Intel® Integrated Performance Primitives Developer Reference

Developer Reference

  • 2020
  • 07/15/2020
  • Public Content
Contents

Lanczos Interpolation

This method is based on the 2-lobed or 3-lobed Lanczos window function as the interpolation function.

Interpolation with the 2-lobed Lanczos Window Function

The interpolation algorithm uses source image intensities at 16 pixels in the neighborhood of the point (
x
S
 ,
y
S
 ) in the source image:
x
S0
 = int(
x
S
 ) - 1;
x
S1
 =
x
S0
 + 1;
x
S2
 =
x
S0
 + 2;
x
S3
 =
x
S0
 + 3;
y
S0
 = int(
y
S
 ) - 1;
y
S1
 =
y
S0
 + 1;
y
S2
 =
y
S0
 + 2;
y
S3
 =
y
S0
 + 3;
First, the intensity values are interpolated along the
x
 -axis to produce four intermediate results
I
0
 ,
I
1
 ,
I
2
 ,
I
3
 :
Then the intensity
D
 (
x
D
 ,
y
D
 ) is computed by interpolating the intermediate values
I
k
 along the
y
 -axis:
Here
a
i
 and
b
k
 are the coefficients defined as
a
i
 =
L
 (
x
S
 -
x
Si
 ),
b
k
 =
L
 (
y
S
 -
y
Si
 ),
where
L
 (
x
 ) is the Lanczos windowed sinc function:
To use this interpolation, use the
ippiResizeLanczos
 function.

Interpolation with the 3-lobed Lanczos Window Function

The interpolation algorithm uses source image intensities at 36 pixels in the neighborhood of the point (
x
S
 ,
y
S
 ) in the source image:
x
S0
 = int(
x
S
 ) - 2;
x
S1
 =
x
S0
 + 1;
x
S2
 =
x
S0
 + 2;
x
S3
 =
x
S0
 + 3;
x
S3
 =
x
S0
 + 4;
x
S3
 =
x
S0
 + 5;
y
S0
 = int(
y
S
 ) - 2;
y
S1
 =
y
S0
 + 1;
y
S2
 =
y
S0
 + 2;
y
S3
 =
y
S0
 + 3;
y
S2
 =
y
S0
 + 4;
y
S2
 =
y
S0
 + 5;
First, the intensity values are interpolated along the
x
 -axis to produce six intermediate results
I
0
 ,
I
1
 , ...
I
5
 :
Then the intensity
D
 (
x
D
 ,
y
D
 ) is computed by interpolating the intermediate values
I
k
 along the
y
 -axis:
Here
a
i
 and
b
k
 are the coefficients defined as
a
i
 =
L
 (
x
S
 -
x
Si
 ),
b
k
 =
L
 (
y
S
 -
y
Si
 ),
where
L
 (
x
 ) is the Lanczos windowed sinc function:
To use this interpolation, set the
interpolation
 parameter to
IPPI_INTER_LANCZOS
 , or use the functions with the
Lanczos
 suffix (pass
interpolation
 =
ippLanczos
 to
GetSize
 functions).

Product and Performance Information

1

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Notice revision #20110804