<s>
In	O
mathematics	O
,	O
bicubic	B-Algorithm
interpolation	I-Algorithm
is	O
an	O
extension	O
of	O
cubic	B-Algorithm
spline	I-Algorithm
interpolation	B-Algorithm
(	O
a	O
method	O
of	O
applying	O
cubic	B-Algorithm
interpolation	I-Algorithm
to	O
a	O
data	O
set	O
)	O
for	O
interpolating	B-Algorithm
data	O
points	O
on	O
a	O
two-dimensional	O
regular	O
grid	O
.	O
</s>
<s>
The	O
interpolated	O
surface	O
(	O
meaning	O
the	O
kernel	O
shape	O
,	O
not	O
the	O
image	O
)	O
is	O
smoother	O
than	O
corresponding	O
surfaces	O
obtained	O
by	O
bilinear	O
interpolation	B-Algorithm
or	O
nearest-neighbor	O
interpolation	B-Algorithm
.	O
</s>
<s>
Bicubic	B-Algorithm
interpolation	I-Algorithm
can	O
be	O
accomplished	O
using	O
either	O
Lagrange	O
polynomials	O
,	O
cubic	B-Algorithm
splines	I-Algorithm
,	O
or	O
cubic	O
convolution	B-Language
algorithm	O
.	O
</s>
<s>
In	O
image	B-Algorithm
processing	I-Algorithm
,	O
bicubic	B-Algorithm
interpolation	I-Algorithm
is	O
often	O
chosen	O
over	O
bilinear	O
or	O
nearest-neighbor	O
interpolation	B-Algorithm
in	O
image	B-Algorithm
resampling	I-Algorithm
,	O
when	O
speed	O
is	O
not	O
an	O
issue	O
.	O
</s>
<s>
In	O
contrast	O
to	O
bilinear	O
interpolation	B-Algorithm
,	O
which	O
only	O
takes	O
4	O
pixels	B-Algorithm
(	O
2×2	O
)	O
into	O
account	O
,	O
bicubic	B-Algorithm
interpolation	I-Algorithm
considers	O
16	O
pixels	B-Algorithm
(	O
4×4	O
)	O
.	O
</s>
<s>
Images	O
resampled	O
with	O
bicubic	B-Algorithm
interpolation	I-Algorithm
can	O
have	O
different	O
interpolation	B-Algorithm
artifacts	B-Algorithm
,	O
depending	O
on	O
the	O
b	O
and	O
c	O
values	O
chosen	O
.	O
</s>
<s>
The	O
interpolation	B-Algorithm
problem	O
consists	O
of	O
determining	O
the	O
16	O
coefficients	O
.	O
</s>
<s>
Bicubic	B-Algorithm
interpolation	I-Algorithm
on	O
an	O
arbitrarily	O
sized	O
regular	O
grid	O
can	O
then	O
be	O
accomplished	O
by	O
patching	O
together	O
such	O
bicubic	B-Algorithm
surfaces	O
,	O
ensuring	O
that	O
the	O
derivatives	O
match	O
on	O
the	O
boundaries	O
.	O
</s>
<s>
Often	O
,	O
applications	O
call	O
for	O
bicubic	B-Algorithm
interpolation	I-Algorithm
using	O
data	O
on	O
a	O
rectilinear	O
grid	O
,	O
rather	O
than	O
the	O
unit	O
square	O
.	O
</s>
<s>
using	O
finite	B-Algorithm
differences	I-Algorithm
.	O
</s>
<s>
Bicubic	B-Algorithm
spline	B-Algorithm
interpolation	I-Algorithm
requires	O
the	O
solution	O
of	O
the	O
linear	O
system	O
described	O
above	O
for	O
each	O
grid	O
cell	O
.	O
</s>
<s>
An	O
interpolator	O
with	O
similar	O
properties	O
can	O
be	O
obtained	O
by	O
applying	O
a	O
convolution	B-Language
with	O
the	O
following	O
kernel	O
in	O
both	O
dimensions	O
:	O
</s>
<s>
Note	O
that	O
for	O
1-dimensional	O
cubic	O
convolution	B-Language
interpolation	B-Algorithm
4	O
sample	O
points	O
are	O
required	O
.	O
</s>
<s>
The	O
bicubic	B-Algorithm
algorithm	O
is	O
frequently	O
used	O
for	O
scaling	O
images	O
and	O
video	O
for	O
display	O
(	O
see	O
bitmap	B-Algorithm
resampling	I-Algorithm
)	O
.	O
</s>
<s>
However	O
,	O
due	O
to	O
the	O
negative	O
lobes	O
on	O
the	O
kernel	O
,	O
it	O
causes	O
overshoot	B-Algorithm
(	O
haloing	B-Algorithm
)	O
.	O
</s>
<s>
This	O
can	O
cause	O
clipping	B-Algorithm
,	O
and	O
is	O
an	O
artifact	O
(	O
see	O
also	O
ringing	B-Algorithm
artifacts	I-Algorithm
)	O
,	O
but	O
it	O
increases	O
acutance	B-Algorithm
(	O
apparent	O
sharpness	O
)	O
,	O
and	O
can	O
be	O
desirable	O
.	O
</s>
