<s>
In	O
computer	B-Application
vision	I-Application
,	O
blob	B-Algorithm
detection	I-Algorithm
methods	O
are	O
aimed	O
at	O
detecting	O
regions	O
in	O
a	O
digital	B-Algorithm
image	I-Algorithm
that	O
differ	O
in	O
properties	O
,	O
such	O
as	O
brightness	O
or	O
color	O
,	O
compared	O
to	O
surrounding	O
regions	O
.	O
</s>
<s>
The	O
most	O
common	O
method	O
for	O
blob	B-Algorithm
detection	I-Algorithm
is	O
convolution	B-Language
.	O
</s>
<s>
Given	O
some	O
property	O
of	O
interest	O
expressed	O
as	O
a	O
function	O
of	O
position	O
on	O
the	O
image	O
,	O
there	O
are	O
two	O
main	O
classes	O
of	O
blob	B-Algorithm
detectors	I-Algorithm
:	O
(	O
i	O
)	O
differential	O
methods	O
,	O
which	O
are	O
based	O
on	O
derivatives	O
of	O
the	O
function	O
with	O
respect	O
to	O
position	O
,	O
and	O
(	O
ii	O
)	O
methods	O
based	O
on	O
local	O
extrema	O
,	O
which	O
are	O
based	O
on	O
finding	O
the	O
local	O
maxima	O
and	O
minima	O
of	O
the	O
function	O
.	O
</s>
<s>
With	O
the	O
more	O
recent	O
terminology	O
used	O
in	O
the	O
field	O
,	O
these	O
detectors	O
can	O
also	O
be	O
referred	O
to	O
as	O
interest	O
point	O
operators	O
,	O
or	O
alternatively	O
interest	O
region	O
operators	O
(	O
see	O
also	O
interest	O
point	O
detection	O
and	O
corner	B-Algorithm
detection	I-Algorithm
)	O
.	O
</s>
<s>
There	O
are	O
several	O
motivations	O
for	O
studying	O
and	O
developing	O
blob	B-Algorithm
detectors	I-Algorithm
.	O
</s>
<s>
One	O
main	O
reason	O
is	O
to	O
provide	O
complementary	O
information	O
about	O
regions	O
,	O
which	O
is	O
not	O
obtained	O
from	O
edge	B-Algorithm
detectors	I-Algorithm
or	O
corner	B-Algorithm
detectors	I-Algorithm
.	O
</s>
<s>
In	O
early	O
work	O
in	O
the	O
area	O
,	O
blob	B-Algorithm
detection	I-Algorithm
was	O
used	O
to	O
obtain	O
regions	O
of	O
interest	O
for	O
further	O
processing	O
.	O
</s>
<s>
These	O
regions	O
could	O
signal	O
the	O
presence	O
of	O
objects	O
or	O
parts	O
of	O
objects	O
in	O
the	O
image	O
domain	O
with	O
application	O
to	O
object	O
recognition	O
and/or	O
object	O
tracking	B-Operating_System
.	O
</s>
<s>
In	O
other	O
domains	O
,	O
such	O
as	O
histogram	B-Algorithm
analysis	O
,	O
blob	O
descriptors	O
can	O
also	O
be	O
used	O
for	O
peak	O
detection	O
with	O
application	O
to	O
segmentation	B-Algorithm
.	O
</s>
<s>
In	O
more	O
recent	O
work	O
,	O
blob	O
descriptors	O
have	O
found	O
increasingly	O
popular	O
use	O
as	O
interest	O
points	O
for	O
wide	O
baseline	O
stereo	B-Algorithm
matching	I-Algorithm
and	O
to	O
signal	O
the	O
presence	O
of	O
informative	O
image	O
features	O
for	O
appearance-based	O
object	O
recognition	O
based	O
on	O
local	O
image	O
statistics	O
.	O
</s>
<s>
One	O
of	O
the	O
first	O
and	O
also	O
most	O
common	O
blob	B-Algorithm
detectors	I-Algorithm
is	O
based	O
on	O
the	O
Laplacian	O
of	O
the	O
Gaussian	O
(	O
LoG	O
)	O
.	O
</s>
<s>
at	O
a	O
certain	O
scale	O
to	O
give	O
a	O
scale	B-Algorithm
space	I-Algorithm
representation	I-Algorithm
.	O
</s>
<s>
and	O
to	O
detect	O
scale-space	B-Algorithm
maxima/minima	O
,	O
that	O
are	O
points	O
that	O
are	O
simultaneously	O
local	O
maxima/minima	O
of	O
with	O
respect	O
to	O
both	O
space	O
and	O
scale	O
(	O
Lindeberg	O
1994	O
,	O
1998	O
)	O
.	O
</s>
<s>
Thus	O
,	O
given	O
a	O
discrete	O
two-dimensional	O
input	O
image	O
a	O
three-dimensional	O
discrete	O
scale-space	B-Algorithm
volume	O
is	O
computed	O
and	O
a	O
point	O
is	O
regarded	O
as	O
a	O
bright	O
(	O
dark	O
)	O
blob	O
if	O
the	O
value	O
at	O
this	O
point	O
is	O
greater	O
(	O
smaller	O
)	O
than	O
the	O
value	O
in	O
all	O
its	O
26	O
neighbours	O
.	O
</s>
<s>
Note	O
that	O
this	O
notion	O
of	O
blob	O
provides	O
a	O
concise	O
and	O
mathematically	O
precise	O
operational	O
definition	O
of	O
the	O
notion	O
of	O
"	O
blob	O
"	O
,	O
which	O
directly	O
leads	O
to	O
an	O
efficient	O
and	O
robust	O
algorithm	O
for	O
blob	B-Algorithm
detection	I-Algorithm
.	O
</s>
<s>
Some	O
basic	O
properties	O
of	O
blobs	O
defined	O
from	O
scale-space	B-Algorithm
maxima	O
of	O
the	O
normalized	O
Laplacian	O
operator	O
are	O
that	O
the	O
responses	O
are	O
covariant	O
with	O
translations	O
,	O
rotations	O
and	O
rescalings	O
in	O
the	O
image	O
domain	O
.	O
</s>
<s>
Thus	O
,	O
if	O
a	O
scale-space	B-Algorithm
maximum	O
is	O
assumed	O
at	O
a	O
point	O
then	O
under	O
a	O
rescaling	O
of	O
the	O
image	O
by	O
a	O
scale	O
factor	O
,	O
there	O
will	O
be	O
a	O
scale-space	B-Algorithm
maximum	O
at	O
in	O
the	O
rescaled	O
image	O
(	O
Lindeberg	O
1998	O
)	O
.	O
</s>
<s>
This	O
in	O
practice	O
highly	O
useful	O
property	O
implies	O
that	O
besides	O
the	O
specific	O
topic	O
of	O
Laplacian	O
blob	B-Algorithm
detection	I-Algorithm
,	O
local	O
maxima/minima	O
of	O
the	O
scale-normalized	O
Laplacian	O
are	O
also	O
used	O
for	O
scale	O
selection	O
in	O
other	O
contexts	O
,	O
such	O
as	O
in	O
corner	B-Algorithm
detection	I-Algorithm
,	O
scale-adaptive	O
feature	O
tracking	B-Operating_System
(	O
Bretzner	O
and	O
Lindeberg	O
1998	O
)	O
,	O
in	O
the	O
scale-invariant	B-Algorithm
feature	I-Algorithm
transform	I-Algorithm
(	O
Lowe	O
2004	O
)	O
as	O
well	O
as	O
other	O
image	O
descriptors	O
for	O
image	B-Algorithm
matching	I-Algorithm
and	O
object	O
recognition	O
.	O
</s>
<s>
The	O
scale	O
selection	O
properties	O
of	O
the	O
Laplacian	O
operator	O
and	O
other	O
closely	O
scale-space	B-Algorithm
interest	O
point	O
detectors	O
are	O
analyzed	O
in	O
detail	O
in	O
(	O
Lindeberg	O
2013a	O
)	O
.	O
</s>
<s>
In	O
(	O
Lindeberg	O
2013b	O
,	O
2015	O
)	O
it	O
is	O
shown	O
that	O
there	O
exist	O
other	O
scale-space	B-Algorithm
interest	O
point	O
detectors	O
,	O
such	O
as	O
the	O
determinant	O
of	O
the	O
Hessian	O
operator	O
,	O
that	O
perform	O
better	O
than	O
Laplacian	O
operator	O
or	O
its	O
difference-of-Gaussians	O
approximation	O
for	O
image-based	O
matching	O
using	O
local	O
SIFT-like	O
image	O
descriptors	O
.	O
</s>
<s>
In	O
the	O
computer	B-Application
vision	I-Application
literature	O
,	O
this	O
approach	O
is	O
referred	O
to	O
as	O
the	O
difference	B-Algorithm
of	I-Algorithm
Gaussians	I-Algorithm
(	O
DoG	O
)	O
approach	O
.	O
</s>
<s>
In	O
a	O
similar	O
fashion	O
as	O
for	O
the	O
Laplacian	O
blob	B-Algorithm
detector	I-Algorithm
,	O
blobs	O
can	O
be	O
detected	O
from	O
scale-space	B-Algorithm
extrema	O
of	O
differences	O
of	O
Gaussians	O
—	O
see	O
(	O
Lindeberg	O
2012	O
,	O
2015	O
)	O
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx1[ 	O
T	O
.	O
Lindeberg	O
``Scale	O
invariant	O
feature	O
transform	O
,	O
Scholarpedia	O
,	O
7(5 )	O
:10491	O
,	O
2012	O
.	O
</s>
<s>
This	O
approach	O
is	O
for	O
instance	O
used	O
in	O
the	O
scale-invariant	B-Algorithm
feature	I-Algorithm
transform	I-Algorithm
(	O
SIFT	O
)	O
algorithm	O
—	O
see	O
Lowe	O
(	O
2004	O
)	O
.	O
</s>
<s>
In	O
terms	O
of	O
scale	O
selection	O
,	O
blobs	O
defined	O
from	O
scale-space	B-Algorithm
extrema	O
of	O
the	O
determinant	O
of	O
the	O
Hessian	O
(	O
DoH	O
)	O
also	O
have	O
slightly	O
better	O
scale	O
selection	O
properties	O
under	O
non-Euclidean	O
affine	O
transformations	O
than	O
the	O
more	O
commonly	O
used	O
Laplacian	O
operator	O
(	O
Lindeberg	O
1994	O
,	O
1998	O
,	O
2015	O
)	O
.	O
</s>
<s>
In	O
simplified	O
form	O
,	O
the	O
scale-normalized	O
determinant	O
of	O
the	O
Hessian	O
computed	O
from	O
Haar	O
wavelets	O
is	O
used	O
as	O
the	O
basic	O
interest	O
point	O
operator	O
in	O
the	O
SURF	B-Algorithm
descriptor	O
(	O
Bay	O
et	O
al	O
.	O
</s>
<s>
2006	O
)	O
for	O
image	B-Algorithm
matching	I-Algorithm
and	O
object	O
recognition	O
.	O
</s>
<s>
A	O
detailed	O
analysis	O
of	O
the	O
selection	O
properties	O
of	O
the	O
determinant	O
of	O
the	O
Hessian	O
operator	O
and	O
other	O
closely	O
scale-space	B-Algorithm
interest	O
point	O
detectors	O
is	O
given	O
in	O
(	O
Lindeberg	O
2013a	O
)	O
showing	O
that	O
the	O
determinant	O
of	O
the	O
Hessian	O
operator	O
has	O
better	O
scale	O
selection	O
properties	O
under	O
affine	O
image	O
transformations	O
than	O
the	O
Laplacian	O
operator	O
.	O
</s>
<s>
In	O
(	O
Lindeberg	O
2013b	O
,	O
2015	O
)	O
T	O
.	O
Lindeberg	O
``Image	O
matching	O
using	O
generalized	O
scale-space	B-Algorithm
interest	O
points	O
"	O
,	O
Journal	O
of	O
Mathematical	O
Imaging	O
and	O
Vision	O
,	O
volume	O
52	O
,	O
number	O
1	O
,	O
pages	O
3-36	O
,	O
2015	O
.	O
it	O
is	O
shown	O
that	O
the	O
determinant	O
of	O
the	O
Hessian	O
operator	O
performs	O
significantly	O
better	O
than	O
the	O
Laplacian	O
operator	O
or	O
its	O
difference-of-Gaussians	O
approximation	O
,	O
as	O
well	O
as	O
better	O
than	O
the	O
Harris	O
or	O
Harris-Laplace	O
operators	O
,	O
for	O
image-based	O
matching	O
using	O
local	O
SIFT-like	O
or	O
SURF-like	O
image	O
descriptors	O
,	O
leading	O
to	O
higher	O
efficiency	O
values	O
and	O
lower	O
1-precision	O
scores	O
.	O
</s>
<s>
A	O
hybrid	O
operator	O
between	O
the	O
Laplacian	O
and	O
the	O
determinant	O
of	O
the	O
Hessian	O
blob	B-Algorithm
detectors	I-Algorithm
has	O
also	O
been	O
proposed	O
,	O
where	O
spatial	O
selection	O
is	O
done	O
by	O
the	O
determinant	O
of	O
the	O
Hessian	O
and	O
scale	O
selection	O
is	O
performed	O
with	O
the	O
scale-normalized	O
Laplacian	O
(	O
Mikolajczyk	O
and	O
Schmid	O
2004	O
)	O
:	O
</s>
<s>
This	O
operator	O
has	O
been	O
used	O
for	O
image	B-Algorithm
matching	I-Algorithm
,	O
object	O
recognition	O
as	O
well	O
as	O
texture	O
analysis	O
.	O
</s>
<s>
The	O
blob	O
descriptors	O
obtained	O
from	O
these	O
blob	B-Algorithm
detectors	I-Algorithm
with	O
automatic	O
scale	O
selection	O
are	O
invariant	O
to	O
translations	O
,	O
rotations	O
and	O
uniform	O
rescalings	O
in	O
the	O
spatial	O
domain	O
.	O
</s>
<s>
The	O
images	O
that	O
constitute	O
the	O
input	O
to	O
a	O
computer	B-Application
vision	I-Application
system	O
are	O
,	O
however	O
,	O
also	O
subject	O
to	O
perspective	O
distortions	O
.	O
</s>
<s>
To	O
obtain	O
blob	O
descriptors	O
that	O
are	O
more	O
robust	O
to	O
perspective	O
transformations	O
,	O
a	O
natural	O
approach	O
is	O
to	O
devise	O
a	O
blob	B-Algorithm
detector	I-Algorithm
that	O
is	O
invariant	O
to	O
affine	O
transformations	O
.	O
</s>
<s>
In	O
practice	O
,	O
affine	O
invariant	O
interest	O
points	O
can	O
be	O
obtained	O
by	O
applying	O
affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
to	O
a	O
blob	O
descriptor	O
,	O
where	O
the	O
shape	O
of	O
the	O
smoothing	O
kernel	O
is	O
iteratively	O
warped	O
to	O
match	O
the	O
local	O
image	O
structure	O
around	O
the	O
blob	O
,	O
or	O
equivalently	O
a	O
local	O
image	O
patch	O
is	O
iteratively	O
warped	O
while	O
the	O
shape	O
of	O
the	O
smoothing	O
kernel	O
remains	O
rotationally	O
symmetric	O
(	O
Lindeberg	O
and	O
Garding	O
1997	O
;	O
Baumberg	O
2000	O
;	O
Mikolajczyk	O
and	O
Schmid	O
2004	O
,	O
Lindeberg	O
2008	O
)	O
.	O
</s>
<s>
In	O
this	O
way	O
,	O
we	O
can	O
define	O
affine-adapted	O
versions	O
of	O
the	O
Laplacian/Difference	O
of	O
Gaussian	O
operator	O
,	O
the	O
determinant	O
of	O
the	O
Hessian	O
and	O
the	O
Hessian-Laplace	O
operator	O
(	O
see	O
also	O
Harris-Affine	B-Algorithm
and	O
Hessian-Affine	B-Algorithm
)	O
.	O
</s>
<s>
In	O
Lindeberg	O
,	O
it	O
was	O
shown	O
that	O
and	O
implies	O
better	O
scale	O
selection	O
properties	O
in	O
the	O
sense	O
that	O
the	O
selected	O
scale	O
levels	O
obtained	O
from	O
a	O
spatio-temporal	O
Gaussian	O
blob	O
with	O
spatial	O
extent	O
and	O
temporal	O
extent	O
will	O
perfectly	O
match	O
the	O
spatial	O
extent	O
and	O
the	O
temporal	O
duration	O
of	O
the	O
blob	O
,	O
with	O
scale	O
selection	O
performed	O
by	O
detecting	O
spatio-temporal	O
scale-space	B-Algorithm
extrema	O
of	O
the	O
differential	O
expression	O
.	O
</s>
<s>
To	O
address	O
this	O
problem	O
,	O
Lindeberg	O
(	O
1993	O
,	O
1994	O
)	O
studied	O
the	O
problem	O
of	O
detecting	O
local	O
maxima	O
with	O
extent	O
at	O
multiple	O
scales	O
in	O
scale	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
By	O
studying	O
how	O
these	O
structures	O
evolve	O
with	O
increasing	O
scales	O
,	O
the	O
notion	O
of	O
scale-space	B-Algorithm
blobs	O
was	O
introduced	O
.	O
</s>
<s>
Beyond	O
local	O
contrast	O
and	O
extent	O
,	O
these	O
scale-space	B-Algorithm
blobs	O
also	O
measured	O
how	O
stable	O
image	O
structures	O
are	O
in	O
scale-space	B-Algorithm
,	O
by	O
measuring	O
their	O
scale-space	B-Algorithm
lifetime	O
.	O
</s>
<s>
While	O
the	O
specific	O
technique	O
that	O
was	O
used	O
in	O
these	O
prototypes	O
can	O
be	O
substantially	O
improved	O
with	O
the	O
current	O
knowledge	O
in	O
computer	B-Application
vision	I-Application
,	O
the	O
overall	O
general	O
approach	O
is	O
still	O
valid	O
,	O
for	O
example	O
in	O
the	O
way	O
that	O
local	O
extrema	O
over	O
scales	O
of	O
the	O
scale-normalized	O
Laplacian	O
operator	O
are	O
nowadays	O
used	O
for	O
providing	O
scale	O
information	O
to	O
other	O
visual	O
processes	O
.	O
</s>
<s>
Compared	O
to	O
other	O
watershed	O
methods	O
,	O
the	O
flooding	B-Protocol
in	O
this	O
algorithm	O
stops	O
once	O
the	O
intensity	O
level	O
falls	O
below	O
the	O
intensity	O
value	O
of	O
the	O
so-called	O
delimiting	O
saddle	O
point	O
associated	O
with	O
the	O
local	O
maximum	O
.	O
</s>
<s>
Moreover	O
,	O
the	O
grey-level	O
blob	B-Algorithm
detection	I-Algorithm
method	O
was	O
embedded	O
in	O
a	O
scale	B-Algorithm
space	I-Algorithm
representation	I-Algorithm
and	O
performed	O
at	O
all	O
levels	O
of	O
scale	O
,	O
resulting	O
in	O
a	O
representation	O
called	O
the	O
scale-space	B-Algorithm
primal	O
sketch	O
.	O
</s>
<s>
This	O
algorithm	O
with	O
its	O
applications	O
in	O
computer	B-Application
vision	I-Application
is	O
described	O
in	O
more	O
detail	O
in	O
Lindeberg	O
's	O
thesisLindeberg	O
,	O
T	O
.	O
(	O
1991	O
)	O
Discrete	O
Scale-Space	B-Algorithm
Theory	I-Algorithm
and	O
the	O
Scale-Space	B-Algorithm
Primal	O
Sketch	O
,	O
PhD	O
thesis	O
,	O
Department	O
of	O
Numerical	O
Analysis	O
and	O
Computing	O
Science	O
,	O
Royal	O
Institute	O
of	O
Technology	O
,	O
S-100	O
44	O
Stockholm	O
,	O
Sweden	O
,	O
May	O
1991	O
.	O
</s>
<s>
Eklundh	O
,	O
"	O
Scale	O
detection	O
and	O
region	O
extraction	O
from	O
a	O
scale-space	B-Algorithm
primal	O
sketch	O
"	O
,	O
in	O
Proc	O
.	O
</s>
<s>
3rd	O
International	O
Conference	O
on	O
Computer	B-Application
Vision	I-Application
,	O
(	O
Osaka	O
,	O
Japan	O
)	O
,	O
pp	O
.	O
</s>
<s>
(	O
See	O
Appendix	O
A.1	O
for	O
the	O
basic	O
definitions	O
for	O
the	O
watershed-based	O
grey-level	O
blob	B-Algorithm
detection	I-Algorithm
algorithm	O
.	O
)	O
T	O
.	O
</s>
<s>
Eklundh	O
,	O
"	O
On	O
the	O
computation	O
of	O
a	O
scale-space	B-Algorithm
primal	O
sketch	O
"	O
,	O
Journal	O
of	O
Visual	O
Communication	O
and	O
Image	O
Representation	O
,	O
vol	O
.	O
</s>
<s>
1991	O
..	O
More	O
detailed	O
treatments	O
of	O
applications	O
of	O
grey-level	O
blob	B-Algorithm
detection	I-Algorithm
and	O
the	O
scale-space	B-Algorithm
primal	O
sketch	O
to	O
computer	B-Application
vision	I-Application
and	O
medical	O
image	O
analysis	O
are	O
given	O
in	O
Lindeberg	O
,	O
T.	O
:	O
Detecting	O
salient	O
blob-like	O
image	O
structures	O
and	O
their	O
scales	O
with	O
a	O
scale-space	B-Algorithm
primal	O
sketch	O
:	O
A	O
method	O
for	O
focus-of-attention	O
,	O
International	O
Journal	O
of	O
Computer	B-Application
Vision	I-Application
,	O
11(3 )	O
,	O
283--318	O
,	O
1993.Lindeberg	O
,	O
T	O
,	O
Lidberg	O
,	O
Par	O
and	O
Roland	O
,	O
P	O
.	O
E	O
..	O
:	O
"	O
Analysis	O
of	O
Brain	O
Activation	O
Patterns	O
Using	O
a	O
3-D	O
Scale-Space	B-Algorithm
Primal	O
Sketch	O
"	O
,	O
Human	O
Brain	O
Mapping	O
,	O
vol	O
7	O
,	O
no	O
3	O
,	O
pp	O
166--194	O
,	O
1999.Jean-Francois	O
Mangin	O
,	O
Denis	O
Rivière	O
,	O
Olivier	O
Coulon	O
,	O
Cyril	O
Poupon	O
,	O
Arnaud	O
Cachia	O
,	O
Yann	O
Cointepas	O
,	O
Jean-Baptiste	O
Poline	O
,	O
Denis	O
Le	O
Bihan	O
,	O
Jean	O
Régis	O
,	O
Dimitri	O
Papadopoulos-Orfanos	O
:	O
"	O
Coordinate-based	O
versus	O
structural	O
approaches	O
to	O
brain	O
image	O
analysis	O
"	O
.	O
</s>
<s>
Based	O
on	O
this	O
idea	O
,	O
they	O
defined	O
a	O
notion	O
of	O
maximally	O
stable	O
extremal	O
regions''	O
and	O
showed	O
how	O
these	O
image	O
descriptors	O
can	O
be	O
used	O
as	O
image	O
features	O
for	O
stereo	B-Algorithm
matching	I-Algorithm
.	O
</s>
