<s>
Scale-space	B-Algorithm
segmentation	I-Algorithm
or	O
multi-scale	O
segmentation	B-Algorithm
is	O
a	O
general	O
framework	O
for	O
signal	O
and	O
image	B-Algorithm
segmentation	I-Algorithm
,	O
based	O
on	O
the	O
computation	O
of	O
image	O
descriptors	O
at	O
multiple	O
scales	O
of	O
smoothing	O
.	O
</s>
<s>
Witkin	O
's	O
seminal	O
work	O
in	O
scale	B-Algorithm
space	I-Algorithm
included	O
the	O
notion	O
that	O
a	O
one-dimensional	O
signal	O
could	O
be	O
unambiguously	O
segmented	O
into	O
regions	O
,	O
with	O
one	O
scale	O
parameter	O
controlling	O
the	O
scale	O
of	O
segmentation	B-Algorithm
.	O
</s>
<s>
There	O
have	O
been	O
numerous	O
research	O
works	O
in	O
this	O
area	O
,	O
out	O
of	O
which	O
a	O
few	O
have	O
now	O
reached	O
a	O
state	O
where	O
they	O
can	O
be	O
applied	O
either	O
with	O
interactive	O
manual	O
intervention	O
(	O
usually	O
with	O
application	O
to	O
medical	B-Application
imaging	I-Application
)	O
or	O
fully	O
automatically	O
.	O
</s>
<s>
Nevertheless	O
,	O
this	O
general	O
idea	O
has	O
inspired	O
several	O
other	O
authors	O
to	O
investigate	O
coarse-to-fine	O
schemes	O
for	O
image	B-Algorithm
segmentation	I-Algorithm
.	O
</s>
<s>
Lindeberg	O
studied	O
the	O
problem	O
of	O
linking	O
local	O
extrema	O
and	O
saddle	O
points	O
over	O
scales	O
,	O
and	O
proposed	O
an	O
image	O
representation	O
called	O
the	O
scale-space	B-Algorithm
primal	O
sketch	O
which	O
makes	O
explicit	O
the	O
relations	O
between	O
structures	O
at	O
different	O
scales	O
,	O
and	O
also	O
makes	O
explicit	O
which	O
image	O
features	O
are	O
stable	O
over	O
large	O
ranges	O
of	O
scale	O
including	O
locally	O
appropriate	O
scales	O
for	O
those	O
.	O
</s>
<s>
Bergholm	O
proposed	O
to	O
detect	O
edges	O
at	O
coarse	O
scales	O
in	O
scale-space	B-Algorithm
and	O
then	O
trace	O
them	O
back	O
to	O
finer	O
scales	O
with	O
manual	O
choice	O
of	O
both	O
the	O
coarse	O
detection	O
scale	O
and	O
the	O
fine	O
localization	O
scale	O
.	O
</s>
<s>
Gauch	O
and	O
Pizer	O
studied	O
the	O
complementary	O
problem	O
of	O
ridges	O
and	O
valleys	O
at	O
multiple	O
scales	O
and	O
developed	O
a	O
tool	O
for	O
interactive	O
image	B-Algorithm
segmentation	I-Algorithm
based	O
on	O
multi-scale	O
watersheds	B-Algorithm
.	O
</s>
<s>
The	O
use	O
of	O
multi-scale	O
watershed	B-Algorithm
with	O
application	O
to	O
the	O
gradient	O
map	O
has	O
also	O
been	O
investigated	O
by	O
Olsen	O
and	O
Nielsen	O
and	O
has	O
been	O
carried	O
over	O
to	O
clinical	O
use	O
by	O
Dam	O
et	O
al	O
.	O
</s>
<s>
A	O
fully	O
automatic	O
brain	O
segmentation	B-Algorithm
algorithm	O
based	O
on	O
closely	O
related	O
ideas	O
of	O
multi-scale	O
watersheds	B-Algorithm
has	O
been	O
presented	O
by	O
Undeman	O
and	O
Lindeberg	O
and	O
been	O
extensively	O
tested	O
in	O
brain	O
databases	O
.	O
</s>
<s>
These	O
ideas	O
for	O
multi-scale	O
image	B-Algorithm
segmentation	I-Algorithm
by	O
linking	O
image	O
structures	O
over	O
scales	O
have	O
also	O
been	O
picked	O
up	O
by	O
Florack	O
and	O
Kuijper	O
.	O
</s>
<s>
Bijaoui	O
and	O
Rué	O
associate	O
structures	O
detected	O
in	O
scale-space	B-Algorithm
above	O
a	O
minimum	O
noise	O
threshold	O
into	O
an	O
object	O
tree	O
which	O
spans	O
multiple	O
scales	O
and	O
corresponds	O
to	O
a	O
kind	O
of	O
feature	O
in	O
the	O
original	O
signal	O
.	O
</s>
<s>
Scale-space	B-Algorithm
segmentation	I-Algorithm
was	O
extended	O
in	O
another	O
direction	O
by	O
Lyon	O
to	O
vector-valued	O
functions	O
of	O
time	O
,	O
where	O
the	O
vector	O
derivative	O
does	O
not	O
have	O
maxima	O
and	O
minima	O
,	O
and	O
the	O
second	O
derivative	O
does	O
not	O
have	O
zero	O
crossings	O
,	O
by	O
putting	O
segment	O
boundaries	O
instead	O
at	O
maxima	O
of	O
the	O
Euclidean	O
magnitude	O
of	O
the	O
vector	O
derivative	O
of	O
the	O
smoothed	O
vector	O
signals	O
.	O
</s>
<s>
This	O
technique	O
has	O
been	O
applied	O
to	O
segmentation	B-Algorithm
of	O
speech	O
and	O
of	O
text	O
.	O
</s>
