<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
geometric	B-Algorithm
hashing	I-Algorithm
is	O
a	O
method	O
for	O
efficiently	O
finding	O
two-dimensional	O
objects	O
represented	O
by	O
discrete	O
points	O
that	O
have	O
undergone	O
an	O
affine	B-Algorithm
transformation	I-Algorithm
,	O
though	O
extensions	O
exist	O
to	O
other	O
object	O
representations	O
and	O
transformations	O
.	O
</s>
<s>
For	O
each	O
point	O
,	O
its	O
quantized	B-Algorithm
transformed	O
coordinates	O
are	O
stored	O
in	O
the	O
hash	B-Algorithm
table	I-Algorithm
as	O
a	O
key	O
,	O
and	O
indices	O
of	O
the	O
basis	O
points	O
as	O
a	O
value	O
.	O
</s>
<s>
Geometric	B-Algorithm
hashing	I-Algorithm
was	O
originally	O
suggested	O
in	O
computer	B-Application
vision	I-Application
for	O
object	O
recognition	O
in	O
2D	O
and	O
3D	O
,	O
but	O
later	O
was	O
applied	O
to	O
different	O
problems	O
such	O
as	O
structural	O
alignment	O
of	O
proteins	O
.	O
</s>
<s>
Geometric	B-Algorithm
hashing	I-Algorithm
is	O
a	O
method	O
used	O
for	O
object	O
recognition	O
.	O
</s>
<s>
This	O
can	O
be	O
accomplished	O
with	O
geometric	B-Algorithm
hashing	I-Algorithm
.	O
</s>
<s>
The	O
method	O
could	O
be	O
used	O
to	O
recognize	O
one	O
of	O
the	O
multiple	O
objects	O
in	O
a	O
base	O
,	O
in	O
this	O
case	O
the	O
hash	B-Algorithm
table	I-Algorithm
should	O
store	O
not	O
only	O
the	O
pose	O
information	O
but	O
also	O
the	O
index	O
of	O
object	O
model	O
in	O
the	O
base	O
.	O
</s>
<s>
For	O
simplicity	O
,	O
this	O
example	O
will	O
not	O
use	O
too	O
many	O
point	O
features	O
and	O
assume	O
that	O
their	O
descriptors	O
are	O
given	O
by	O
their	O
coordinates	O
only	O
(	O
in	O
practice	O
local	B-General_Concept
descriptors	I-General_Concept
such	O
as	O
SIFT	B-Algorithm
could	O
be	O
used	O
for	O
indexing	O
)	O
.	O
</s>
<s>
For	O
2D	O
space	O
and	O
similarity	B-Algorithm
transformation	I-Algorithm
the	O
basis	O
is	O
defined	O
by	O
a	O
pair	O
of	O
points	O
.	O
</s>
<s>
The	O
coordinates	O
should	O
be	O
discretised	O
to	O
make	O
recognition	O
robust	B-General_Concept
to	O
noise	O
,	O
we	O
take	O
the	O
bin	O
size	O
0.25	O
.	O
</s>
<s>
Store	O
the	O
basis	O
in	O
a	O
hash	B-Algorithm
table	I-Algorithm
indexed	O
by	O
the	O
features	O
(	O
only	O
transformed	O
coordinates	O
in	O
this	O
case	O
)	O
.	O
</s>
<s>
We	O
provide	O
the	O
hash	B-Algorithm
table	I-Algorithm
after	O
two	O
iterations	O
,	O
the	O
pair	O
(	O
P1	O
,	O
P3	O
)	O
is	O
selected	O
for	O
the	O
second	O
one	O
.	O
</s>
<s>
Hash	B-Algorithm
Table	I-Algorithm
:	O
</s>
<s>
Most	O
hash	B-Algorithm
tables	I-Algorithm
cannot	O
have	O
identical	O
keys	O
mapped	O
to	O
different	O
values	O
.	O
</s>
<s>
So	O
in	O
real	O
life	O
one	O
wo	O
n’t	O
encode	O
basis	O
keys	O
(	O
1.0	O
,	O
0.0	O
)	O
and	O
(	O
-1.0	O
,	O
0.0	O
)	O
in	O
a	O
hash	B-Algorithm
table	I-Algorithm
.	O
</s>
<s>
Compare	O
all	O
the	O
transformed	O
point	O
features	O
in	O
the	O
input	O
image	O
with	O
the	O
hash	B-Algorithm
table	I-Algorithm
.	O
</s>
<s>
Therefore	O
,	O
geometric	B-Algorithm
hashing	I-Algorithm
should	O
be	O
able	O
to	O
find	O
the	O
object	O
,	O
too	O
.	O
</s>
<s>
Actually	O
,	O
using	O
3	O
points	O
for	O
the	O
basis	O
is	O
another	O
approach	O
for	O
geometric	B-Algorithm
hashing	I-Algorithm
.	O
</s>
