<s>
Shape	B-General_Concept
context	I-General_Concept
is	O
a	O
feature	O
descriptor	O
used	O
in	O
object	O
recognition	O
.	O
</s>
<s>
Serge	O
Belongie	O
and	O
Jitendra	O
Malik	O
proposed	O
the	O
term	O
in	O
their	O
paper	O
"	O
Matching	O
with	O
Shape	B-General_Concept
Contexts	I-General_Concept
"	O
in	O
2000	O
.	O
</s>
<s>
The	O
shape	B-General_Concept
context	I-General_Concept
is	O
intended	O
to	O
be	O
a	O
way	O
of	O
describing	O
shapes	O
that	O
allows	O
for	O
measuring	O
shape	O
similarity	O
and	O
the	O
recovering	O
of	O
point	O
correspondences	O
.	O
</s>
<s>
is	O
defined	O
to	O
be	O
the	O
shape	B-General_Concept
context	I-General_Concept
of	O
.	O
</s>
<s>
The	O
fact	O
that	O
the	O
shape	B-General_Concept
context	I-General_Concept
is	O
a	O
rich	O
and	O
discriminative	O
descriptor	O
can	O
be	O
seen	O
in	O
the	O
figure	O
below	O
,	O
in	O
which	O
the	O
shape	B-General_Concept
contexts	I-General_Concept
of	O
two	O
different	O
versions	O
of	O
the	O
letter	O
"	O
A	O
"	O
are	O
shown	O
.	O
</s>
<s>
(	O
c	O
)	O
is	O
the	O
diagram	O
of	O
the	O
log-polar	O
bins	O
used	O
to	O
compute	O
the	O
shape	B-General_Concept
context	I-General_Concept
.	O
</s>
<s>
(	O
d	O
)	O
is	O
the	O
shape	B-General_Concept
context	I-General_Concept
for	O
the	O
point	O
marked	O
with	O
a	O
circle	O
in	O
(	O
a	O
)	O
,	O
(	O
e	O
)	O
is	O
that	O
for	O
the	O
point	O
marked	O
as	O
a	O
diamond	O
in	O
(	O
b	O
)	O
,	O
and	O
(	O
f	O
)	O
is	O
that	O
for	O
the	O
triangle	O
.	O
</s>
<s>
As	O
can	O
be	O
seen	O
,	O
since	O
(	O
d	O
)	O
and	O
(	O
e	O
)	O
are	O
the	O
shape	B-General_Concept
contexts	I-General_Concept
for	O
two	O
closely	O
related	O
points	O
,	O
they	O
are	O
quite	O
similar	O
,	O
while	O
the	O
shape	B-General_Concept
context	I-General_Concept
in	O
(	O
f	O
)	O
is	O
very	O
different	O
.	O
</s>
<s>
Translational	O
invariance	O
comes	O
naturally	O
to	O
shape	B-General_Concept
context	I-General_Concept
.	O
</s>
<s>
Shape	B-General_Concept
contexts	I-General_Concept
are	O
empirically	O
demonstrated	O
to	O
be	O
robust	O
to	O
deformations	O
,	O
noise	O
,	O
and	O
outliers	O
using	O
synthetic	O
point	O
set	O
matching	O
experiments	O
.	O
</s>
<s>
One	O
can	O
provide	O
complete	O
rotational	O
invariance	O
in	O
shape	B-General_Concept
contexts	I-General_Concept
.	O
</s>
<s>
A	O
complete	O
system	O
that	O
uses	O
shape	B-General_Concept
contexts	I-General_Concept
for	O
shape	O
matching	O
consists	O
of	O
the	O
following	O
steps	O
(	O
which	O
will	O
be	O
covered	O
in	O
more	O
detail	O
in	O
the	O
Details	O
of	O
Implementation	O
section	O
)	O
:	O
</s>
<s>
Compute	O
the	O
shape	B-General_Concept
context	I-General_Concept
of	O
each	O
point	O
found	O
in	O
step	O
1	O
.	O
</s>
<s>
affine	B-Algorithm
,	O
thin	B-Algorithm
plate	I-Algorithm
spline	I-Algorithm
,	O
etc	O
.	O
)	O
</s>
<s>
Use	O
a	O
weighted	O
sum	O
of	O
the	O
shape	B-General_Concept
context	I-General_Concept
distance	O
,	O
the	O
image	O
appearance	O
distance	O
,	O
and	O
the	O
bending	O
energy	O
(	O
a	O
measure	O
of	O
how	O
much	O
transformation	O
is	O
required	O
to	O
bring	O
the	O
two	O
shapes	O
into	O
alignment	O
)	O
.	O
</s>
<s>
To	O
identify	O
the	O
unknown	O
shape	O
,	O
use	O
a	O
nearest-neighbor	B-Algorithm
classifier	I-Algorithm
to	O
compare	O
its	O
shape	O
distance	O
to	O
shape	O
distances	O
of	O
known	O
objects	O
.	O
</s>
<s>
These	O
can	O
be	O
simply	O
obtained	O
using	O
the	O
Canny	B-Algorithm
edge	I-Algorithm
detector	I-Algorithm
and	O
picking	O
a	O
random	O
set	O
of	O
points	O
from	O
the	O
edges	O
.	O
</s>
<s>
shape	B-General_Concept
contexts	I-General_Concept
)	O
g(k )	O
and	O
h(k )	O
.	O
</s>
<s>
As	O
shape	B-General_Concept
contexts	I-General_Concept
are	O
distributions	O
represented	O
as	O
histograms	O
,	O
it	O
is	O
natural	O
to	O
use	O
the	O
χ2	B-General_Concept
test	O
statistic	O
as	O
the	O
"	O
shape	B-General_Concept
context	I-General_Concept
cost	O
"	O
of	O
matching	O
the	O
two	O
points	O
:	O
</s>
<s>
In	O
addition	O
to	O
the	O
shape	B-General_Concept
context	I-General_Concept
cost	O
,	O
an	O
extra	O
cost	O
based	O
on	O
the	O
appearance	O
can	O
be	O
added	O
.	O
</s>
<s>
This	O
can	O
be	O
done	O
in	O
time	O
using	O
the	O
Hungarian	B-Algorithm
method	I-Algorithm
,	O
although	O
there	O
are	O
more	O
efficient	O
algorithms	O
.	O
</s>
<s>
The	O
affine	B-Algorithm
model	I-Algorithm
is	O
a	O
standard	O
choice	O
:	O
.	O
</s>
<s>
The	O
least	B-Algorithm
squares	I-Algorithm
solution	O
for	O
the	O
matrix	O
and	O
the	O
translational	O
offset	O
vector	O
o	O
is	O
obtained	O
by	O
:	O
</s>
<s>
The	O
thin	B-Algorithm
plate	I-Algorithm
spline	I-Algorithm
(	O
TPS	O
)	O
model	O
is	O
the	O
most	O
widely	O
used	O
model	O
for	O
transformations	O
when	O
working	O
with	O
shape	B-General_Concept
contexts	I-General_Concept
.	O
</s>
<s>
Shape	B-General_Concept
context	I-General_Concept
distance	O
:	O
this	O
is	O
the	O
symmetric	O
sum	O
of	O
shape	B-General_Concept
context	I-General_Concept
matching	O
costs	O
over	O
best	O
matching	O
points	O
:	O
</s>
<s>
Now	O
that	O
we	O
have	O
a	O
way	O
of	O
calculating	O
the	O
distance	O
between	O
two	O
shapes	O
,	O
we	O
can	O
use	O
a	O
nearest	B-General_Concept
neighbor	I-General_Concept
classifier	B-General_Concept
(	O
k-NN	B-General_Concept
)	O
with	O
distance	O
defined	O
as	O
the	O
shape	O
distance	O
calculated	O
here	O
.	O
</s>
<s>
The	O
authors	O
Serge	O
Belongie	O
and	O
Jitendra	O
Malik	O
tested	O
their	O
approach	O
on	O
the	O
MNIST	B-General_Concept
database	I-General_Concept
.	O
</s>
<s>
The	O
next	O
experiment	O
performed	O
on	O
shape	B-General_Concept
contexts	I-General_Concept
involved	O
the	O
20	O
common	O
household	O
objects	O
in	O
the	O
.	O
</s>
<s>
A	O
1-NN	O
classifier	B-General_Concept
was	O
used	O
.	O
</s>
<s>
The	O
authors	O
also	O
developed	O
an	O
editing	O
algorithm	O
based	O
on	O
shape	B-General_Concept
context	I-General_Concept
similarity	O
and	O
k-medoid	B-Algorithm
clustering	O
that	O
improved	O
on	O
their	O
performance	O
.	O
</s>
<s>
Shape	B-General_Concept
contexts	I-General_Concept
were	O
used	O
to	O
retrieve	O
the	O
closest	O
matching	O
trademarks	O
from	O
a	O
database	O
to	O
a	O
query	O
trademark	O
(	O
useful	O
in	O
detecting	O
trademark	O
infringement	O
)	O
.	O
</s>
