<s>
This	O
article	O
describes	O
shape	B-Algorithm
analysis	I-Algorithm
to	O
analyze	O
and	O
process	O
geometric	O
shapes	O
.	O
</s>
<s>
Shape	B-Algorithm
analysis	I-Algorithm
is	O
the	O
(	O
mostly	O
)	O
automatic	O
analysis	O
of	O
geometric	O
shapes	O
,	O
for	O
example	O
using	O
a	O
computer	O
to	O
detect	O
similarly	O
shaped	O
objects	O
in	O
a	O
database	O
or	O
parts	O
that	O
fit	O
together	O
.	O
</s>
<s>
Most	O
commonly	O
a	O
boundary	B-Algorithm
representation	I-Algorithm
is	O
used	O
to	O
describe	O
the	O
object	O
with	O
its	O
boundary	O
(	O
usually	O
the	O
outer	O
shell	O
,	O
see	O
also	O
3D	O
model	O
)	O
.	O
</s>
<s>
constructive	O
solid	O
geometry	O
)	O
or	O
point	O
based	O
representations	O
(	O
point	B-Algorithm
clouds	I-Algorithm
)	O
can	O
be	O
used	O
to	O
represent	O
shape	O
.	O
</s>
<s>
Once	O
the	O
objects	O
are	O
given	O
,	O
either	O
by	O
modeling	O
(	O
computer-aided	B-Application
design	I-Application
)	O
,	O
by	O
scanning	O
(	O
3D	B-Algorithm
scanner	I-Algorithm
)	O
or	O
by	O
extracting	O
shape	O
from	O
2D	O
or	O
3D	O
images	O
,	O
they	O
have	O
to	O
be	O
simplified	O
before	O
a	O
comparison	O
can	O
be	O
achieved	O
.	O
</s>
<s>
Shape	B-Algorithm
analysis	I-Algorithm
is	O
used	O
in	O
many	O
application	O
fields	O
:	O
</s>
<s>
computer-aided	B-Application
design	I-Application
and	O
computer-aided	O
manufacturing	O
to	O
process	O
and	O
to	O
compare	O
designs	O
of	O
mechanical	O
parts	O
or	O
design	O
objects	O
.	O
</s>
<s>
Many	O
descriptors	O
are	O
invariant	O
with	O
respect	O
to	O
congruency	O
,	O
meaning	O
that	O
congruent	O
shapes	O
(	O
shapes	O
that	O
could	O
be	O
translated	O
,	O
rotated	O
and	O
mirrored	O
)	O
will	O
have	O
the	O
same	O
descriptor	O
(	O
for	O
example	O
moment	O
or	O
spherical	O
harmonic	O
based	O
descriptors	O
or	O
Procrustes	B-Algorithm
analysis	I-Algorithm
operating	O
on	O
point	B-Algorithm
clouds	I-Algorithm
)	O
.	O
</s>
<s>
Such	O
descriptors	O
are	O
commonly	O
based	O
on	O
geodesic	O
distances	O
measures	O
along	O
the	O
surface	O
of	O
an	O
object	O
or	O
on	O
other	O
isometry	O
invariant	O
characteristics	O
such	O
as	O
the	O
Laplace	O
–	O
Beltrami	O
spectrum	O
(	O
see	O
also	O
spectral	B-Algorithm
shape	I-Algorithm
analysis	I-Algorithm
)	O
.	O
</s>
