied	O
to	O
later	O
match	O
them	O
.	O
</s>
<s>
Image	B-Algorithm
registration	I-Algorithm
involves	O
matching	O
features	O
in	O
a	O
set	O
of	O
images	O
or	O
using	O
direct	O
alignment	O
methods	O
to	O
search	O
for	O
image	O
alignments	O
that	O
minimize	O
the	O
sum	B-Algorithm
of	I-Algorithm
absolute	I-Algorithm
differences	I-Algorithm
between	O
overlapping	O
pixels	O
.	O
</s>
<s>
Additionally	O
,	O
users	O
may	O
input	O
a	O
rough	O
model	O
of	O
the	O
panorama	B-Application
to	O
help	O
the	O
feature	O
matching	O
stage	O
,	O
so	O
that	O
e.g.	O
</s>
<s>
To	O
estimate	O
a	O
robust	O
model	O
from	O
the	O
data	O
,	O
a	O
common	O
method	O
used	O
is	O
known	O
as	O
RANSAC	B-Algorithm
.	O
</s>
<s>
The	O
name	O
RANSAC	B-Algorithm
is	O
an	O
abbreviation	O
for	O
"	O
RANdom	B-Algorithm
SAmple	I-Algorithm
Consensus	I-Algorithm
"	O
.	O
</s>
<s>
The	O
RANSAC	B-Algorithm
algorithm	O
has	O
found	O
many	O
applications	O
in	O
computer	O
vision	O
,	O
including	O
the	O
simultaneous	O
solving	O
of	O
the	O
correspondence	B-Algorithm
problem	I-Algorithm
and	O
the	O
estimation	O
of	O
the	O
fundamental	O
matrix	O
related	O
to	O
a	O
pair	O
of	O
stereo	O
cameras	O
.	O
</s>
<s>
For	O
the	O
problem	O
of	O
homography	B-Algorithm
estimation	O
,	O
RANSAC	B-Algorithm
works	O
by	O
trying	O
to	O
fit	O
several	O
models	O
using	O
some	O
of	O
the	O
point	O
pairs	O
and	O
then	O
checking	O
if	O
the	O
models	O
were	O
able	O
to	O
relate	O
most	O
of	O
the	O
points	O
.	O
</s>
<s>
The	O
best	O
model	O
–	O
the	O
homography	B-Algorithm
,	O
which	O
produces	O
the	O
highest	O
number	O
of	O
correct	O
matches	O
–	O
is	O
then	O
chosen	O
as	O
the	O
answer	O
for	O
the	O
problem	O
;	O
thus	O
,	O
if	O
the	O
ratio	O
of	O
number	O
of	O
outliers	O
to	O
data	O
points	O
is	O
very	O
low	O
,	O
the	O
RANSAC	B-Algorithm
outputs	O
a	O
decent	O
model	O
fitting	O
the	O
data	O
.	O
</s>
<s>
Panotools	B-Application
and	O
its	O
various	O
derivative	O
programs	O
use	O
this	O
method	O
.	O
</s>
<s>
Alignment	O
,	O
in	O
simple	O
terms	O
,	O
is	O
a	O
change	O
in	O
the	O
coordinates	O
system	O
so	O
that	O
it	O
adopts	O
a	O
new	O
coordinate	O
system	O
which	O
outputs	O
image	B-Algorithm
matching	I-Algorithm
the	O
required	O
viewpoint	O
.	O
</s>
<s>
The	O
types	O
of	O
transformations	O
an	O
image	O
may	O
go	O
through	O
are	O
pure	O
translation	O
,	O
pure	O
rotation	O
,	O
a	O
similarity	O
transform	O
which	O
includes	O
translation	O
,	O
rotation	O
and	O
scaling	O
of	O
the	O
image	O
which	O
needs	O
to	O
be	O
transformed	O
,	O
Affine	B-Algorithm
or	O
projective	O
transform	O
.	O
</s>
<s>
Projective	O
transformation	O
is	O
the	O
farthest	O
an	O
image	O
can	O
transform	O
(	O
in	O
the	O
set	O
of	O
two	O
dimensional	O
planar	O
transformations	O
)	O
,	O
where	O
only	O
visible	O
features	O
that	O
are	O
preserved	O
in	O
the	O
transformed	O
image	O
are	O
straight	O
lines	O
whereas	O
parallelism	O
is	O
maintained	O
in	O
an	O
affine	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
where	O
x	O
is	O
points	O
in	O
the	O
old	O
coordinate	O
system	O
,	O
x’	O
is	O
the	O
corresponding	B-Algorithm
points	I-Algorithm
in	O
the	O
transformed	O
image	O
and	O
H	O
is	O
the	O
homography	B-Algorithm
matrix	O
.	O
</s>
<s>
The	O
homography	B-Algorithm
matrix	O
H	O
has	O
8	O
parameters	O
or	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
where	O
A	O
is	O
the	O
matrix	O
constructed	O
using	O
the	O
coordinates	O
of	O
correspondences	B-Algorithm
and	O
h	O
is	O
the	O
one	O
dimensional	O
vector	O
of	O
the	O
9	O
elements	O
of	O
the	O
reshaped	O
homography	B-Algorithm
matrix	O
.	O
</s>
<s>
Since	O
we	O
have	O
8	O
degrees	O
of	O
freedom	O
the	O
algorithm	O
requires	O
at	O
least	O
four	O
point	O
correspondences	B-Algorithm
.	O
</s>
<s>
In	O
case	O
when	O
RANSAC	B-Algorithm
is	O
used	O
to	O
estimate	O
the	O
homography	B-Algorithm
and	O
multiple	O
correspondences	B-Algorithm
are	O
available	O
the	O
correct	O
homography	B-Algorithm
matrix	O
is	O
the	O
one	O
with	O
the	O
maximum	O
number	O
of	O
inliers	O
.	O
</s>
<s>
Compositing	O
can	O
be	O
automatically	O
done	O
since	O
the	O
algorithm	O
now	O
knows	O
which	O
correspondences	B-Algorithm
overlap	O
.	O
</s>
<s>
Image	O
blending	O
involves	O
executing	O
the	O
adjustments	O
figured	O
out	O
in	O
the	O
calibration	O
stage	O
,	O
combined	O
with	O
remapping	O
of	O
the	O
images	O
to	O
an	O
output	O
projection	B-Application
.	O
</s>
<s>
Colors	O
are	O
adjusted	B-Algorithm
between	O
images	O
to	O
compensate	O
for	O
exposure	O
differences	O
.	O
</s>
<s>
If	O
applicable	O
,	O
high	O
dynamic	O
range	O
merging	O
is	O
done	O
along	O
with	O
motion	B-Algorithm
compensation	I-Algorithm
and	O
deghosting	O
.	O
</s>
<s>
For	O
image	O
segments	O
that	O
have	O
been	O
taken	O
from	O
the	O
same	O
point	O
in	O
space	O
,	O
stitched	B-Algorithm
images	I-Algorithm
can	O
be	O
arranged	O
using	O
one	O
of	O
various	O
map	B-Application
projections	I-Application
.	O
</s>
<s>
Rectilinear	O
projection	B-Application
,	O
where	O
the	O
stitched	B-Algorithm
image	I-Algorithm
is	O
viewed	O
on	O
a	O
two-dimensional	O
plane	O
intersecting	O
the	O
panosphere	O
in	O
a	O
single	O
point	O
.	O
</s>
<s>
One	O
case	O
of	O
rectilinear	O
projection	B-Application
is	O
the	O
use	O
of	O
cube	O
faces	O
with	O
cubic	O
mapping	O
for	O
panorama	B-Application
viewing	O
.	O
</s>
<s>
Panorama	B-Application
is	O
mapped	O
to	O
six	O
squares	O
,	O
each	O
cube	O
face	O
showing	O
90	O
by	O
90	O
degree	O
area	O
of	O
the	O
panorama	B-Application
.	O
</s>
<s>
Cylindrical	O
projection	B-Application
,	O
where	O
the	O
stitched	B-Algorithm
image	I-Algorithm
shows	O
a	O
360°	O
horizontal	O
field	O
of	O
view	O
and	O
a	O
limited	O
vertical	O
field	O
of	O
view	O
.	O
</s>
<s>
Panoramas	B-Application
in	O
this	O
projection	B-Application
are	O
meant	O
to	O
be	O
viewed	O
as	O
though	O
the	O
image	O
is	O
wrapped	O
into	O
a	O
cylinder	O
and	O
viewed	O
from	O
within	O
.	O
</s>
<s>
Spherical	B-Application
projection	I-Application
or	O
equirectangular	O
projection	B-Application
—	O
which	O
is	O
strictly	O
speaking	O
another	O
cylindrical	O
projection	B-Application
—	O
where	O
the	O
stitched	B-Algorithm
image	I-Algorithm
shows	O
a	O
360°	O
horizontal	O
by	O
180°	O
vertical	O
field	O
of	O
view	O
i.e.	O
</s>
<s>
Panoramas	B-Application
in	O
this	O
projection	B-Application
are	O
meant	O
to	O
be	O
viewed	O
as	O
though	O
the	O
image	O
is	O
wrapped	O
into	O
a	O
sphere	O
and	O
viewed	O
from	O
within	O
.	O
</s>
<s>
When	O
viewed	O
on	O
a	O
2D	O
plane	O
,	O
horizontal	O
lines	O
appear	O
curved	O
as	O
in	O
a	O
cylindrical	O
projection	B-Application
,	O
while	O
vertical	O
lines	O
remain	O
vertical	O
.	O
</s>
<s>
Since	O
a	O
panorama	B-Application
is	O
basically	O
a	O
map	O
of	O
a	O
sphere	O
,	O
various	O
other	O
mapping	O
projections	B-Application
from	O
cartographers	O
can	O
also	O
be	O
used	O
if	O
so	O
desired	O
.	O
</s>
<s>
Additionally	O
there	O
are	O
specialized	O
projections	B-Application
which	O
may	O
have	O
more	O
aesthetically	O
pleasing	O
advantages	O
over	O
normal	O
cartography	O
projections	B-Application
such	O
as	O
Hugin	B-Application
's	O
Panini	O
projection	B-Application
-	O
named	O
after	O
Italian	O
vedutismo	O
painter	O
Giovanni	O
Paolo	O
Panini	O
-	O
or	O
PTgui	B-Language
's	O
Vedutismo	O
projection	B-Application
.	O
</s>
<s>
Different	O
projections	B-Application
may	O
be	O
combined	O
in	O
same	O
image	O
for	O
fine	O
tuning	O
the	O
final	O
look	O
of	O
the	O
output	O
image	O
.	O
</s>
<s>
Stereographic	O
projection	B-Application
or	O
fisheye	O
projection	B-Application
can	O
be	O
used	O
to	O
form	O
a	O
little	O
planet	O
panorama	B-Application
by	O
pointing	O
the	O
virtual	O
camera	O
straight	O
down	O
and	O
setting	O
the	O
field	O
of	O
view	O
large	O
enough	O
to	O
show	O
the	O
whole	O
ground	O
and	O
some	O
of	O
the	O
areas	O
above	O
it	O
;	O
pointing	O
the	O
virtual	O
camera	O
upwards	O
creates	O
a	O
tunnel	O
effect	O
.	O
</s>
<s>
Conformality	O
of	O
the	O
stereographic	O
projection	B-Application
may	O
produce	O
more	O
visually	O
pleasing	O
result	O
than	O
equal	O
area	O
fisheye	O
projection	B-Application
as	O
discussed	O
in	O
the	O
stereo-graphic	O
projection	B-Application
's	O
article	O
.	O
</s>
<s>
The	O
use	O
of	O
images	O
not	O
taken	O
from	O
the	O
same	O
place	O
(	O
on	O
a	O
pivot	O
about	O
the	O
entrance	O
pupil	O
of	O
the	O
camera	O
)	O
can	O
lead	O
to	O
parallax	B-Device
errors	O
in	O
the	O
final	O
product	O
.	O
</s>
<s>
"	O
Blind	O
stitching	O
"	O
through	O
feature-based	O
alignment	O
methods	O
(	O
see	O
autostitch	B-Application
)	O
,	O
as	O
opposed	O
to	O
manual	O
selection	O
and	O
stitching	O
,	O
can	O
cause	O
imperfections	O
in	O
the	O
assembly	O
of	O
the	O
panorama	B-Application
.	O
</s>
<s>
Dedicated	O
programs	O
include	O
Autostitch	B-Application
,	O
Hugin	B-Application
,	O
Ptgui	B-Language
,	O
Panorama	B-Application
Tools	I-Application
,	O
Microsoft	B-Application
Research	I-Application
Image	I-Application
Composite	I-Application
Editor	I-Application
and	O
CleVR	B-Algorithm
Stitcher	I-Algorithm
.	O
</s>
<s>
Many	O
other	O
programs	O
can	O
also	O
stitch	O
multiple	O
images	O
;	O
a	O
popular	O
example	O
is	O
Adobe	O
Systems	O
 '	O
Photoshop	B-Operating_System
,	O
which	O
includes	O
a	O
tool	O
known	O
as	O
Photomerge	O
and	O
,	O
in	O
the	O
latest	O
versions	O
,	O
the	O
new	O
Auto-Blend	O
.	O
</s>
<s>
Image	B-Algorithm
Stitching	I-Algorithm
module	O
for	O
QuickPHOTO	O
microscope	O
software	O
enables	O
to	O
interactively	O
stitch	O
together	O
multiple	O
fields	O
of	O
view	O
from	O
microscope	O
using	O
camera	O
's	O
live	O
view	O
.	O
</s>
