<s>
Shape	B-Algorithm
factors	I-Algorithm
are	O
dimensionless	O
quantities	O
used	O
in	O
image	B-General_Concept
analysis	I-General_Concept
and	O
microscopy	O
that	O
numerically	O
describe	O
the	O
shape	O
of	O
a	O
particle	O
,	O
independent	O
of	O
its	O
size	O
.	O
</s>
<s>
Shape	B-Algorithm
factors	I-Algorithm
are	O
calculated	O
from	O
measured	O
dimensions	O
,	O
such	O
as	O
diameter	O
,	O
chord	O
lengths	O
,	O
area	O
,	O
perimeter	B-Application
,	O
centroid	O
,	O
moments	O
,	O
etc	O
.	O
</s>
<s>
The	O
dimensions	O
of	O
the	O
particles	O
are	O
usually	O
measured	O
from	O
two-dimensional	O
cross-sections	B-Application
or	O
projections	O
,	O
as	O
in	O
a	O
microscope	O
field	O
,	O
but	O
shape	B-Algorithm
factors	I-Algorithm
also	O
apply	O
to	O
three-dimensional	O
objects	O
.	O
</s>
<s>
The	O
dimensionless	O
quantities	O
often	O
represent	O
the	O
degree	O
of	O
deviation	B-General_Concept
from	O
an	O
ideal	O
shape	O
,	O
such	O
as	O
a	O
circle	O
,	O
sphere	O
or	O
equilateral	O
polyhedron	O
.	O
</s>
<s>
Shape	B-Algorithm
factors	I-Algorithm
are	O
often	O
normalized	O
,	O
that	O
is	O
,	O
the	O
value	O
ranges	O
from	O
zero	O
to	O
one	O
.	O
</s>
<s>
A	O
shape	B-Algorithm
factor	I-Algorithm
equal	O
to	O
one	O
usually	O
represents	O
an	O
ideal	O
case	O
or	O
maximum	O
symmetry	O
,	O
such	O
as	O
a	O
circle	O
,	O
sphere	O
,	O
square	O
or	O
cube	O
.	O
</s>
<s>
The	O
most	O
common	O
shape	B-Algorithm
factor	I-Algorithm
is	O
the	O
aspect	B-Device
ratio	I-Device
,	O
a	O
function	O
of	O
the	O
largest	O
diameter	O
and	O
the	O
smallest	O
diameter	O
orthogonal	B-Application
to	O
it	O
:	O
</s>
<s>
The	O
normalized	O
aspect	B-Device
ratio	I-Device
varies	O
from	O
approaching	O
zero	O
for	O
a	O
very	O
elongated	O
particle	O
,	O
such	O
as	O
a	O
grain	O
in	O
a	O
cold-worked	O
metal	O
,	O
to	O
near	O
unity	O
for	O
an	O
equiaxed	O
grain	O
.	O
</s>
<s>
Another	O
very	O
common	O
shape	B-Algorithm
factor	I-Algorithm
is	O
the	O
circularity	O
(	O
or	O
isoperimetric	O
quotient	O
)	O
,	O
a	O
function	O
of	O
the	O
perimeter	B-Application
P	O
and	O
the	O
area	O
A	O
:	O
</s>
<s>
The	O
less-common	O
elongation	O
shape	B-Algorithm
factor	I-Algorithm
is	O
defined	O
as	O
the	O
square	O
root	O
of	O
the	O
ratio	O
of	O
the	O
two	O
second	O
moments	O
in	O
of	O
the	O
particle	O
around	O
its	O
principal	O
axes	O
.	O
</s>
<s>
The	O
compactness	O
shape	B-Algorithm
factor	I-Algorithm
is	O
a	O
function	O
of	O
the	O
polar	O
second	O
moment	O
in	O
of	O
a	O
particle	O
and	O
a	O
circle	O
of	O
equal	O
area	O
A	O
.	O
</s>
<s>
The	O
fcomp	O
of	O
a	O
circle	O
is	O
one	O
,	O
and	O
much	O
less	O
than	O
one	O
for	O
the	O
cross-section	B-Application
of	O
an	O
I-beam	O
.	O
</s>
<s>
The	O
waviness	O
shape	B-Algorithm
factor	I-Algorithm
of	O
the	O
perimeter	B-Application
is	O
a	O
function	O
of	O
the	O
convex	O
portion	O
Pcvx	O
of	O
the	O
perimeter	B-Application
to	O
the	O
total	O
.	O
</s>
<s>
Greenland	O
,	O
the	O
largest	O
island	O
in	O
the	O
world	O
,	O
has	O
an	O
area	O
of	O
2,166,086	O
km2	O
;	O
a	O
coastline	O
(	O
perimeter	B-Application
)	O
of	O
39,330	O
km	O
;	O
a	O
north	O
–	O
south	O
length	O
of	O
2670km	O
;	O
and	O
an	O
east	O
–	O
west	O
length	O
of	O
1290km	O
.	O
</s>
<s>
The	O
aspect	B-Device
ratio	I-Device
is	O
agreeable	O
with	O
an	O
eyeball-estimate	O
on	O
a	O
globe	O
.	O
</s>
<s>
A	O
low	O
value	O
of	O
circularity	O
does	O
not	O
necessarily	O
indicate	O
a	O
lack	O
of	O
symmetry	O
,	O
and	O
shape	B-Algorithm
factors	I-Algorithm
are	O
not	O
limited	O
to	O
microscopic	O
objects	O
.	O
</s>
