<s>
Within	O
the	O
field	O
of	O
computer	O
graphics	O
,	O
unbiased	B-Application
rendering	I-Application
refers	O
to	O
any	O
rendering	O
technique	O
that	O
does	O
not	O
introduce	O
systematic	O
error	O
,	O
or	O
bias	O
,	O
into	O
the	O
radiance	O
approximation	O
.	O
</s>
<s>
Because	O
of	O
this	O
,	O
an	O
unbiased	B-Application
rendering	I-Application
technique	O
can	O
produce	O
a	O
reference	O
image	O
to	O
compare	O
against	O
renders	O
that	O
use	O
other	O
techniques	O
.	O
</s>
<s>
In	O
simple	O
terms	O
,	O
unbiased	B-Application
rendering	I-Application
tries	O
to	O
mimic	O
the	O
real	O
world	O
as	O
closely	O
as	O
possible	O
without	O
taking	O
short	O
cuts	O
.	O
</s>
<s>
Path	B-Algorithm
tracing	I-Algorithm
and	O
its	O
derivatives	O
can	O
be	O
unbiased	O
,	O
whereas	O
ray	B-Algorithm
tracing	I-Algorithm
was	O
originally	O
biased	O
.	O
</s>
<s>
The	O
error	O
found	O
in	O
a	O
render	O
produced	O
by	O
an	O
unbiased	B-Application
rendering	I-Application
technique	O
is	O
due	O
to	O
random	O
statistical	O
variance	O
,	O
which	O
manifests	O
as	O
high-frequency	O
noise	B-Algorithm
.	O
</s>
<s>
Variance	O
is	O
reduced	O
by	O
(	O
standard	B-General_Concept
deviation	I-General_Concept
by	O
)	O
for	O
data	O
,	O
meaning	O
that	O
four	O
times	O
as	O
many	O
data	O
are	O
needed	O
to	O
halve	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
error	O
;	O
this	O
makes	O
unbiased	B-Application
rendering	I-Application
techniques	O
less	O
attractive	O
for	O
realtime	O
or	O
interactive	O
applications	O
.	O
</s>
<s>
This	O
means	O
that	O
an	O
image	O
produced	O
by	O
an	O
unbiased	B-Application
renderer	I-Application
that	O
appears	O
noiseless	O
and	O
smooth	O
is	O
probabilistically	O
correct	O
.	O
</s>
<s>
A	O
biased	B-Application
rendering	I-Application
method	O
is	O
not	O
necessarily	O
wrong	O
,	O
and	O
can	O
still	O
produce	O
images	O
close	O
to	O
those	O
given	O
by	O
the	O
rendering	O
equation	O
if	O
the	O
estimator	O
is	O
consistent	O
.	O
</s>
<s>
These	O
methods	O
,	O
however	O
,	O
introduce	O
a	O
certain	O
bias	O
error	O
(	O
usually	O
in	O
the	O
form	O
of	O
a	O
blur	O
)	O
in	O
efforts	O
to	O
reduce	O
the	O
variance	O
(	O
high-frequency	O
noise	B-Algorithm
)	O
.	O
</s>
<s>
Often	O
biased	B-Application
rendering	I-Application
is	O
optimized	O
to	O
compute	O
faster	O
at	O
the	O
cost	O
of	O
accuracy	O
.	O
</s>
<s>
Path	B-Algorithm
tracing	I-Algorithm
,	O
an	O
unbiased	O
approach	O
at	O
its	O
core	O
,	O
cannot	O
consistently	O
handle	O
caustics	O
generated	O
from	O
a	O
point	O
light	O
source	O
,	O
as	O
it	O
is	O
highly	O
unlikely	O
to	O
randomly	O
generate	O
the	O
singular	O
path	O
that	O
directly	O
reflects	O
into	O
the	O
point	O
.	O
</s>
<s>
Progressive	O
photon	B-Application
mapping	I-Application
(	O
PPM	O
)	O
,	O
a	O
biased	B-Application
rendering	I-Application
technique	O
,	O
can	O
actually	O
handle	O
caustics	O
quite	O
well	O
.	O
</s>
<s>
Although	O
biased	O
,	O
PPM	O
is	O
provably	O
consistent	O
,	O
meaning	O
that	O
as	O
the	O
number	O
of	O
samples	O
goes	O
to	O
infinity	B-Application
,	O
the	O
bias	O
error	O
goes	O
to	O
zero	O
(	O
like	O
an	O
unbiased	O
technique	O
)	O
,	O
and	O
the	O
probability	O
that	O
the	O
estimate	O
is	O
correct	O
reaches	O
one	O
.	O
</s>
