<s>
Range	B-Algorithm
segmentation	I-Algorithm
is	O
the	O
task	O
of	O
segmenting	B-Algorithm
(	O
dividing	O
)	O
a	O
range	B-Algorithm
image	I-Algorithm
,	O
an	O
image	O
containing	O
depth	O
information	O
for	O
each	O
pixel	O
,	O
into	O
segments	O
(	O
regions	O
)	O
,	O
so	O
that	O
all	O
the	O
points	O
of	O
the	O
same	O
surface	O
belong	O
to	O
the	O
same	O
region	O
,	O
there	O
is	O
no	O
overlap	O
between	O
different	O
regions	O
and	O
the	O
union	O
of	O
these	O
regions	O
generates	O
the	O
entire	O
image	O
.	O
</s>
<s>
There	O
have	O
been	O
two	O
main	O
approaches	O
to	O
the	O
range	B-Algorithm
segmentation	I-Algorithm
problem	O
:	O
region-based	O
range	B-Algorithm
segmentation	I-Algorithm
and	O
edge-based	O
range	B-Algorithm
segmentation	I-Algorithm
.	O
</s>
<s>
Region-based	O
range	B-Algorithm
segmentation	I-Algorithm
algorithms	O
can	O
be	O
further	O
categorized	O
into	O
two	O
major	O
groups	O
:	O
parametric	O
model-based	O
range	B-Algorithm
segmentation	I-Algorithm
algorithms	O
and	O
region-growing	O
algorithms	O
.	O
</s>
<s>
Region-growing	O
algorithms	O
start	O
by	O
segmenting	B-Algorithm
an	O
image	O
into	O
initial	O
regions	O
.	O
</s>
<s>
A	O
drawback	O
of	O
algorithms	O
of	O
this	O
group	O
is	O
that	O
in	O
general	O
they	O
produce	O
distorted	O
boundaries	O
because	O
the	O
segmentation	B-Algorithm
usually	O
is	O
carried	O
out	O
at	O
region	O
level	O
instead	O
of	O
pixel	O
level	O
.	O
</s>
<s>
Edge-based	O
range	B-Algorithm
segmentation	I-Algorithm
algorithms	O
are	O
based	O
on	O
edge	B-Algorithm
detection	I-Algorithm
and	O
labeling	O
edges	O
using	O
the	O
jump	O
boundaries	O
(	O
discontinuities	O
)	O
.	O
</s>
<s>
They	O
apply	O
an	O
edge	O
detector	O
to	O
extract	O
edges	O
from	O
a	O
range	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
A	O
typical	O
example	O
of	O
edge-based	O
range	B-Algorithm
segmentation	I-Algorithm
algorithms	O
is	O
presented	O
by	O
Fan	O
et	O
al	O
.	O
</s>
<s>
The	O
segmentation	B-Algorithm
procedure	O
starts	O
by	O
detecting	O
discontinuities	O
using	O
zero-crossing	O
and	O
curvature	O
values	O
.	O
</s>
<s>
The	O
image	O
is	O
segmented	O
at	O
discontinuities	O
to	O
obtain	O
an	O
initial	O
segmentation	B-Algorithm
.	O
</s>
<s>
At	O
the	O
next	O
step	O
,	O
the	O
initial	O
segmentation	B-Algorithm
is	O
refined	O
by	O
fitting	O
quadratics	O
whose	O
coefficients	O
are	O
calculated	O
based	O
on	O
the	O
Least	B-Algorithm
squares	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
In	O
general	O
,	O
a	O
drawback	O
of	O
edge-based	O
range	B-Algorithm
segmentation	I-Algorithm
algorithms	O
is	O
that	O
although	O
they	O
produce	O
clean	O
and	O
well	O
defined	O
boundaries	O
between	O
different	O
regions	O
,	O
they	O
tend	O
to	O
produce	O
gaps	O
between	O
boundaries	O
.	O
</s>
<s>
In	O
addition	O
,	O
for	O
curved	O
surfaces	O
,	O
discontinuities	O
are	O
smooth	O
and	O
hard	O
to	O
locate	O
and	O
therefore	O
these	O
algorithms	O
tend	O
to	O
under-segment	O
the	O
range	B-Algorithm
image	I-Algorithm
.	O
</s>
<s>
Although	O
the	O
range	B-Algorithm
image	I-Algorithm
segmentation	I-Algorithm
problem	O
has	O
been	O
studied	O
for	O
a	O
number	O
of	O
years	O
,	O
the	O
task	O
of	O
segmenting	B-Algorithm
range	B-Algorithm
images	I-Algorithm
of	O
curved	O
surfaces	O
is	O
yet	O
to	O
be	O
satisfactorily	O
resolved	O
.	O
</s>
