<s>
In	O
computer	B-Application
vision	I-Application
,	O
speeded	B-Algorithm
up	I-Algorithm
robust	I-Algorithm
features	I-Algorithm
(	O
SURF	O
)	O
is	O
a	O
patented	O
local	O
feature	B-Algorithm
detector	O
and	O
descriptor	O
.	O
</s>
<s>
It	O
can	O
be	O
used	O
for	O
tasks	O
such	O
as	O
object	O
recognition	O
,	O
image	B-Algorithm
registration	I-Algorithm
,	O
classification	B-General_Concept
,	O
or	O
3D	B-Algorithm
reconstruction	I-Algorithm
.	O
</s>
<s>
It	O
is	O
partly	O
inspired	O
by	O
the	O
scale-invariant	B-Algorithm
feature	I-Algorithm
transform	I-Algorithm
(	O
SIFT	O
)	O
descriptor	O
.	O
</s>
<s>
To	O
detect	O
interest	O
points	O
,	O
SURF	O
uses	O
an	O
integer	O
approximation	O
of	O
the	O
determinant	O
of	O
Hessian	O
blob	B-Algorithm
detector	I-Algorithm
,	O
which	O
can	O
be	O
computed	O
with	O
3	O
integer	O
operations	O
using	O
a	O
precomputed	O
integral	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
Its	O
feature	B-Algorithm
descriptor	O
is	O
based	O
on	O
the	O
sum	O
of	O
the	O
Haar	B-Algorithm
wavelet	I-Algorithm
response	O
around	O
the	O
point	O
of	O
interest	O
.	O
</s>
<s>
These	O
can	O
also	O
be	O
computed	O
with	O
the	O
aid	O
of	O
the	O
integral	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
SURF	O
was	O
first	O
published	O
by	O
Herbert	B-Algorithm
Bay	I-Algorithm
,	O
Tinne	O
Tuytelaars	O
,	O
and	O
Luc	O
Van	O
Gool	O
,	O
and	O
presented	O
at	O
the	O
2006	O
European	O
Conference	O
on	O
Computer	B-Application
Vision	I-Application
.	O
</s>
<s>
The	O
image	O
is	O
transformed	O
into	O
coordinates	O
,	O
using	O
the	O
multi-resolution	B-Algorithm
pyramid	I-Algorithm
technique	I-Algorithm
,	O
to	O
copy	O
the	O
original	O
image	O
with	O
Pyramidal	O
Gaussian	O
or	O
Laplacian	O
Pyramid	B-Algorithm
shape	O
to	O
obtain	O
an	O
image	O
with	O
the	O
same	O
size	O
but	O
with	O
reduced	O
bandwidth	O
.	O
</s>
<s>
This	O
achieves	O
a	O
special	O
blurring	O
effect	O
on	O
the	O
original	O
image	O
,	O
called	O
Scale-Space	B-Algorithm
and	O
ensures	O
that	O
the	O
points	O
of	O
interest	O
are	O
scale	O
invariant	O
.	O
</s>
<s>
SURF	O
uses	O
square-shaped	O
filters	O
as	O
an	O
approximation	O
of	O
Gaussian	B-Error_Name
smoothing	I-Error_Name
.	O
</s>
<s>
Filtering	O
the	O
image	O
with	O
a	O
square	O
is	O
much	O
faster	O
if	O
the	O
integral	B-Algorithm
image	I-Algorithm
is	O
used	O
:	O
</s>
<s>
The	O
sum	O
of	O
the	O
original	O
image	O
within	O
a	O
rectangle	O
can	O
be	O
evaluated	O
quickly	O
using	O
the	O
integral	B-Algorithm
image	I-Algorithm
,	O
requiring	O
evaluations	O
at	O
the	O
rectangle	O
's	O
four	O
corners	O
.	O
</s>
<s>
SURF	O
uses	O
a	O
blob	B-Algorithm
detector	I-Algorithm
based	O
on	O
the	O
Hessian	O
matrix	O
to	O
find	O
points	O
of	O
interest	O
.	O
</s>
<s>
In	O
other	O
feature	B-Algorithm
detection	O
algorithms	O
,	O
the	O
scale	B-Algorithm
space	I-Algorithm
is	O
usually	O
realized	O
as	O
an	O
image	B-Algorithm
pyramid	I-Algorithm
.	O
</s>
<s>
Images	O
are	O
repeatedly	O
smoothed	O
with	O
a	O
Gaussian	O
filter	O
,	O
then	O
they	O
are	O
subsampled	O
to	O
get	O
the	O
next	O
higher	O
level	O
of	O
the	O
pyramid	B-Algorithm
.	O
</s>
<s>
The	O
scale	B-Algorithm
space	I-Algorithm
is	O
divided	O
into	O
a	O
number	O
of	O
octaves	O
,	O
where	O
an	O
octave	O
refers	O
to	O
a	O
series	O
of	O
response	O
maps	O
of	O
covering	O
a	O
doubling	O
of	O
scale	O
.	O
</s>
<s>
In	O
SURF	O
,	O
the	O
lowest	O
level	O
of	O
the	O
scale	B-Algorithm
space	I-Algorithm
is	O
obtained	O
from	O
the	O
output	O
of	O
the	O
9×9	O
filters	O
.	O
</s>
<s>
Hence	O
,	O
unlike	O
previous	O
methods	O
,	O
scale	B-Algorithm
spaces	I-Algorithm
in	O
SURF	O
are	O
implemented	O
by	O
applying	O
box	O
filters	O
of	O
different	O
sizes	O
.	O
</s>
<s>
Accordingly	O
,	O
the	O
scale	B-Algorithm
space	I-Algorithm
is	O
analyzed	O
by	O
up-scaling	O
the	O
filter	O
size	O
rather	O
than	O
iteratively	O
reducing	O
the	O
image	O
size	O
.	O
</s>
<s>
The	O
following	O
layers	O
are	O
obtained	O
by	O
filtering	O
the	O
image	O
with	O
gradually	O
bigger	O
masks	O
,	O
taking	O
into	O
account	O
the	O
discrete	O
nature	O
of	O
integral	B-Algorithm
images	I-Algorithm
and	O
the	O
specific	O
filter	O
structure	O
.	O
</s>
<s>
Scale	B-Algorithm
space	I-Algorithm
interpolation	O
is	O
especially	O
important	O
in	O
this	O
case	O
,	O
as	O
the	O
difference	O
in	O
scale	O
between	O
the	O
first	O
layers	O
of	O
every	O
octave	O
is	O
relatively	O
large	O
.	O
</s>
<s>
The	O
goal	O
of	O
a	O
descriptor	O
is	O
to	O
provide	O
a	O
unique	O
and	O
robust	O
description	O
of	O
an	O
image	B-Algorithm
feature	I-Algorithm
,	O
e.g.	O
,	O
by	O
describing	O
the	O
intensity	O
distribution	O
of	O
the	O
pixels	O
within	O
the	O
neighbourhood	O
of	O
the	O
point	O
of	O
interest	O
.	O
</s>
<s>
The	O
Haar	B-Algorithm
wavelet	I-Algorithm
responses	O
in	O
both	O
x	O
-	O
and	O
y-directions	O
within	O
a	O
circular	O
neighbourhood	O
of	O
radius	O
around	O
the	O
point	O
of	O
interest	O
are	O
computed	O
,	O
where	O
is	O
the	O
scale	O
at	O
which	O
the	O
point	O
of	O
interest	O
was	O
detected	O
.	O
</s>
<s>
The	O
interest	O
region	O
is	O
split	O
into	O
smaller	O
4x4	O
square	O
sub-regions	O
,	O
and	O
for	O
each	O
one	O
,	O
the	O
Haar	B-Algorithm
wavelet	I-Algorithm
responses	O
are	O
extracted	O
at	O
5x5	O
regularly	O
spaced	O
sample	O
points	O
.	O
</s>
