Cubic Interpolation
The cubic interpolation algorithm (see Figure ,
) in the source image:
Cubic
Interpolation
) uses source image intensities at sixteen pixels in the
neighborhood of the point (x
S
y
S
x
S0
x
S
x
S1
x
S0
x
S2
x
S0
x
S3
x
S0
y
S0
y
S
y
S1
y
S0
y
S2
y
S0
y
S3
y
S0
First, for each
the algorithm
determines four cubic polynomials
((
(
(
y
Sk
F
0
x
),
F
1
x
),
F
2
x
), and
F
3
x
):
F
k
x
) =
a
k
x
3 +
b
k
x
2 +
c
k
x
+
d
k
k
≤ 3
such that
F
k
x
S0
S
(x
S0
y
Sk
F
k
x
S1
S
(x
S1
y
Sk
F
k
x
S2
S
(x
S2
y
Sk
F
k
x
S3
S
(x
S3
y
Sk
In Figure
Cubic Interpolation
, these
polynomials are shown by solid curves.
Then, the algorithm determines a cubic polynomial
(
F
y
y
) such that
F
y
y
S0
F
0
x
S
F
y
y
S1
F
1
x
S
F
y
y
S2
F
2
x
S
F
y
y
S3
F
3
x
S
The polynomial
(
F
y
y
) is represented by the dashed
curve in Figure Cubic Interpolation
.
Finally, the sought intensity
,
) is set to the value
().
D
(x
D
y
D
F
y
y
S
To use the cubic interpolation, set the
interpolation
parameter to
IPPI_INTER_CUBIC
.
Cubic Interpolation
