<s>
A	O
distance	B-Algorithm
transform	I-Algorithm
,	O
also	O
known	O
as	O
distance	B-Algorithm
map	I-Algorithm
or	O
distance	B-Algorithm
field	I-Algorithm
,	O
is	O
a	O
derived	O
representation	O
of	O
a	O
digital	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
Distance	B-Algorithm
fields	I-Algorithm
can	O
also	O
be	O
signed	O
,	O
in	O
the	O
case	O
where	O
it	O
is	O
important	O
to	O
distinguish	O
whether	O
the	O
point	O
is	O
inside	O
or	O
outside	O
of	O
the	O
shape	O
.	O
</s>
<s>
The	O
map	O
labels	O
each	O
pixel	B-Algorithm
of	O
the	O
image	O
with	O
the	O
distance	O
to	O
the	O
nearest	O
obstacle	O
pixel	B-Algorithm
.	O
</s>
<s>
A	O
most	O
common	O
type	O
of	O
obstacle	O
pixel	B-Algorithm
is	O
a	O
boundary	O
pixel	B-Algorithm
in	O
a	O
binary	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
See	O
the	O
image	O
for	O
an	O
example	O
of	O
a	O
Chebyshev	O
distance	B-Algorithm
transform	I-Algorithm
on	O
a	O
binary	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
one	O
may	O
speak	O
of	O
Manhattan	B-Algorithm
distance	I-Algorithm
transform	I-Algorithm
,	O
if	O
the	O
underlying	O
metric	O
is	O
Manhattan	O
distance	O
.	O
</s>
<s>
There	O
are	O
several	O
algorithms	O
to	O
compute	O
the	O
distance	B-Algorithm
transform	I-Algorithm
for	O
these	O
different	O
distance	O
metrics	O
,	O
however	O
the	O
computation	O
of	O
the	O
exact	O
Euclidean	O
distance	B-Algorithm
transform	I-Algorithm
(	O
EEDT	O
)	O
needs	O
special	O
treatment	O
if	O
it	O
is	O
computed	O
on	O
the	O
image	O
grid	O
.	O
</s>
<s>
Recently	O
,	O
distance	B-Algorithm
transform	I-Algorithm
computation	O
has	O
also	O
been	O
proposed	O
using	O
a	O
static	O
Schrodinger	O
's	O
equation	O
.	O
</s>
<s>
This	O
particular	O
approach	O
has	O
the	O
benefit	O
of	O
obtaining	O
an	O
analytical	O
closed-form	O
solution	O
to	O
distance	B-Algorithm
transforms	I-Algorithm
,	O
and	O
of	O
computing	O
the	O
average	O
distance	B-Algorithm
transform	I-Algorithm
over	O
a	O
set	O
of	O
distance	B-Algorithm
transforms	I-Algorithm
,	O
owing	O
to	O
the	O
linearity	O
of	O
the	O
Schrödinger	O
equation	O
.	O
</s>
<s>
Further	O
,	O
this	O
approach	O
has	O
also	O
been	O
leveraged	O
to	O
extend	O
distance	B-Algorithm
transforms	I-Algorithm
to	O
line-segments	O
and	O
curves	O
.	O
</s>
<s>
Applications	O
are	O
digital	B-Algorithm
image	I-Algorithm
processing	I-Algorithm
(	O
e.g.	O
,	O
blurring	O
effects	O
,	O
skeletonizing	B-Algorithm
)	O
,	O
motion	O
planning	O
in	O
robotics	O
,	O
medical-image	O
analysis	O
for	O
prenatal	O
genetic	O
testing	O
,	O
and	O
even	O
pathfinding	B-Algorithm
.	O
</s>
<s>
Uniformly-sampled	O
signed	O
distance	B-Algorithm
fields	I-Algorithm
have	O
been	O
used	O
for	O
GPU-accelerated	O
font	O
smoothing	O
,	O
for	O
example	O
by	O
Valve	O
researchers	O
.	O
</s>
<s>
Signed	O
distance	B-Algorithm
fields	I-Algorithm
can	O
also	O
be	O
used	O
for	O
(	O
3D	O
)	O
solid	O
modelling	O
.	O
</s>
<s>
Rendering	O
on	O
typical	O
GPU	B-Architecture
hardware	O
requires	O
conversion	O
to	O
polygon	O
meshes	O
,	O
e.g.	O
</s>
<s>
by	O
the	O
marching	B-Algorithm
cubes	I-Algorithm
algorithm	I-Algorithm
.	O
</s>
