<s>
Gradient	B-General_Concept
vector	I-General_Concept
flow	I-General_Concept
(	O
GVF	O
)	O
,	O
a	O
computer	B-Application
vision	I-Application
framework	O
introduced	O
by	O
Chenyang	O
Xu	O
and	O
Jerry	O
L	O
.	O
Prince	O
,	O
is	O
the	O
vector	O
field	O
that	O
is	O
produced	O
by	O
a	O
process	O
that	O
smooths	O
and	O
diffuses	O
an	O
input	O
vector	O
field	O
.	O
</s>
<s>
It	O
is	O
widely	O
used	O
in	O
image	O
analysis	O
and	O
computer	B-Application
vision	I-Application
applications	O
for	O
object	O
tracking	O
,	O
shape	O
recognition	O
,	O
segmentation	B-Algorithm
,	O
and	O
edge	B-Algorithm
detection	I-Algorithm
.	O
</s>
<s>
In	O
particular	O
,	O
it	O
is	O
commonly	O
used	O
in	O
conjunction	O
with	O
active	B-General_Concept
contour	I-General_Concept
model	I-General_Concept
.	O
</s>
<s>
Finding	O
objects	O
or	O
homogeneous	O
regions	O
in	O
images	O
is	O
a	O
process	O
known	O
as	O
image	B-Algorithm
segmentation	I-Algorithm
.	O
</s>
<s>
active	B-General_Concept
contour	I-General_Concept
or	O
a	O
snake	B-General_Concept
,	O
so	O
that	O
it	O
passes	O
through	O
the	O
edge	O
map	O
in	O
a	O
smooth	O
way	O
,	O
therefore	O
defining	O
the	O
object	O
itself	O
.	O
</s>
<s>
Since	O
the	O
edge	O
map	O
has	O
its	O
highest	O
intensities	O
directly	O
on	O
the	O
edge	O
and	O
drops	O
to	O
zero	O
away	O
from	O
the	O
edge	O
,	O
these	O
gradient	O
vectors	O
provide	O
directions	O
for	O
the	O
active	B-General_Concept
contour	I-General_Concept
to	O
move	O
.	O
</s>
<s>
When	O
the	O
gradient	O
vectors	O
are	O
zero	O
,	O
the	O
active	B-General_Concept
contour	I-General_Concept
will	O
not	O
move	O
,	O
and	O
this	O
is	O
the	O
correct	O
behavior	O
when	O
the	O
contour	O
rests	O
on	O
the	O
peak	O
of	O
the	O
edge	O
map	O
itself	O
.	O
</s>
<s>
However	O
,	O
because	O
the	O
edge	O
itself	O
is	O
defined	O
by	O
local	O
operators	O
,	O
these	O
gradient	O
vectors	O
will	O
also	O
be	O
zero	O
far	O
away	O
from	O
the	O
edge	O
and	O
therefore	O
the	O
active	B-General_Concept
contour	I-General_Concept
will	O
not	O
move	O
toward	O
the	O
edge	O
when	O
initialized	O
far	O
away	O
from	O
the	O
edge	O
.	O
</s>
<s>
Some	O
newer	O
purposes	O
including	O
defining	O
a	O
continuous	O
medial	O
axis	O
representation	O
,	O
regularizing	O
image	O
anisotropic	O
diffusion	O
algorithms	O
,	O
finding	O
the	O
centers	O
of	O
ribbon-like	O
objects	O
,	O
constructing	O
graphs	O
for	O
optimal	O
surface	O
segmentations	B-Algorithm
,	O
creating	O
a	O
shape	O
prior	O
,	O
and	O
much	O
more	O
.	O
</s>
<s>
A	O
learning	O
based	O
probabilistic	O
weighted	O
GVF	O
extension	O
was	O
proposed	O
in	O
to	O
further	O
improve	O
the	O
segmentation	B-Algorithm
for	O
images	O
with	O
severely	O
cluttered	O
textures	O
or	O
high	O
levels	O
of	O
noise	O
.	O
</s>
<s>
forces	O
when	O
the	O
snake	B-General_Concept
gets	O
close	O
to	O
the	O
boundary	O
.	O
</s>
<s>
It	O
is	O
also	O
capable	O
of	O
moving	O
active	B-General_Concept
contours	I-General_Concept
into	O
concave	O
regions	O
of	O
an	O
object	O
's	O
boundary	O
.	O
</s>
<s>
is	O
no	O
actual	O
edge	O
map	O
,	O
active	B-General_Concept
contour	I-General_Concept
will	O
converge	O
to	O
the	O
perceptual	O
edge	O
because	O
the	O
GVF	O
vectors	O
drive	O
them	O
there	O
(	O
see	O
)	O
.	O
</s>
<s>
snake	B-General_Concept
or	O
active	O
surfaces	O
and	O
implicit	O
models	O
including	O
geometric	O
deformable	O
models	O
.	O
</s>
<s>
Operator	O
Splitting	O
schema	O
for	O
rapid	O
computation	O
of	O
this	O
segmentation	B-Algorithm
method	O
.	O
</s>
<s>
to	O
achieve	O
even	O
better	O
segmentation	B-Algorithm
for	O
images	O
with	O
complex	O
geometric	O
objects	O
.	O
</s>
<s>
for	O
improved	O
ultrasound	O
image	B-Algorithm
segmentation	I-Algorithm
without	O
hand-tuned	O
parameters	O
.	O
</s>
