<s>
The	O
generalized	B-Algorithm
Hough	I-Algorithm
transform	I-Algorithm
(	O
GHT	O
)	O
,	O
introduced	O
by	O
Dana	O
H	O
.	O
Ballard	O
in	O
1981	O
,	O
is	O
the	O
modification	O
of	O
the	O
Hough	B-Algorithm
transform	I-Algorithm
using	O
the	O
principle	O
of	O
template	B-Algorithm
matching	I-Algorithm
.	O
</s>
<s>
The	O
Hough	B-Algorithm
transform	I-Algorithm
was	O
initially	O
developed	O
to	O
detect	O
analytically	O
defined	O
shapes	O
(	O
e.g.	O
,	O
line	O
,	O
circle	O
,	O
ellipse	O
etc	O
.	O
)	O
.	O
</s>
<s>
This	O
modification	O
enables	O
the	O
Hough	B-Algorithm
transform	I-Algorithm
to	O
be	O
used	O
to	O
detect	O
an	O
arbitrary	O
object	O
described	O
with	O
its	O
model	O
.	O
</s>
<s>
With	O
the	O
generalized	B-Algorithm
Hough	I-Algorithm
transform	I-Algorithm
,	O
the	O
problem	O
of	O
finding	O
the	O
model	O
's	O
position	O
is	O
transformed	O
to	O
a	O
problem	O
of	O
finding	O
the	O
transformation	O
's	O
parameter	O
that	O
maps	O
the	O
model	O
into	O
the	O
image	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
binary	B-Algorithm
image	I-Algorithm
where	O
pixels	O
can	O
be	O
either	O
black	O
or	O
white	O
,	O
every	O
black	O
pixel	O
of	O
the	O
image	O
can	O
be	O
a	O
black	O
pixel	O
of	O
the	O
desired	O
pattern	O
thus	O
creating	O
a	O
locus	O
of	O
reference	O
points	O
in	O
the	O
Hough	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
The	O
maximum	O
points	O
of	O
the	O
Hough	B-Algorithm
space	I-Algorithm
indicate	O
possible	O
reference	O
points	O
of	O
the	O
pattern	O
in	O
the	O
image	O
.	O
</s>
<s>
This	O
maximum	O
can	O
be	O
found	O
by	O
scanning	O
the	O
Hough	B-Algorithm
space	I-Algorithm
or	O
by	O
solving	O
a	O
relaxed	B-Application
set	I-Application
of	I-Application
equations	I-Application
,	O
each	O
of	O
them	O
corresponding	O
to	O
a	O
black	O
pixel	O
.	O
</s>
<s>
It	O
was	O
a	O
precursor	O
to	O
Ballard	O
's	O
algorithm	O
that	O
was	O
restricted	O
to	O
translation	B-Algorithm
and	O
did	O
not	O
account	O
for	O
rotation	O
and	O
scale	O
changes	O
.	O
</s>
<s>
To	O
generalize	O
the	O
Hough	O
algorithm	O
to	O
non-analytic	O
curves	O
,	O
Ballard	O
defines	O
the	O
following	O
parameters	O
for	O
a	O
generalized	O
shape	O
:	O
a={y,s,θ}	O
where	O
y	O
is	O
a	O
reference	O
origin	O
for	O
the	O
shape	O
,	O
θ	O
is	O
its	O
orientation	O
,	O
and	O
s	O
=	O
(	O
sx	O
,	O
sy	O
)	O
describes	O
two	O
orthogonal	B-Application
scale	O
factors	O
.	O
</s>
<s>
Another	O
property	O
which	O
will	O
be	O
useful	O
in	O
describing	O
the	O
composition	O
of	O
generalized	B-Algorithm
Hough	I-Algorithm
transforms	I-Algorithm
is	O
the	O
change	O
of	O
reference	O
point	O
.	O
</s>
<s>
If	O
the	O
shape	O
S	O
has	O
a	O
composite	O
structure	O
consisting	O
of	O
subparts	O
S1	O
,	O
S2	O
,	O
..	O
SN	O
and	O
the	O
reference	O
points	O
for	O
the	O
shapes	O
S	O
,	O
S1	O
,	O
S2	O
,	O
..	O
SN	O
are	O
y	O
,	O
y1	O
,	O
y2	O
,	O
..	O
yn	O
,	O
respectively	O
,	O
then	O
for	O
a	O
scaling	O
factor	O
s	O
and	O
orientation	O
θ	O
,	O
the	O
generalized	B-Algorithm
Hough	I-Algorithm
transform	I-Algorithm
Rs(ɸ )	O
is	O
given	O
by	O
.	O
</s>
<s>
The	O
composite	O
smoothing	O
template	O
H(y )	O
is	O
given	O
as	O
a	O
composite	O
convolution	B-Language
of	O
individual	O
smoothing	O
templates	O
of	O
the	O
sub-shapes	O
.	O
</s>
<s>
Observing	O
that	O
the	O
global	O
Hough	B-Algorithm
transform	I-Algorithm
can	O
be	O
obtained	O
by	O
the	O
summation	O
of	O
local	O
Hough	B-Algorithm
transforms	I-Algorithm
of	O
disjoint	O
sub-region	O
,	O
Heather	O
and	O
Yang	O
proposed	O
a	O
method	O
which	O
involves	O
the	O
recursive	O
subdivision	O
of	O
the	O
image	O
into	O
sub-images	O
,	O
each	O
with	O
their	O
own	O
parameter	O
space	O
,	O
and	O
organized	O
in	O
a	O
quadtree	B-Data_Structure
structure	O
.	O
</s>
<s>
(	O
0	O
)	O
Convert	O
the	O
sample	O
shape	O
image	O
into	O
an	O
edge	O
image	O
using	O
any	O
edge	B-Algorithm
detecting	I-Algorithm
algorithm	O
like	O
Canny	B-Algorithm
edge	I-Algorithm
detector	I-Algorithm
.	O
</s>
