Lanczos filter

Graph of the Lanczos filter for a = 3

The Lanczos filter is often used in computer graphics inserted reconstruction filter . It was developed in 1979 by the meteorologist Claude E. Duchon and is named after the Hungarian mathematician Cornelius Lanczos .

The Lanczos filter is defined as a sinc function multiplied by a window function in order to ensure a gradual decrease towards the ends. The window function is itself part of the sinc function. This results in the following definition:

${\displaystyle L(x)={\begin{cases}\mathrm {sinc} (x)\,\mathrm {sinc} \!\left({\frac {x}{a}}\right)&{\text{wenn }}-a<x<a,a\neq 0\\1&{\text{wenn }}x=0\\0&{\text{ansonsten}}\end{cases}}}$

in which

${\displaystyle \mathrm {sinc} (x)={\frac {\sin(\pi x)}{\pi x}}}$

The parameter a determines the size of the wearer and is typically 2 or 3.

Due to the window function, the Lanczos filter leads to less ringing than with a truncated Sinc filter.

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  A raster graphic enlarged with a box filter (pixel repetition)

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  The same graphic enlarged with the Lanczos filter

literature

• Claude E. Duchon: Lanczos Filtering in One and Two Dimensions. In: Journal of Applied Meteorology. 18, No. 8, 1979, ISSN  0894-8763 , pp. 1016-1022 ( PDF, 460 kB ).
• Matt Pharr, Greg Humphreys: Physically Based Rendering. From theory to implementation . Morgan Kaufmann, London 2004, ISBN 01-2553-180-X , pp. 279-367. ( PDF, 7 MB ).
• Ken Turkowski, Steve Gabriel: Filters for Common Resampling Tasks. In: Andrew Glassner: Graphics Gems I, pp. 147-165. Academic Press, Boston 1990, ISBN 0-12-286165-5