<s>
Hough	B-Algorithm
transforms	I-Algorithm
are	O
techniques	O
for	O
object	B-General_Concept
detection	I-General_Concept
,	O
a	O
critical	O
step	O
in	O
many	O
implementations	O
of	O
computer	B-Application
vision	I-Application
,	O
or	O
data	B-Application
mining	I-Application
from	O
images	O
.	O
</s>
<s>
Specifically	O
,	O
the	O
Randomized	B-Algorithm
Hough	I-Algorithm
transform	I-Algorithm
is	O
a	O
probabilistic	O
variant	O
to	O
the	O
classical	O
Hough	B-Algorithm
transform	I-Algorithm
,	O
and	O
is	O
commonly	O
used	O
to	O
detect	O
curves	O
(	O
straight	O
line	O
,	O
circle	O
,	O
ellipse	O
,	O
etc	O
.	O
)	O
</s>
<s>
The	O
basic	O
idea	O
of	O
Hough	B-Algorithm
transform	I-Algorithm
(	O
HT	O
)	O
is	O
to	O
implement	O
a	O
voting	O
procedure	O
for	O
all	O
potential	O
curves	O
in	O
the	O
image	O
,	O
and	O
at	O
the	O
termination	O
of	O
the	O
algorithm	O
,	O
curves	O
that	O
do	O
exist	O
in	O
the	O
image	O
will	O
have	O
relatively	O
high	O
voting	O
scores	O
.	O
</s>
<s>
Randomized	B-Algorithm
Hough	I-Algorithm
transform	I-Algorithm
(	O
RHT	O
)	O
is	O
different	O
from	O
HT	O
in	O
that	O
it	O
tries	O
to	O
avoid	O
conducting	O
the	O
computationally	O
expensive	O
voting	O
process	O
for	O
every	O
nonzero	O
pixel	O
in	O
the	O
image	O
by	O
taking	O
advantage	O
of	O
the	O
geometric	O
properties	O
of	O
analytical	B-Algorithm
curves	O
,	O
and	O
thus	O
improve	O
the	O
time	O
efficiency	O
and	O
reduce	O
the	O
storage	O
requirement	O
of	O
the	O
original	O
algorithm	O
.	O
</s>
<s>
Although	O
Hough	B-Algorithm
transform	I-Algorithm
(	O
HT	O
)	O
has	O
been	O
widely	O
used	O
in	O
curve	B-Algorithm
detection	I-Algorithm
,	O
it	O
has	O
two	O
major	O
drawbacks	O
:	O
First	O
,	O
for	O
each	O
nonzero	O
pixel	O
in	O
the	O
image	O
,	O
the	O
parameters	O
for	O
the	O
existing	O
curve	O
and	O
redundant	O
ones	O
are	O
both	O
accumulated	O
during	O
the	O
voting	O
procedure	O
.	O
</s>
<s>
Second	O
,	O
the	O
accumulator	B-General_Concept
array	O
(	O
or	O
Hough	B-Algorithm
space	I-Algorithm
)	O
is	O
predefined	O
in	O
a	O
heuristic	O
way	O
.	O
</s>
<s>
In	O
comparison	O
with	O
HT	O
,	O
RHT	O
takes	O
advantage	O
of	O
the	O
fact	O
that	O
some	O
analytical	B-Algorithm
curves	O
can	O
be	O
fully	O
determined	O
by	O
a	O
certain	O
number	O
of	O
points	O
on	O
the	O
curve	O
.	O
</s>
<s>
Update	O
the	O
accumulator	B-General_Concept
array	O
and	O
corresponding	O
scores	O
.	O
</s>
<s>
They	O
can	O
be	O
found	O
by	O
fitting	O
a	O
straight	O
line	O
using	O
least	B-Algorithm
squares	I-Algorithm
technique	O
for	O
a	O
small	O
window	O
of	O
neighboring	O
pixels	O
.	O
</s>
<s>
With	O
the	O
ellipse	O
parameters	O
determined	O
from	O
previous	O
stage	O
,	O
the	O
accumulator	B-General_Concept
array	O
can	O
be	O
updated	O
correspondingly	O
.	O
</s>
<s>
Different	O
from	O
classical	O
Hough	B-Algorithm
transform	I-Algorithm
,	O
RHT	O
does	O
not	O
keep	O
"	O
grid	O
of	O
buckets	O
"	O
as	O
the	O
accumulator	B-General_Concept
array	O
.	O
</s>
<s>
Rather	O
,	O
it	O
first	O
calculates	O
the	O
similarities	O
between	O
the	O
newly	O
detected	O
ellipse	O
and	O
the	O
ones	O
already	O
stored	O
in	O
accumulator	B-General_Concept
array	O
.	O
</s>
<s>
As	O
long	O
as	O
the	O
similarity	O
exceeds	O
some	O
predefined	O
threshold	O
,	O
replace	O
the	O
one	O
in	O
the	O
accumulator	B-General_Concept
with	O
the	O
average	O
of	O
both	O
ellipses	O
and	O
add	O
1	O
to	O
its	O
score	O
.	O
</s>
<s>
Otherwise	O
,	O
initialize	O
this	O
ellipse	O
to	O
an	O
empty	O
position	O
in	O
the	O
accumulator	B-General_Concept
and	O
assign	O
a	O
score	O
of	O
1	O
.	O
</s>
<s>
Once	O
the	O
score	O
of	O
one	O
candidate	O
ellipse	O
exceeds	O
the	O
threshold	O
,	O
it	O
is	O
determined	O
as	O
existing	O
in	O
the	O
image	O
(	O
in	O
other	O
words	O
,	O
this	O
ellipse	O
is	O
detected	O
)	O
,	O
and	O
should	O
be	O
removed	O
from	O
the	O
image	O
and	O
accumulator	B-General_Concept
array	O
so	O
that	O
the	O
algorithm	O
can	O
detect	O
other	O
potential	O
ellipses	O
faster	O
.	O
</s>
<s>
Replace	O
the	O
one	O
in	O
the	O
accumulator	B-General_Concept
with	O
the	O
average	O
of	O
two	O
ellipses	O
and	O
add	O
1	O
to	O
the	O
score	O
;	O
</s>
<s>
Insert	O
the	O
ellipse	O
into	O
an	O
empty	O
position	O
in	O
the	O
accumulator	B-General_Concept
with	O
a	O
score	O
of	O
1	O
;	O
</s>
<s>
Empty	O
the	O
accumulator	B-General_Concept
;	O
</s>
