<s>
Mathematical	B-Algorithm
morphology	I-Algorithm
(	O
MM	O
)	O
is	O
a	O
theory	O
and	O
technique	O
for	O
the	O
analysis	O
and	O
processing	O
of	O
geometrical	O
structures	O
,	O
based	O
on	O
set	O
theory	O
,	O
lattice	O
theory	O
,	O
topology	B-Architecture
,	O
and	O
random	O
functions	O
.	O
</s>
<s>
MM	O
is	O
most	O
commonly	O
applied	O
to	O
digital	B-Algorithm
images	I-Algorithm
,	O
but	O
it	O
can	O
be	O
employed	O
as	O
well	O
on	O
graphs	O
,	O
surface	B-Algorithm
meshes	I-Algorithm
,	O
solids	O
,	O
and	O
many	O
other	O
spatial	O
structures	O
.	O
</s>
<s>
Topological	B-Architecture
and	O
geometrical	O
continuous-space	O
concepts	O
such	O
as	O
size	O
,	O
shape	O
,	O
convexity	O
,	O
connectivity	O
,	O
and	O
geodesic	O
distance	O
,	O
were	O
introduced	O
by	O
MM	O
on	O
both	O
continuous	O
and	O
discrete	O
spaces	O
.	O
</s>
<s>
MM	O
is	O
also	O
the	O
foundation	O
of	O
morphological	B-Algorithm
image	I-Algorithm
processing	I-Algorithm
,	O
which	O
consists	O
of	O
a	O
set	O
of	O
operators	O
that	O
transform	O
images	O
according	O
to	O
the	O
above	O
characterizations	O
.	O
</s>
<s>
The	O
basic	O
morphological	O
operators	O
are	O
erosion	B-Algorithm
,	O
dilation	B-Algorithm
,	O
opening	B-Algorithm
and	O
closing	B-Algorithm
.	O
</s>
<s>
MM	O
was	O
originally	O
developed	O
for	O
binary	B-Algorithm
images	I-Algorithm
,	O
and	O
was	O
later	O
extended	O
to	O
grayscale	O
functions	O
and	O
images	O
.	O
</s>
<s>
Mathematical	B-Algorithm
Morphology	I-Algorithm
was	O
developed	O
in	O
1964	O
by	O
the	O
collaborative	O
work	O
of	O
Georges	O
Matheron	O
and	O
Jean	O
Serra	O
,	O
at	O
the	O
École	O
des	O
Mines	O
de	O
Paris	O
,	O
France	O
.	O
</s>
<s>
Matheron	O
supervised	O
the	O
PhD	O
thesis	O
of	O
Serra	O
,	O
devoted	O
to	O
the	O
quantification	O
of	O
mineral	O
characteristics	O
from	O
thin	O
cross	B-Application
sections	I-Application
,	O
and	O
this	O
work	O
resulted	O
in	O
a	O
novel	O
practical	O
approach	O
,	O
as	O
well	O
as	O
theoretical	O
advancements	O
in	O
integral	O
geometry	O
and	O
topology	B-Architecture
.	O
</s>
<s>
In	O
1968	O
,	O
the	O
Centre	B-Algorithm
de	I-Algorithm
Morphologie	I-Algorithm
Mathématique	I-Algorithm
was	O
founded	O
by	O
the	O
École	O
des	O
Mines	O
de	O
Paris	O
in	O
Fontainebleau	O
,	O
France	O
,	O
led	O
by	O
Matheron	O
and	O
Serra	O
.	O
</s>
<s>
During	O
the	O
rest	O
of	O
the	O
1960s	O
and	O
most	O
of	O
the	O
1970s	O
,	O
MM	O
dealt	O
essentially	O
with	O
binary	B-Algorithm
images	I-Algorithm
,	O
treated	O
as	O
sets	O
,	O
and	O
generated	O
a	O
large	O
number	O
of	O
binary	O
operators	O
and	O
techniques	O
:	O
Hit-or-miss	B-Algorithm
transform	I-Algorithm
,	O
dilation	B-Algorithm
,	O
erosion	B-Algorithm
,	O
opening	B-Algorithm
,	O
closing	B-Algorithm
,	O
granulometry	B-Algorithm
,	O
thinning	O
,	O
skeletonization	B-Algorithm
,	O
ultimate	O
erosion	B-Algorithm
,	O
conditional	O
bisector	O
,	O
and	O
others	O
.	O
</s>
<s>
Besides	O
extending	O
the	O
main	O
concepts	O
(	O
such	O
as	O
dilation	B-Algorithm
,	O
erosion	B-Algorithm
,	O
etc	O
.	O
)	O
</s>
<s>
to	O
functions	O
,	O
this	O
generalization	O
yielded	O
new	O
operators	O
,	O
such	O
as	O
morphological	B-Algorithm
gradients	I-Algorithm
,	O
top-hat	B-Algorithm
transform	I-Algorithm
and	O
the	O
Watershed	B-Algorithm
(	O
MM	O
's	O
main	O
segmentation	B-Algorithm
approach	O
)	O
.	O
</s>
<s>
This	O
generalization	O
brought	O
flexibility	O
to	O
the	O
theory	O
,	O
enabling	O
its	O
application	O
to	O
a	O
much	O
larger	O
number	O
of	O
structures	O
,	O
including	O
color	B-Algorithm
images	I-Algorithm
,	O
video	O
,	O
graphs	O
,	O
meshes	B-Algorithm
,	O
etc	O
.	O
</s>
<s>
In	O
1993	O
,	O
the	O
first	O
International	O
Symposium	O
on	O
Mathematical	B-Algorithm
Morphology	I-Algorithm
(	O
ISMM	O
)	O
took	O
place	O
in	O
Barcelona	O
,	O
Spain	O
.	O
</s>
